arXiv:1509.04662v2 [nucl-ex] 25 Apr 2016 · 2016-04-27 · arXiv:1509.04662v2 [nucl-ex] 25 Apr 2016 ... c˝

Single electron yields from semileptonic charm and bottom hadron decays in Au+Aucollisions at

radicsNN = 200 GeV

A Adare13 C Aidala39 44 NN Ajitanand63 Y Akiba57 58 R Akimoto12 J Alexander63 M Alfred23

K Aoki32 57 N Apadula28 64 Y Aramaki12 57 H Asano35 57 EC Aschenauer7 ET Atomssa64 TC Awes53

B Azmoun7 V Babintsev24 M Bai6 NS Bandara43 B Bannier64 KN Barish8 B Bassalleck50 S Bathe5 58

V Baublis56 S Baumgart57 A Bazilevsky7 M Beaumier8 S Beckman13 R Belmont13 44 68 A Berdnikov60

Y Berdnikov60 D Black8 DS Blau34 JS Bok50 51 K Boyle58 ML Brooks39 J Bryslawskyj5 H Buesching7

V Bumazhnov24 S Butsyk50 S Campbell14 28 C-H Chen58 64 CY Chi14 M Chiu7 IJ Choi25 JB Choi10

S Choi62 RK Choudhury4 P Christiansen41 T Chujo67 O Chvala8 V Cianciolo53 Z Citron64 69 BA Cole14

M Connors64 N Cronin45 64 N Crossette45 M Csanad17 T Csorgo70 S Dairaku35 57 TW Danley52

A Datta43 50 MS Daugherity1 G David7 K DeBlasio50 K Dehmelt64 A Denisov24 A Deshpande58 64

EJ Desmond7 O Dietzsch61 L Ding28 A Dion28 64 PB Diss42 JH Do71 M Donadelli61 L DrsquoOrazio42

O Drapier36 A Drees64 KA Drees6 JM Durham39 64 A Durum24 S Edwards6 YV Efremenko53

T Engelmore14 A Enokizono53 57 59 S Esumi67 KO Eyser7 8 B Fadem45 N Feege64 DE Fields50

M Finger9 M Finger Jr9 F Fleuret36 SL Fokin34 JE Frantz52 A Franz7 AD Frawley19 Y Fukao57

T Fusayasu47 K Gainey1 C Gal64 P Gallus15 P Garg3 A Garishvili65 I Garishvili38 H Ge64

F Giordano25 A Glenn38 X Gong63 M Gonin36 Y Goto57 58 R Granier de Cassagnac36 N Grau2

SV Greene68 M Grosse Perdekamp25 Y Gu63 T Gunji12 T Hachiya57 JS Haggerty7 KI Hahn18

H Hamagaki12 HF Hamilton1 SY Han18 J Hanks64 S Hasegawa29 TOS Haseler20 K Hashimoto57 59

R Hayano12 S Hayashi12 X He20 TK Hemmick64 T Hester8 JC Hill28 RS Hollis8 K Homma22

B Hong33 T Horaguchi67 T Hoshino22 N Hotvedt28 J Huang7 S Huang68 T Ichihara57 58 H Iinuma32

Y Ikeda57 67 K Imai29 Y Imazu57 J Imrek16 M Inaba67 A Iordanova8 D Isenhower1 A Isinhue45

D Ivanishchev56 BV Jacak64 M Javani20 M Jezghani20 J Jia7 63 X Jiang39 BM Johnson7 KS Joo46

D Jouan54 DS Jumper25 J Kamin64 S Kanda12 BH Kang21 JH Kang71 JS Kang21 J Kapustinsky39

K Karatsu35 57 D Kawall43 AV Kazantsev34 T Kempel28 JA Key50 V Khachatryan64 PK Khandai3

A Khanzadeev56 KM Kijima22 BI Kim33 C Kim33 DJ Kim30 E-J Kim10 GW Kim18 M Kim62

Y-J Kim25 YK Kim21 B Kimelman45 E Kinney13 E Kistenev7 R Kitamura12 J Klatsky19

D Kleinjan8 P Kline64 T Koblesky13 B Komkov56 J Koster58 D Kotchetkov52 D Kotov56 60

F Krizek30 K Kurita57 59 M Kurosawa57 58 Y Kwon71 GS Kyle51 R Lacey63 YS Lai14 JG Lajoie28

A Lebedev28 DM Lee39 J Lee18 KB Lee39 KS Lee33 S Lee71 SH Lee64 SR Lee10 MJ Leitch39

MAL Leite61 M Leitgab25 B Lewis64 X Li11 SH Lim71 LA Linden Levy38 MX Liu39 D Lynch7

CF Maguire68 YI Makdisi6 M Makek69 72 A Manion64 VI Manko34 E Mannel7 14 T Maruyama29

M McCumber13 39 PL McGaughey39 D McGlinchey13 19 C McKinney25 A Meles51 M Mendoza8

B Meredith25 Y Miake67 T Mibe32 J Midori22 AC Mignerey42 A Milov69 DK Mishra4 JT Mitchell7

S Miyasaka57 66 S Mizuno57 67 AK Mohanty4 S Mohapatra63 P Montuenga25 HJ Moon46

T Moon71 DP Morrison7 lowast M Moskowitz45 TV Moukhanova34 T Murakami35 57 J Murata57 59

A Mwai63 T Nagae35 S Nagamiya32 57 K Nagashima22 JL Nagle13 dagger MI Nagy17 70 I Nakagawa57 58

H Nakagomi57 67 Y Nakamiya22 KR Nakamura35 57 T Nakamura57 K Nakano57 66 C Nattrass65

PK Netrakanti4 M Nihashi22 57 T Niida67 S Nishimura12 R Nouicer7 58 T Novak31 70 N Novitzky30 64

A Nukariya12 AS Nyanin34 H Obayashi22 E OrsquoBrien7 CA Ogilvie28 K Okada58 JD Orjuela Koop13

JD Osborn44 A Oskarsson41 K Ozawa12 32 R Pak7 V Pantuev26 V Papavassiliou51 IH Park18 JS Park62

S Park62 SK Park33 SF Pate51 L Patel20 M Patel28 H Pei28 J-C Peng25 DV Perepelitsa7 14

GDN Perera51 DYu Peressounko34 J Perry28 R Petti7 64 C Pinkenburg7 R Pinson1 RP Pisani7

ML Purschke7 H Qu1 J Rak30 BJ Ramson44 I Ravinovich69 KF Read53 65 D Reynolds63 V Riabov49 56

Y Riabov56 60 E Richardson42 T Rinn28 N Riveli52 D Roach68 G Roche40 Dagger SD Rolnick8

M Rosati28 Z Rowan5 JG Rubin44 MS Ryu21 B Sahlmueller64 N Saito32 T Sakaguchi7 H Sako29

V Samsonov49 56 M Sarsour20 S Sato29 S Sawada32 B Schaefer68 BK Schmoll65 K Sedgwick8 R Seidl57 58

A Sen20 65 R Seto8 P Sett4 A Sexton42 D Sharma64 69 I Shein24 T-A Shibata57 66 K Shigaki22

M Shimomura28 48 67 K Shoji57 P Shukla4 A Sickles7 25 CL Silva39 D Silvermyr41 53 KS Sim33

BK Singh3 CP Singh3 V Singh3 M Skolnik45 M Slunecka9 M Snowball39 S Solano45 RA Soltz38

WE Sondheim39 SP Sorensen65 IV Sourikova7 PW Stankus53 P Steinberg7 E Stenlund41 M Stepanov43 Dagger

A Ster70 SP Stoll7 T Sugitate22 A Sukhanov7 T Sumita57 J Sun64 J Sziklai70 EM Takagui61

A Takahara12 A Taketani57 58 Y Tanaka47 S Taneja64 K Tanida58 62 MJ Tannenbaum7 S Tarafdar3 69

A Taranenko49 63 E Tennant51 R Tieulent20 A Timilsina28 T Todoroki57 67 M Tomasek15 27 H Torii22

CL Towell1 R Towell1 RS Towell1 I Tserruya69 Y Tsuchimoto12 C Vale7 HW van Hecke39 M Vargyas17

E Vazquez-Zambrano14 A Veicht14 J Velkovska68 R Vertesi70 M Virius15 B Voas28 V Vrba15 27

E Vznuzdaev56 XR Wang51 58 D Watanabe22 K Watanabe57 59 Y Watanabe57 58 YS Watanabe12 32

F Wei51 S Whitaker28 AS White44 SN White7 D Winter14 S Wolin25 CL Woody7 M Wysocki13 53

B Xia52 L Xue20 S Yalcin64 YL Yamaguchi12 64 A Yanovich24 J Ying20 S Yokkaichi57 58 JH Yoo33

I Yoon62 Z You39 I Younus37 50 H Yu55 IE Yushmanov34 WA Zajc14 A Zelenski6 S Zhou11 and L Zou8

(PHENIX Collaboration)1Abilene Christian University Abilene Texas 79699 USA

2Department of Physics Augustana University Sioux Falls South Dakota 57197 USA3Department of Physics Banaras Hindu University Varanasi 221005 India

4Bhabha Atomic Research Centre Bombay 400 085 India5Baruch College City University of New York New York New York 10010 USA

6Collider-Accelerator Department Brookhaven National Laboratory Upton New York 11973-5000 USA7Physics Department Brookhaven National Laboratory Upton New York 11973-5000 USA

8University of California-Riverside Riverside California 92521 USA9Charles University Ovocny trh 5 Praha 1 116 36 Prague Czech Republic

10Chonbuk National University Jeonju 561-756 Korea11Science and Technology on Nuclear Data Laboratory China Institute of Atomic Energy Beijing 102413 P R China

12Center for Nuclear Study Graduate School of Science University of Tokyo 7-3-1 Hongo Bunkyo Tokyo 113-0033 Japan13University of Colorado Boulder Colorado 80309 USA

14Columbia University New York New York 10027 and Nevis Laboratories Irvington New York 10533 USA15Czech Technical University Zikova 4 166 36 Prague 6 Czech Republic

16Debrecen University H-4010 Debrecen Egyetem ter 1 Hungary17ELTE Eotvos Lorand University H-1117 Budapest Pazmany P s 1A Hungary

18Ewha Womans University Seoul 120-750 Korea19Florida State University Tallahassee Florida 32306 USA

20Georgia State University Atlanta Georgia 30303 USA21Hanyang University Seoul 133-792 Korea

22Hiroshima University Kagamiyama Higashi-Hiroshima 739-8526 Japan23Department of Physics and Astronomy Howard University Washington DC 20059 USA

24IHEP Protvino State Research Center of Russian Federation Institute for High Energy Physics Protvino 142281 Russia25University of Illinois at Urbana-Champaign Urbana Illinois 61801 USA

26Institute for Nuclear Research of the Russian Academy of Sciences prospekt 60-letiya Oktyabrya 7a Moscow 117312 Russia27Institute of Physics Academy of Sciences of the Czech Republic Na Slovance 2 182 21 Prague 8 Czech Republic

28Iowa State University Ames Iowa 50011 USA29Advanced Science Research Center Japan Atomic Energy Agency 2-4Shirakata Shirane Tokai-mura Naka-gun Ibaraki-ken 319-1195 Japan

30Helsinki Institute of Physics and University of Jyvaskyla POBox 35 FI-40014 Jyvaskyla Finland31Karoly Roberts University College H-3200 Gyngyos Matraiut 36 Hungary

32KEK High Energy Accelerator Research Organization Tsukuba Ibaraki 305-0801 Japan33Korea University Seoul 136-701 Korea

34National Research Center ldquoKurchatov Instituterdquo Moscow 123098 Russia35Kyoto University Kyoto 606-8502 Japan

36Laboratoire Leprince-Ringuet Ecole Polytechnique CNRS-IN2P3 Route de Saclay F-91128 Palaiseau France37Physics Department Lahore University of Management Sciences Lahore 54792 Pakistan

38Lawrence Livermore National Laboratory Livermore California 94550 USA39Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

40LPC Universite Blaise Pascal CNRS-IN2P3 Clermont-Fd 63177 Aubiere Cedex France41Department of Physics Lund University Box 118 SE-221 00 Lund Sweden

42University of Maryland College Park Maryland 20742 USA43Department of Physics University of Massachusetts Amherst Massachusetts 01003-9337 USA

44Department of Physics University of Michigan Ann Arbor Michigan 48109-1040 USA45Muhlenberg College Allentown Pennsylvania 18104-5586 USA

46Myongji University Yongin Kyonggido 449-728 Korea47Nagasaki Institute of Applied Science Nagasaki-shi Nagasaki 851-0193 Japan

48Nara Womenrsquos University Kita-uoya Nishi-machi Nara 630-8506 Japan49National Research Nuclear University MEPhI Moscow Engineering Physics Institute Moscow 115409 Russia

50University of New Mexico Albuquerque New Mexico 87131 USA51New Mexico State University Las Cruces New Mexico 88003 USA

52Department of Physics and Astronomy Ohio University Athens Ohio 45701 USA

53Oak Ridge National Laboratory Oak Ridge Tennessee 37831 USA54IPN-Orsay Univ Paris-Sud CNRSIN2P3 Universite Paris-Saclay BP1 F-91406 Orsay France

55Peking University Beijing 100871 P R China56PNPI Petersburg Nuclear Physics Institute Gatchina Leningrad region 188300 Russia57RIKEN Nishina Center for Accelerator-Based Science Wako Saitama 351-0198 Japan

58RIKEN BNL Research Center Brookhaven National Laboratory Upton New York 11973-5000 USA59Physics Department Rikkyo University 3-34-1 Nishi-Ikebukuro Toshima Tokyo 171-8501 Japan

60Saint Petersburg State Polytechnic University St Petersburg 195251 Russia61Universidade de Sao Paulo Instituto de Fısica Caixa Postal 66318 Sao Paulo CEP05315-970 Brazil

62Department of Physics and Astronomy Seoul National University Seoul 151-742 Korea63Chemistry Department Stony Brook University SUNY Stony Brook New York 11794-3400 USA

64Department of Physics and Astronomy Stony Brook University SUNY Stony Brook New York 11794-3800 USA65University of Tennessee Knoxville Tennessee 37996 USA

66Department of Physics Tokyo Institute of Technology Oh-okayama Meguro Tokyo 152-8551 Japan67Center for Integrated Research in Fundamental Science and Engineering University of Tsukuba Tsukuba Ibaraki 305 Japan

68Vanderbilt University Nashville Tennessee 37235 USA69Weizmann Institute Rehovot 76100 Israel

70Institute for Particle and Nuclear Physics Wigner Research Centre for Physics HungarianAcademy of Sciences (Wigner RCP RMKI) H-1525 Budapest 114 POBox 49 Budapest Hungary

71Yonsei University IPAP Seoul 120-749 Korea72University of Zagreb Faculty of Science Department of Physics Bijenicka 32 HR-10002 Zagreb Croatia

(Dated August 14 2019)

The PHENIX Collaboration at the Relativistic Heavy Ion Collider has measured open heavy flavorproduction in minimum bias Au+Au collisions at

radicsNN = 200 GeV via the yields of electrons from

semileptonic decays of charm and bottom hadrons Previous heavy flavor electron measurementsindicated substantial modification in the momentum distribution of the parent heavy quarks dueto the quark-gluon plasma created in these collisions For the first time using the PHENIX siliconvertex detector to measure precision displaced tracking the relative contributions from charm andbottom hadrons to these electrons as a function of transverse momentum are measured in Au+Aucollisions We compare the fraction of electrons from bottom hadrons to previously publishedresults extracted from electron-hadron correlations in p+p collisions at

radicsNN = 200 GeV and find

the fractions to be similar within the large uncertainties on both measurements for pT gt 4 GeVcWe use the bottom electron fractions in Au+Au and p+p along with the previously measured heavyflavor electron RAA to calculate the RAA for electrons from charm and bottom hadron decaysseparately We find that electrons from bottom hadron decays are less suppressed than those fromcharm for the region 3 lt pT lt 4 GeVc

PACS numbers 2575Dw

I INTRODUCTION

High-energy heavy ion collisions at the RelativisticHeavy Ion Collider (RHIC) and the Large Hadron Col-lider (LHC) create matter that is well described as anequilibrated system with initial temperatures in excessof 340ndash420 MeV [1ndash5] In this regime the matter is un-derstood to be a quark-gluon plasma (QGP) with boundhadronic states no longer in existence as the temperaturesfar exceed the transition temperature of approximately155 MeV calculated by lattice quantum chromodynamics(QCD) [6] This QGP follows hydrodynamical flow be-havior with extremely small dissipation characterized bythe shear viscosity to entropy density ratio ηs asymp 14πand is thus termed a near-perfect fluid [1 7ndash9]

Charm and bottom quarks (mc asymp 13 GeVc2 and

lowast PHENIX Co-Spokesperson morrisonbnlgovdagger PHENIX Co-Spokesperson jamienaglecoloradoeduDagger Deceased

mb asymp 42 GeVc2) are too heavy to be significantly pro-duced via the interaction of thermal particles in the QGPThus the dominant production mechanism is via hardinteractions between partons in the incoming nuclei ieinteractions that involve large momentum transfer q2Once produced these heavy quarks are not destroyed bythe strong interaction and thus propagate through theQGP and eventually emerge in heavy flavor hadrons forexample D and B mesons

Early measurement of heavy flavor electrons from thePHENIX Collaboration in Au+Au collisions at RHIC in-dicated that although the total heavy flavor productionscales with the number of binary collisions within un-certainties [10 11] the momentum distribution of theseheavy quarks is significantly modified when comparedwith that in p+p collisions [12 13] These results indi-cate a large suppression for high-pT gt 5 GeVc electronsand a substantial elliptic flow for pT = 03ndash30 GeVcelectrons from heavy quark decays Here and through-out the paper we use ldquoelectronsrdquo to refer to both elec-trons and positrons The suppression of the charm quark

has since been confirmed through the direct reconstruc-tion of D mesons by the STAR Collaboration [14] InPb+Pb collisions at the LHC at

radicsNN

= 276 TeV simi-lar momentum distribution modifications of heavy flavorelectrons and D mesons have been measured [15 16]Recently the CMS experiment has reported first mea-surements of B rarr Jψ [17] and b-jets [18] in Pb+Pbcollisions In contrast to this suppression pattern foundin Au+Au collisions d+Au and peripheral Cu+Cu col-lisions at

radicsNN

= 200 GeV exhibit an enhancement atintermediate electron pT in the heavy flavor electronspectrum [19 20] that must be understood in terms ofa mechanism that enhances the pT spectrum eg theCronin effect [21] That mechanism potentially moder-ates the large suppression observed in Au+Au collisionsatradicsNN

= 200 GeV It is notable that in central Au+Aucollisions at

radicsNN

= 62 GeV an enhancement is also ob-served at intermediate pT [22]

The possibility that charm quarks follow the QGPflow was postulated early on [23] and more detailedLangevin-type calculations with drag and diffusion ofthese heavy quarks yield a reasonable description of theelectron data [24ndash29] Many of these theory calculationsincorporate radiative and collisional energy loss of theheavy quarks in the QGP that are particularly impor-tant at high-pT where QGP flow effects are expected tobe sub-dominant The large suppression of heavy flavorelectrons extending up to pT asymp 9 GeVc has been a par-ticular challenge to understand theoretically in part dueto an expected suppression of radiation in the directionof the heavy quarks propagation ndash often referred to asthe ldquodead-conerdquo effect [30]

This observation of the high-pT suppression [31 32] isall the more striking because perturbative QCD (pQCD)calculations indicate a substantial contribution from bot-tom quark decays for pT gt 5 GeVc [33] First measure-ments in p+p collisions at 200 GeV via electron-hadroncorrelations confirm this expected bottom contribution tothe electrons that increases as a function of pT [34 35]To date there are no direct measurements at RHIC ofthe contribution of bottom quarks in Au+Au collisions

For the specific purpose of separating the contribu-tions of charm and bottom quarks at midrapidity thePHENIX Collaboration has added micro-vertexing capa-bilities in the form of a silicon vertex tracker (VTX) Thedifferent lifetimes and kinematics for charm and bottomhadrons decaying to electrons enables separation of theircontributions with measurements of displaced tracks (iethe decay electron not pointing back to the collision ver-tex) In this paper we report on first results of separatedcharm and bottom yields via single electrons in minimumbias (MB) Au+Au collisions at

radicsNN

= 200 GeV

II PHENIX DETECTOR

As detailed in Ref [36] the PHENIX detector wasoriginally designed with precision charged particle recon-

struction combined with excellent electron identificationIn 2011 the VTX was installed thus enabling micro-vertexing capabilities The dataset utilized in this anal-ysis comprises Au+Au collisions at

radicsNN

= 200 GeV

A Global detectors and MB trigger

A set of global event-characterization detectors are uti-lized to select Au+Au events and eliminate backgroundcontributions Two beam-beam counters (BBC) coveringpseudorapidity 30 lt |η| lt 39 and full azimuth are lo-cated at plusmn 144 meters along the beam axis and relativeto the nominal beam-beam collision point Each of theBBCs comprises 64 Cerenkov counters

Based on the coincidence of the BBCs Au+Au colli-sions are selected via an online MB trigger which requiresat least two counters on each side of the BBC to fire TheMB sample covers 96plusmn 3 of the total inelastic Au+Aucross section as determined by comparison with MonteCarlo Glauber models [37] The BBC detectors also en-able a selection on the z-vertex position of the collision asdetermined by the time-of-flight difference between hitsin the two sets of BBC counters The z-vertex resolu-tion of the BBC is approximately σz = 06 cm in centralAu+Au collisions A selection within approximately plusmn12cm of the nominal detector center was implemented andsim 85 of all Au+Au collisions within that selection wererecorded by the PHENIX high-bandwidth data acquisi-tion system

B The central arms

Electrons (e+ and eminus) are reconstructed using two cen-tral spectrometer arms as shown in Fig 1(a) each ofwhich covers the pseudorapidity range |η| lt 035 andwith azimuthal angle ∆φ = π2 The detector config-uration of the central arms is the same as in previousPHENIX Collaboration heavy flavor electron publica-tions [12 13] Charged particle tracks are reconstructedoutside of an axial magnetic field using layers of driftchamber (DC) and multi-wire proportional pad cham-bers (PC) The momentum resolution is σpp 07oplus 09 p (GeVc) For central arm charged particlereconstructions the trajectory is only measured for ra-dial positions r gt 202 meters and the momentum vec-tor is calculated by assuming the track originates at theAu+Au collision point determined by the BBC detectorsand assuming 0 radial distance

Electron identification is performed by hits in a ringimaging Cerenkov detector (RICH) and a confirming en-ergy deposit in an electromagnetic calorimeter (EMCal)The RICH uses CO2 gas at atmospheric pressure as aCerenkov radiator Electrons and pions begin to ra-diate in the RICH at pT gt 20 MeVc and pT gt 49GeVc respectively The EMCal is composed of foursectors in each arm The bottom two sectors of the east

arm are lead-glass and the other six are lead-scintillatorThe energy resolution of the EMCal is σEE 45 oplus83

radicE(GeV) and σEE 43 oplus 77

radicE(GeV) for

lead-scintillator and lead-glass respectively

South Side View

Beam View

PHENIX Detector2011

PbSc PbSc

PbSc PbGl

PC1 PC1

PC3PC2

Central Magnet

CentralMagnet

North M

uon MagnetSouth Muon Magnet

TECPC3

RICH RICH

ZDC NorthZDC South

Aerogel

TOF-W 79 m = 26 ft

109 m = 36 ft

185 m = 60 ft

beampipe

Outer ca

FIG 1 (Color Online) (a) A schematic view of the PHENIXdetector configuration for the 2011 run (b) A schematic viewof the VTX detector with the individual ladders shown

C The VTX detector

In 2011 the central detector was upgraded with theVTX detector as shown in Fig 1 In addition a newberyllium beam pipe with 216 cm inner diameter and 760microm nominal thickness was installed to reduce multiple-scattering before the VTX detector

The VTX detector [38ndash40] consists of four radial layersof silicon detectors as shown in Fig 1(b) The detectoris separated into two arms each with nominal accep-tance ∆φ asymp 08π centered on the acceptance of the outerPHENIX central arm spectrometers The detector cov-ers pseudorapidity |η| lt 12 for collisions taking place atz = 0 The VTX can precisely measure the vertex posi-tion of a collision within |z| lt 10 cm range of the center

of the VTXThe two inner layers referred to as B0 and B1 of the

VTX detector comprise silicon pixel detectors as detailedin Ref [41] B0 (B1) comprises 10 (20) ladders with acentral radial position of 26 (51) cm The silicon pixeltechnology is based on the ALICE1LHCb sensor-readoutchip [42] which was developed at CERN Each ladderis electrically divided into two independent half-laddersEach ladder comprises four sensor modules mounted ona mechanical support made from carbon-fiber compos-ite Each sensor module comprises a silicon pixel sensorwith a pixel size of 50 microm(φ) times 425 microm(z) bump-bondedwith four pixel readout chips One pixel readout chipreads 256 (φ)times 32 (z)= 8192 pixels and covers approxi-mately 13 cm (∆φ)times 14 cm (∆z) of the active area ofthe sensor The position resolution is σφ = 144 microm inthe azimuthal direction

The two outer layers of the VTX detector referred toas B2 and B3 are constructed using silicon stripixel sen-sors as detailed in Ref [41] The B2 (B3) layer comprises16 (24) silicon stripixel ladders at a central radial distanceof 118 (167) cm The stripixel sensor is a novel siliconsensor and is a single-sided N-type DC-coupled two-dimensional (2-D) sensitive detector [43 44] One sensorhas an active area of approximately 30 mm times 60 mmwhich is divided into two independent sectors of 30 mmtimes 30 mm Each sector is divided into 384 times 30 pixelsEach pixel has an effective size of 80 microm (φ) times 1000 microm(z) leading to a position resolution of σφ=23 microm A pixelcomprises two implants (A and B) interleaved such thateach of the implants registers half of the charge depositedby ionizing particles There are 30 A implants along thebeam direction connected to form a 30 mm long X-stripand 30 B implants are connected with a stereo angle of80 mrad to form a U-strip X-strip and U-strip are visu-alized in [44] When a charged particle hits a pixel boththe X- and the U-strip sharing the pixel register a hitThus the hit pixel is determined as the intersection ofthe two strips The stripixel sensor is read out with theSVX4 chip developed by a FNAL-LBNL Collaboration[45]

The total number of channels in the VTX pixel andstripixel layers is 39 million pixels and 034 million stripsThe compositions of the pixel and strip are illustrated in[41 44] The main characteristics of the VTX detectorare summarized in Table I

III ANALYSIS

A Overview

The purpose of the analysis is to separate the electronsfrom charm and bottom hadron decays The life time ofB mesons (cτB0= 455 microm cτBplusmn = 491 microm [46]) is sub-stantially longer than that of D mesons (cτD0 = 123 micromcτDplusmn = 312 microm) and the decay kinematics are differ-ent This means that the distribution of values for the

TABLE I A summary of the VTX detector For each layer (B0 to B3) the detector type the central radius (r) ladder length(l) sensor thickness (t) sensor active area (∆φ times ∆z) the number of sensors per ladder (NS) the number of ladders (NL)pixelstrip size in φ (∆φ) and z (∆z) the number of read-out channels (Nch) and the average radiation length including thesupport and on-board electronics (X0) are given

sensor active area pixelstrip size

type r(cm) l(cm) t (microm) ∆φ(cm) ∆z(cm) NS NL ∆φ (microm) ∆z (microm) Nch X0()

B0 pixel 26 228 200 128 556 4 10 50 425 13times 106 13

B1 pixel 51 228 200 128 556 4 20 50 425 26times 106 13

B2 stripixel 118 318 625 307 600 5 16 80 3times 104 12times 105 52

distance of closest approach (DCA) of the track to theprimary vertex for electrons from bottom decays will bebroader than that of electrons from charm decays Thereare other sources of electrons namely Dalitz decays of π0

and η photon conversions Ke3 decays and Jψ rarr e+eminus

decays With the exception of electrons from Ke3 decaysthese background components have DCA distributionsnarrower than those from charm decay electrons Thuswe can separate b rarr e c rarr e and background electronsvia precise measurement of the DCA distribution

In the first step of the analysis we select good eventswhere the collision vertex is within the acceptance of theVTX detector and its function is normal (Sec III B) Wethen reconstruct electrons in the PHENIX central arms(Sec III C) The electron tracks are then associated withhits in the VTX detector and their DCA is measured(Sec III D) At this point we have the DCA distributionof inclusive electrons that has contributions from heavyflavor (brarr e and crarr e) and several background compo-nents

The next step is to determine the DCA shape and nor-malization of all background components (Sec III E)They include mis-identified hadrons background elec-trons with large DCA caused by high-multiplicity effectsphotonic electrons (Dalitz decay electrons photon con-versions) and electrons from Ke3 and quarkonia decaysThe shapes of the DCA distributions of the various back-ground electrons are determined via data driven methodsor Monte Carlo simulation We then determine the nor-malization of those background electron components inthe data (Sec III F)

Because the amount of the VTX detector materialis substantial (13 of one radiation length) the largestsource of background electrons is photon conversionwithin the VTX We suppress this background by a con-version veto cut (Sec III E 3)

Once the shape and the normalization of all back-ground components are determined and subtracted wearrive at the DCA distribution of heavy flavor decay elec-trons that can be described as a sum of brarr e and crarr eDCA distributions The heavy flavor DCA distributionis decomposed by an unfolding method (Sec III G)

B Event selection

The data set presented in this analysis is from Au+Aucollisions at

radicsNN

= 200 GeV recorded in 2011 after thesuccessful commissioning of the VTX detector As de-tailed earlier the MB Au+Au data sample was recordedusing the BBC trigger sampling 96plusmn 3 of the inelasticAu+Au cross section A number of offline cuts were ap-plied for optimizing the detector acceptance uniformityand data quality as described below After all cuts adata sample of 24times109 Au+Au events was analyzed

1 z-vertex selection

The acceptance of the PHENIX central arm spectrom-eters covers collisions with z-vertex within plusmn 30 cm of thenominal interaction point The VTX detector is morerestricted in |z| acceptance as the B0 and B1 layerscover only |z| lt 114 cm Thus the BBC trigger se-lected only events within the narrower vertex range of|zBBC| lt 12 cm In the offline reconstruction the tracksreconstructed from VTX information alone are used toreconstruct the Au+Au collision vertex with resolutionσz = 75 microm All Au+Au events in the analysis are re-quired to have a z-vertex within plusmn10 cm as reconstructedby the VTX

2 Data quality assurance

Due to a number of detector commissioning issues inthis first data taking period for the VTX the data qual-ity varies substantially Therefore we divide the entire2011 Au+Au data taking period into four periods Theacceptance of the detector changes significantly betweenthese periods

In addition several cuts are applied to ensure the qual-ity and the stability of the data Applying electron iden-tification cuts described in Sec III C 2 the electron tohadron ratios were checked for each run a continuousdata taking period typically lasting of order one hourand three runs out of 547 with ratios outside of 5σ from

the mean were discarded The B2 and B3 stripixel lay-ers had an issue in stability of read-out electronics wheresome of the sensor modules would drop out resultingin a reduced acceptance within a given run Additionalinstabilities also existed in the B0 and B1 pixel layersDetailed channel by channel maps characterizing deadhot and unstable channels were generated for all layerswithin a given run These maps were used to mask deadhot and unstable channels from the analysis as well asto define the fiducial area of the VTX in simulations

During this first year of data taking the instabilityof the read-out electronics discussed above caused sig-nificant run-to-run variations in the acceptance and ef-ficiency of the detector It is therefore not possible toreliably calculate the absolute acceptance and efficiencycorrection while maintaining a large fraction of the to-tal data set statistics Instead we report on the relativeyields of charm and bottom to total heavy flavor Wehave checked that the DCA distributions are consistentbetween running periods and are not impacted by thechanging acceptance Thus we can measure the shape ofthe DCA distribution using the entire data set In thefollowing we use the shape of the measured DCA distri-bution only to separate brarr e and crarr e components

C Electron reconstruction in central arms

1 Track reconstruction

Charged particle tracks are reconstructed using theouter central arm detectors DC and PC as detailed inRef [13] The DC has six types of wire modules stackedradially named X1 U1 V1 X2 U2 and V2 The Xwires run parallel to the beam axis in order to measurethe φ-coordinate of the track and the U and V wires havestereo angles varying from 54 to 60 degrees Tracks arerequired to have hits in both the X1 and X2 sectionsalong with uniquely associated hits in the U or V stereowires and at least one matching PC hit to reduce mis-reconstructed tracks The track momentum vector is de-termined assuming the particle originated at the Au+Aucollision vertex as reconstructed by the BBC

2 Electron identification

Electron candidates are selected by matching trackswith hits in the RICH and energy clusters in the EMCalThe details on the electron selection cuts are given inRef [12] In this analysis we select electron candidateswithin 15 lt pT [GeVc] lt 50 and we briefly describethe cuts in the RICH and EMCal below

Cerenkov photons from an electron track produce aring-shaped cluster in the RICH At least three associ-ated PMT hits are required in the RICH and a ring-shapecut is applied The center of the ring is required to bewithin 5 cm of the track projection The probability

that the associated cluster in the EMCal comes from anelectromagnetic shower is calculated based on the showershape Based on that probability tracks are selected in away that maintains high efficiency for electrons while re-jecting hadrons Further the energy (E) in the EMCal isrequired to match the track determined momentum (p)This match is calculated as dep = (Ep minus microEp)σEpwhere microEp and σEp are the mean and standard devia-tion respectively of a Gaussian fit to the Ep distributiondetermined as a function of momentum (see Fig 2) Acut of dep gt minus2 is used to further reject hadrons thathave an Ep ratio lt 1 because they do not deposit theirfull energy in the EMCal

In high-multiplicity Au+Au events there is a signifi-cant probability for a random association between thetrack and hits in the RICH and EMCal This mis-identified hadron probability is estimated as follows Thez lt 0 and z gt 0 sides of the RICH have their hitsswapped in software and the tracks are re-associatedwith RICH hits Because the two longitudinal sides ofthe RICH are identical this gives a good estimate of therandom hadron background in the electron sample

The distribution of electron candidates at pT =20ndash25GeVc for the normalized EMCal energy to track mo-mentum ratio dep defined above is shown in Fig 2There is a large peak near zero from true electrons asexpected and a clear low-side tail from mis-identifiedhadron Also shown is the result of the above swapmethod The difference between the data and the ldquoswaprdquodistribution (red) is explained as contributions from off-vertex electrons caused by conversions from the outerlayer of the VTX and weak decay In the final account-ing for all contributions to the identified-electron DCAdistribution we utilize this swap method to statisticallyestimate the contribution of mis-identified hadron in eachpT selection as detailed in Section III E 1

)σdep (-4 -3 -2 -1 0 1 2 3 4

electron

mis-identified BG

FIG 2 (Color Online) Matching variable between the re-constructed track momentum (p) and the energy measured inthe EMCal (E) dep = (Ep minus microEp)σEp The black dis-tribution is for identified electrons with pT = 20ndash25 GeVcand the red distribution is the estimated contribution frommis-identified electrons via the RICH swap-method

D DCA measurement with the VTX

Charged particle tracks reconstructed in the centralarms must be associated with VTX hits in order to cal-culate their DCA Three-dimensional (3-D) hit positionsin the 4 layers of VTX are reconstructed For each col-lision the primary vertex is reconstructed by the VTXThen central arm tracks are associated with hits in theVTX and VTX-associated tracks are formed Finallythe DCA between the primary vertex and the VTX-associated tracks are measured

1 VTX alignment

In order to achieve good DCA resolution to separateb rarr e and c rarr e alignment of the detector laddersto high precision is required The detector alignmentis accomplished via an iterative procedure of matchingouter central arm tracks from the DC and PC to theVTX hits The procedure is convergent for the positionof each ladder The alignment was repeated each timethe detector was repositioned following a service accessThe final alignment contribution to the DCA resolutionin both φ and z is a few tens of microns

2 VTX hit reconstruction

For layers B0 and B1 clusters of hit pixels are formedby connecting contiguous hit pixels by a recursive cluster-ing algorithm An average cluster size is 26 (67) pixelsfor the pixel (stripixel) The center of the cluster in thelocal 2-D coordinate system of the sensor is calculated asthe hit position

For B2 and B3 layers 2D hit points on the sensor arereconstructed from the X-view and the U-view Hit linesin the X-view (U-view) are formed by clustering contigu-ous hit X-strips (U-strips) weighted by deposited chargesand then 2D hit points are formed as the intersections ofall hit lines in X- and U- views When one hit line in U-view crosses more than two hit lines in X-view ghost hitscan be formed because which crossing point is the truehit is ambiguous These ghost hits increase the numberof reconstructed 2D hits approximately by 50 (30) inB2 (B3) in central Au+Au collisions The ghost hit ratewas studied using a full geant3 [47] simulation with theHIJING [48] generator as input However because theoccupancy of the detector at the reconstructed 2D hitpoint level is low less than 01 these ghost hits do notcause any significant issue in the analysis

The positions of all 2-D hits in the VTX are then trans-ferred into the global PHENIX 3-D coordinate systemCorrection of the sensor position and orientation deter-mined by the alignment procedure described in the previ-ous section is applied in the coordinate transformationThe resulting 3-D hit positions in the global coordinatesystem are then used in the subsequent analysis

3 The primary vertex reconstruction

With the VTX hit information alone charged particletracks can be reconstructed only with modest momen-tum resolution δpp asymp 10 due to the limited magneticfield integrated over the VTX volume and the multiplescattering within the VTX These tracks can be utilizedto determine the collision vertex in three-dimensions (z0along the beam axis and x0y0 in the transverse plane)for each Au+Au event under the safe assumption thatthe majority of particles originate at the collision vertexThis vertex position is called the primary vertex position

The position resolution of the primary vertex for eachdirection depends on the sensor pixel and strip sizes theprecision of the detector alignment and the number ofparticles used for the primary vertex calculation and theirmomentum in each event For MB Au+Au collisionsthe resolution values are σx = 96 microm σy = 43 microm andσz = 75 microm The worse resolution in x compared toy is due to the orientation of the two VTX arms Forcomparison the beam profile in the transverse plane isσlumix asymp σlumi

y asymp 90 microm in the 2011 Au+Au run

4 Association of a central arm track with VTX

Each central arm track is projected from the DCthrough the magnetic field to the VTX detector Hitsin VTX are then associated with the track using a recur-sive windowing algorithm as follows

The association starts from layer B3 VTX hits in thatlayer that are within a certain (∆φtimes∆z) window aroundthe track projection are searched If hits are found in thiswindow the track is connected to each of the found hitsand then projected inward to the next layer In this casethe search window in the next layer is decreased becausethere is much less uncertainty in projection to the nextlayer If no hit is found the layer is skipped and thetrack is projected inward to the next layer keeping thesize of the projection window This process continuesuntil the track reaches layer B0 and a chain of VTX hitsthat can be associated with the track is formed Thewindow sizes are momentum dependent and determinedfrom a full geant3 simulation of the detector so that theinefficiency of track reconstruction due to the window sizeis negligible

After all possible chains of VTX hits that can be as-sociated with a given central arm track are found by therecursive algorithm a track model fit is performed foreach of these possible chains and the χ2 of the fit χ2

vtxis calculated The effect of multiple scattering in eachVTX layer is taken into account in calculation of χ2

vtxThen the best chain is chosen based on the value of χ2

and the number of associated hits This best chain andits track model are called a VTX-associated track Notethat at most one VTX-associated track is formed fromeach central arm track

In this analysis we require that VTX-associated tracks

have associated hits in at least the first three layers ieB0 B1 and B2 An additional track requirement isχ2vtxNDF lt 2 for pT lt 2 GeVc and χ2

vtxNDF lt 3for pT gt 2 GeVc where NDF is the number of degreesof freedom in the track fit

5 DCAT and DCAL

Using the primary vertex position determined abovethe DCA of a track is calculated separately in the trans-verse plane (DCAT ) and along the beam axis (DCAL)Because by design the DCAT has a better resolution thanDCAL we first find DCAT with a track model of a circletrajectory assuming the uniform magnetic field over theVTX We define DCAT as

DCAT equiv LminusR (1)

where L is the distance from the collision vertex to thecenter of the circle defining the particle trajectory andR is the radius of the circle as shown in Fig 3 DCAL isthe distance between the z-coordinate of the point DCAT

found and z-coordinate of the primary vertex

It is notable that DCAT has a sign in this defini-tion The distinction between positive and negative val-ues of DCATmdashwhether the trajectory is bending towardsor away from the primary vertexmdashis useful since cer-tain background contributions have asymmetric distri-butions in positive and negative DCAT as discussed insection III E For electrons the positive side of DCAT

distribution has less background contribution There isno such positivenegative asymmetry in DCAL

Primary vertex

FIG 3 (Color Online) Illustration of the definition of DCAT

equiv L - R in the transverse plane

6 DCA measurement

For each VTX-associated track the DCA is calcu-lated separately in the radial and longitudinal direction(DCAT and DCAL) from the track model and the pri-mary vertex position Shown in Fig 4 is the resultingDCAT and DCAL distributions for all VTX-associatedtracks with pT = 20ndash25 GeVc Since the vast majorityof charged tracks are hadrons originating at the primaryvertex we observe a large peak around DCAT DCAL =0 that is well fit to a Gaussian distribution where the σrepresents the DCAT DCAL resolution A selection of|DCAL | lt 01 cm is applied to reduce background

There are broad tails for |DCAT | gt 003 cm MonteCarlo simulation shows that the main source of the broadtails is the decay of long lived light hadrons such as Λ andK0S The DCAT resolution as a function of the track pT is

extracted using a Gaussian fit to the peak and is shown inFig 4 c) The DCAT resolution is approximately 75 micromfor the 10ndash15 GeVc bin and decreases with increasingpT as the effect of multiple scattering becomes smaller forhigher pT The DCAT resolution becomes less than 60microm for pT gt 4 GeVc where it is limited by the positionresolution of the primary vertex

We divide the electrons into five pT bins and show theDCAT distributions for each in Fig 5 These distribu-tions are in integer-value counts and are not correctedfor acceptance and efficiency The DCA distributions in-clude various background components other than heavyflavor contributions The background components arealso shown in the figure and are discussed in the nextsection (Section III E)

While the DCAT distributions in Fig 5 are plottedwithin |DCAT | lt 015 cm only a |DCAT | lt 01 cm isused in the analysis to extract the charm and bottomyield described later At large DCAT the distribution isdominated by high-multiplicity background (Sec III E 2)and therefore provides little constraint in the extractionof the charm and bottom contributions

E DCA distribution of Background Components

The sample of candidate electron tracks that pass allthe analysis cuts described above contains contributionsfrom a number of sources other than the desired elec-trons from semi-leptonic decays of charm and bottomhadrons In order to extract the heavy flavor contri-butions all background components must be fully ac-counted for and their DCAT shapes as a function of pTincorporated These background components are listedin the order presented below

1 Misidentified hadrons

2 High-multiplicity background

3 Photonic electrons

[cm]LDCA-02 -01 0 01 02

610 All TracksMB

lt 25T

20 lt p

[cm]TDCA-015 -01 -005 0 005 01 015

710All TracksMB

lt 25T

20 lt p

[GeVc]T

p1 15 2 25 3 35 4 45

micro [σ

FIG 4 Distance-of-closest-approach distributions for (a)along the beam axis DCAL and (b) transverse plane DCAT forall VTX-associated tracks in Au+Au at

radicsNN = 200 GeV in

the range 20 lt pT [ GeVc] lt 25 (c) The DCAT resolutionas a function of pT for all tracks

4 Kaon decay electrons

5 Heavy-quarkonia decay electrons

As described in this and the following section all back-ground components are constrained by PHENIX mea-surements in Au+Au and are fully simulated through ageant3 description of the detector This method is sim-ilar to the cocktail method of background subtraction

used in the previous analysis of inclusive heavy flavorelectrons [12]

Next we describe these background sources and theirDCA distributions The first two components are causedby detector and multiplicity effects DCA distributionsand normalization of these two components are deter-mined by data driven methods as detailed in this sec-tion The last three components are background elec-trons that are not the result of semi-leptonic decays ofheavy flavor hadrons Their DCA distributions are de-termined by Monte Carlo simulation and their normal-ization is determined by a bootstrap method describedin section III F Of those background electrons photonicelectrons are the dominant contribution We developed aconversion veto cut to suppress this background (III E 3)

1 Mis-identified hadron

As detailed in the discussion on electron identificationthere is a nonzero contribution from mis-identified elec-trons This contribution is modeled via the RICH swap-method described in Section III C 2 From this swapmethod we obtain the probability that a charged hadronis mis-identified as an electron as a function of pT Thisprobability is then applied to the DCA distribution ofcharged hadrons to obtain the DCA distribution of mis-identified hadrons

The resulting DCAT distribution is shown in eachpanel of Fig 5 Note that this component is properlynormalized automatically For each pT bin the DCAdistribution of mis-identified prompt hadrons has a nar-row Gaussian peak at DCAT = 0 The broad tails forlarge |DCAT | are mainly caused by decays of Λ and K0

S In all pT bins the magnitude of this background is nomore than 10 of the data for all DCAT

Due to the high multiplicity in Au+Au collisions anelectron candidate track in the central arms can be asso-ciated with random VTX hits Such random associationscan cause a background that has a very broad DCAT dis-tribution Although the total yield of this background isonly 01 of the data its contribution is significant atlarge DCAT where we separate brarr e and crarr e

To evaluate the effect of event multiplicity on thereconstruction performance we embed simulated sin-gle electronsmdashie the response of the PHENIX detec-tor to single electrons that is obtained from a geant3simulationmdashinto data events containing VTX detectorhits from real Au+Au collisions The events are then pro-cessed through the standard reconstruction software toevaluate the reconstruction performance in MB Au+Aucollisions

The reconstructed DCAT and DCAL for embeddedprimary electrons in MB Au+Au collisions is shown in

[cm]TDCA-015 -01 -005 0 005 01 015

lt 200eT

150 lt p

(a)=200 GeVNNsAu+Au MB PHENIX 2011

[cm]TDCA-015 -01 -005 0 005 01 015

lt 250eT

200 lt p

(b)=200 GeVNNsAu+Au MB PHENIX 2011

[cm]TDCA-015 -01 -005 0 005 01 015

lt 300eT

250 lt p

(c)=200 GeVNNsAu+Au MB PHENIX 2011

[cm]TDCA-015 -01 -005 0 005 01 015

lt 400eT

300 lt p

(d)=200 GeVNNsAu+Au MB PHENIX 2011

[cm]TDCA-015 -01 -005 0 005 01 015

lt 500eT

400 lt p

(e)=200 GeVNNsAu+Au MB PHENIX 2011 Data

Mis-identified hadron

Random

Dalitz

Conversion

FIG 5 (Color Online) DCAT distributions for electrons in MB Au+Au atradicsNN = 200 GeV that pass the reconstruction and

conversion veto cut in the indicated five electron-pT selections Also shown are the normalized contributions for the variousbackground components detailed in Section III E

Fig 6 Here the histograms labeled as ldquoSingle Elec- tronsrdquo show the reconstructed DCAT and DCAL dis-

[cm]TDCA-015 -01 -005 0 005 01 015

eSingle Electrons 20ltp

| lt 01 cmL

Embedded |DCA

| lt 018 cmL

Embedded 013 lt |DCA

| [cm]L

|DCA0 005 01 015 02 025 03 035 04 045

Embedded

| [cm]L

|DCA0 005 01 015 02 025 03 035

lt 02T008 lt DCA

FIG 6 (Color Online) Simulated primary electron (a)DCAT and (b) DCAL distribution before and after embed-ding in real Au+Au data

tributions of primary electrons before embedding TheDCAT distribution comprises a narrow Gaussian withno large DCAT tail and the DCAL distribution com-prises a similar but slightly broader Gaussian with nolarge tail The blue filled triangles show the DCAT

and DCAL distributions after embedding The DCAT

and DCAL distributions comprise a Gaussian peaked atDCAT (DCAL) sim 0 which is consistent with the distri-bution before embedding This demonstrates that theDCA resolution of the VTX is not affected by the highmultiplicity environment However the embedded distri-

are dominated by random associations as they are notpresent in the ldquoSingle Electronrdquo sample We thereforeuse the DCAT distribution for tracks with large |DCAL|as an estimate of this random high-multiplicity back-ground We choose the region 013 lt |DCAL| cm lt 018to represent this background and restrict our signal to|DCAL| lt 01 cm The DCAT distribution of trackswith 013 lt |DCAL| cm lt 018 must be normalized inorder to be used as an estimate of the high-multiplicitybackground for tracks within |DCAL| lt 01 cm Thisnormalization is determined by matching the integratedyield of embedded primary electrons in each |DCAL| re-gion for 008 lt DCAT cm lt 02 as shown in the inlayof Fig 6(b) The region 008 lt DCAT cm lt 02 is dom-inated by random associations as shown in Fig 6(a)and is therefore safe to use for determining the normal-ization The normalization of the high-multiplicity back-ground is determined to be 289 plusmn 029 The red filledcircles in Fig 6(a) show the embedded DCAT distri-bution with large DCAL (013 lt |DCAL| cm lt 018)This distribution agrees with the embedded DCAT dis-tribution (blue filled triangles in Fig 6) for large DCAT This demonstrates that the tails for large DCAT are wellnormalized by the distribution of electrons with largeDCAL However there is a small excess in the region005 lt |DCAT | cm lt 010 that is not accounted for bythe distribution with large DCAL We address this excessin the systematic uncertainties as described in Sec III Hwhere it is found to have only a small effect on the ex-traction of brarr e and crarr e

In each panel of Fig 5 the high-multiplicity back-ground is shown as a red line It is determined fromthe DCAT distribution of the data within 013 lt|DCAL| cm lt 018 as described above The numberof electron tracks in the large DCAL region is small Wetherefore fit the resulting DCAT data in each pT bin witha smooth function to obtain the shape of the red curvesshown in Fig 5 A second order polynomial is used inthe lowest pT bin where there are enough statistics toconstrain it The higher pT bins are fit with a constantvalue All curves are multiplied by the same normaliza-tion factor determined from embedded simulations asdescribed above

3 Photonic electrons and conversion veto cut

Photon conversions and Dalitz decays of light neutralmesons (π0 and η) are the largest electron backgroundWe refer to this background as photonic electron back-ground as it is produced by external or internal conver-sion of photons

The PHENIX Collaboration has previously publishedthe yields of π0 and η mesons in Au+Au collisions atradicsNN

= 200 GeV [49 50] In addition to the electronsfrom Dalitz decays of these mesons the decay photons

may convert to an e+eminus pair in the detector material inthe beam pipe or each layer of the VTX The PHENIXCollaboration has also published the yields of direct pho-tons in Au+Au collisions at

radicsNN

= 200 GeV [3 51]that can also be a source for conversions

In principle with these measured yields combined withsimple decay kinematics and a detailed geant3 descrip-tion of the detector material and reconstruction algo-rithm one could fully account for these photonic electroncontributions as a function of DCAT and pT Howeversystematic uncertainties on the measured yields for theπ0 η and direct photons would then dominate the uncer-tainty of the heavy flavor electron extraction Thereforewe utilize the VTX detector itself to help reject thesecontributions in a controlled manner

We require that at least the first three layers of theVTX have hits associated with the electron track Con-versions in B1 and subsequent layers are rejected by therequirement of a B0 hit leaving only conversions in B0and the beam pipe The requirement of B1 and B2 hitsenables us to impose a conversion veto cut described be-low that suppresses conversions from the beam pipe andB0

The conversion veto cut rejects tracks with anotherVTX hit within a certain window in ∆φ and ∆z aroundhits associated with a VTX-associated track Photonsthat convert to an e+eminus pair in the beam pipe will leavetwo nearby hits in the first layer (B0) andor subsequentlayers of the VTX and thus be rejected by the conversionveto cut Similarly conversions in B0 will result in twonearby hits in the second layer (B1) andor subsequentouter layers The same is true for e+eminus from a Dalitzdecay though with a larger separation due to a largeropening angle of the pair

Figure 7(a) shows distribution of chrg ∆φ of hits in B0relative to the electron track where chrg is the charge ofthe track The red (circle) histogram shows the data inMB Au+Au collisions If the track at the origin is not anelectron we have a flat distribution due to random hitsin the detector These random hits have been subtractedin Fig 7(a) The transverse momentum of the electrontrack is in the interval 1 lt pT GeVc lt 2

As mentioned above these correlated hits around elec-tron tracks are caused by the partner e+ or eminus of Dalitzdecays or photon conversions The left-right asymmetryof the distribution is caused by the fact that the part-ner eplusmn track is separated from the electron track by themagnetic field and the direction of the separation is de-termined by the charge of the electron track In the dis-tribution of chrg ∆φ the partner track is bent towardsthe positive direction

The black (triangle) histogram in Fig 7(a) shows thedistribution from Monte Carlo simulations In the simu-lation the response of the PHENIX detector to single π0sis modeled by geant3 and the resulting hits in the VTXand the central arms are then reconstructed by the samereconstruction code as the data The correlated hits inthe simulation are caused by the Dalitz decay of π0 and

[rad]φ∆ chrg-006 -004 -002 0 002 004 006

510 (data)plusmne(sim)plusmnPhotonic e

at B0φ∆ chrg

[GeVc]T

p0 05 1 15 2 25 3 35 4 45 5

]φ∆

vs pφ∆ chrgVeto residual B0 (

FIG 7 (Color Online) (a) Distribution of correlated hitsin B0 near electron tracks for 1 lt pT lt 2 GeVc The red(circle) points are from Au+Au data and the black (triangle)points are from Monte Carlo simulation The insert in (a)illustrates the electron pairs from Dalitz decays (b) The win-dow of the conversion veto cut for B0 layer (hatched) and thehit distribution near electron track in 2D space of chrg ∆φ vspT of electrons in Au+Au collisions (See the text for details)

photon conversion in the material of the beam pipe andthe VTX itself The simulation reproduces the data wellfor chrg ∆φ gt 0 There is a difference between the dataand the simulation for chrg ∆φ lt 0 This is caused by asubtle interplay between the conversions and high mul-tiplicity effects The difference disappears for peripheralcollisions Similar correlated hits are observed in B1 to

B3 layers in the data and they are also well explained bythe simulation

We define a ldquowindowrdquo of the conversion veto cutaround an electron track in each layer B0 to B3 andrequire that there is no hit other than the hit associ-ated with the electron track in the window Since a pho-tonic electron (Dalitz and conversion) tends to have acorrelated hit in the window as one can see in Fig 7this conversion veto cut rejects photonic background Alarger window size can reject photonic background moreeffectively but this can also reduce the efficiency for theheavy flavor electron signal due to random hits in thewindow The window for the conversion veto cut is acompromise in terms of the rejection factor on photonicbackgrounds and efficiency for heavy flavor electrons Weoptimized the size of the window of the conversion vetocut based on a full geant3 simulation

The red hatched area shown in Fig 7(b) shows the win-dow of the conversion veto cut in layer B0 The windowsize is asymmetric since correlated hits are mainly in thepositive side of chrg ∆φ The window size is reduced forhigher electron pT since the distribution of correlated hitsbecomes narrower for higher pT The windows for B1-B3are similarly determined based on geant3 simulation

Figure 8 shows the survival fraction of the conversionveto cut for electrons from photon conversions and Dalitzdecays as a function of electron pT from a full geant3simulation of the detector with hits run through the re-construction software The survival probability for con-versions is less than 30 at pT = 1 GeVc and decreasesfurther at higher pT The survival probability for Dalitzdecays is higher since a Dalitz decay partner is more likelyto fall outside of the window of the conversion veto cutdue to the larger opening angle Also shown in Fig 8 isthe survival fraction of electrons from heavy flavor decayswhich pass the conversion veto cut (SHF) As expectedtheir efficiency for passing the conversion veto cut is quitehigh and pT independent

The efficiencies shown in Fig 8 are calculated withoutthe Au+Au high-multiplicity that may randomly pro-vide a hit satisfying the conversion veto cut Since theseare random coincidences they are a common reductionfor all sources including the desired signal mdash heavy fla-vor electrons This common reduction factor δrandom ismeasured from the reduction of the hadron track yieldby the conversion veto cut to be 35 at pT = 1 GeVcto 25 at pT = 5 GeVc for MB Au+Au collisionsNote that when we determine the DCAT distribution ofthe various background components using a full geant3simulation we apply the same conversion veto cuts

The DCAT distributions from photonic backgroundprocesses that survive the conversion veto cut are shownin Fig 5 The means of the DCAT distributions fromDalitz decays and conversions are shifted to negativeDCAT values due to the mis-reconstruction of the mo-mentum caused by the assumption that the tracks orig-inate at the primary vertex as explained in the nextparagraph The shift is largest at the lowest pT bin and

[GeVc]eT

p0 1 2 3 4 5 6 7S

c+bγ eerarr 0π

γ eerarr η

eerarr γdirect conversions

FIG 8 (Color Online) The survival rate as a function ofelectron pT (peT ) for electrons from photon conversion (black)Dalitz decay of π0 (red) η (green) electrons from direct pho-ton (blue) and heavy flavor decay electrons (dark orange)

decreases with increasing pT

For Dalitz electrons the shift is due to the energy lossvia induced radiation (bremsstrahlung) The total radi-ation length of the VTX is approximately 13 as shownin Table I Thus a Dalitz electron coming from the pri-mary vertex loses approximately 1minus eminus013 asymp 12 of itsenergy on average when it passes through the VTX Themomentum measured by the DC is close to the one af-ter the energy loss due to the reconstruction algorithmSince the momentum determined by the DC is used whenprojecting inward from the hit in B0 to the primary ver-tex and in calculation of DCAT this results in a slightshift in the DCAT distribution This effect is fully ac-counted for in the DCAT template of Dalitz electronssince it is generated through the full geant3 and recon-struction simulation

In the case of conversions the effect is even largeras one can clearly see in Fig 5 While a photon goesstraight from the primary vertex to the beam pipe orB0 layer where it converts DCAT is calculated assum-ing that the electron track is bent by the magnetic fieldThus the DCAT distribution is shifted by the differenceof the actual straight line trajectory and the calculatedbent trajectory Again this is fully accounted for withthe full geant3 simulation The effect is verified by se-lecting conversion electrons with a reversed conversionveto cut

The background from Ke3 decays (K0S Kplusmn rarr eνπ)

contributes electrons over a broad range of DCAT dueto the long lifetime of the kaons Both contributions aredetermined using pythia and a full geant3 simulationtaking into account the exact track reconstruction elec-tron identification cuts and conversion veto cut The re-sulting DCAT distribution for these kaon decays is shownin Fig 5 As expected though the overall yield is smallthis contributes at large DCAT in the lower pT bins andis negligible at higher pT

5 Quarkonia

Quarkonia (Jψ and Υ) decay into electron pairs Dueto the short lifetime these decays contribute to electronsemanating from the primary vertex The Jψ yields inAu+Au collisions at

radicsNN

= 200 GeV have been mea-sured by the PHENIX Collaboration [52] The detailedmodeling of these contributions out to high pT is detailedin Ref [12] While these measurements include a smallfraction of B rarr Jψ decays all Jψrsquos are consideredprompt when modeling the DCAT distribution The Jψcontribution is shown in Fig 5 and is quite small andpeaked about DCAT = 0 as expected Thus the system-atic uncertainty from the quarkonium yields in Au+Aucollisions is negligible in all electron pT bins

F Normalization of electron backgroundcomponents

If the detector performance were stable we could con-vert the DCAT distributions from counts into absolutelynormalized yields Then one could straightforwardlysubtract the similarly absolutely normalized backgroundcontributions described abovemdashwith the normalizationconstrained by the previously published PHENIX yieldsfor π0 η etc However due to detector instability dur-ing the 2011 run such absolute normalization of back-ground contributions can have a large systematic uncer-tainty Thus we bootstrap the relative normalization ofthese background contributions utilizing our publishedAu+Au results [12] from data taken in 2004

The idea of the method is the following PHENIXmeasured the invariant yield of open heavy flavor decayelectrons from the 2004 dataset In this 2004 analysiswe first measured inclusive electrons (ie the sum ofbackground electrons and heavy flavor electrons) Wethen determined and subtracted the background electroncomponents from the inclusive electron yields to obtainthe heavy flavor contribution Thus the ratio of the back-ground components to the heavy flavor contribution weredetermined and published in [12] We use these ratios todetermine the normalization of background componentsin the 2011 data as described in the next paragraph

Some backgrounds have the same ratio to signal regard-less of the year the data was collected while others willdiffer due to the additional detector material added bythe VTX

The invariant yield in Au+Au collisions atradicsNN

= 200 GeV of heavy flavor electrons and back-ground electrons from Dalitz decays is a physicalobservable independent of the year the data was takenThus we can use the ratio of heavy flavorDalitz that isdetermined in the 2004 analysis in the 2011 data On theother hand the invariant yield of conversion electronsdepends on the detector material present and is thusdifferent in the 2011 data taking period with the VTXinstalled compared with the 2004 data We account forthis difference by calculating the fraction of nonphotonicelectrons in the 2011 data A detailed description of thenormalization procedure is given in Appendix VI

With this bootstrapped normalization completed thecorrectly normalized background components are shownfor all five pT bins vs DCAT in Fig 5 Note that thenormalization of mis-identified hadron and random back-ground is determined from the data as explained in sec-tions III E 1 and III E 2 respectively The electron yieldbeyond the sum of these background components is fromthe combination of charm and bottom heavy flavor elec-trons

G Unfolding

1 Introduction

With the DCAT distributions as a function of electronpT and the various background components in hand weproceed to extract the remaining charm and bottom com-ponents If one knew the shape of the parent charm andbottom hadron pT and rapidity distributions one couldcalculate in advance the DCAT shape for electrons fromeach heavy flavor via a model of the decay kinematicsSince the decay lengths of charm and bottom hadrons aresignificantly different they will yield different DCAT dis-tributions In this case one could simultaneously fit theDCAT distribution for each pT bin with all backgroundcomponents fixed across pT bins and extract the one freeparameter the ratio of charm to bottom contributionsHowever the pT distribution of charm hadrons is knownto be significantly modified in Au+Au collisions mdash seefor example Ref [14] For bottom hadrons this is alsolikely to be the case Therefore one does not know a pri-ori the heavy flavor DCAT distribution since it dependson the parent pT distribution

Since the DCAT distributions for all electron pT re-sult from the same parent charm and bottom hadron pTspectrum one can perform a simultaneous fit to all theelectron pT and DCAT data in order to find the mostlikely heavy flavor parent hadron pT distributions Theestimation of a set of most likely model parameters usinga simultaneous fit to data is often referred to as unfold-

ing Statistical inference techniques are often employedto solve such problems see for example the extraction ofreconstructed jet cross sections [53]

The DCAT distributions are in counts and have notbeen corrected for the pT -dependent reconstruction effi-ciency in Au+Au collisions and therefore hold no yieldinformation To further constrain the extraction of thecharm and bottom components we include the totalheavy flavor electron invariant yield as measured byPHENIX [12] in Au+Au collisions at

radicsNN

= 200 GeVThis measurement is more accurate than currently avail-able with the 2011 data set where the VTX acceptancechanges with time

The unfolding procedure using a particular samplingmethod (described in Section III G 2) chooses a set oftrial charm and bottom parent hadron yields The trialset of yields is multiplied by a decay matrix (describedin Section III G 4) which encodes the probability for ahadron in a given pT interval to decay to an electron atmidrapidity as a function of electron pT and DCAT Theresulting distributions of electron pT and DCAT are com-pared with the measured data using a likelihood func-tion (described in Section III G 3) In order to dampendiscontinuities and oscillatory behavior a penalty uponthe likelihood (described in Section III G 5) is added toenforce smoothness in the resulting hadron pT distribu-tions

2 Unfolding method

Here we apply Bayesian inference techniques to theunfolding problem A detailed pedagogical introductionto these techniques is given in Ref [54] Techniques in-volving maximum likelihood estimation or maximum aposteriori estimation often used in frequentist statisticscan at best compute only a point estimate and confidenceinterval associated with individual model parameters Incontrast Bayesian unfolding techniques have the impor-tant advantage of providing a joint probability densityover the full set of model parameters In this analysisthe vector of model parameters θ is the vector of parentcharm and bottom hadron yields binned in pT

Given a vector of measured data x and our vector ofmodel parameters θ we use Bayesrsquo theorem

p(θ|x) =P (x|θ)π(θ)

P (x) (2)

to compute the posterior probability density p(θ|x)from the likelihood P (x|θ) and prior information π(θ)The function P (x|θ) quantifies the likelihood of observ-ing the data given a vector of model parameters Infrequentist statistics the P (x|θ) is often used alone todetermine the best set of model parameters Bayesianinference on the other hand allows for the inclusion ofthe analyzerrsquos a priori knowledge about the model pa-rameters as encoded in π(θ) The implementation ofπ(θ) used in this analysis is discussed in Sec III G 5 The

denominator P (x) serves as an overall normalization ofthe combined likelihood P (x|θ)π(θ) such that p(θ|x) canbe interpreted as a probability density In this analysisp(θ|x) gives the probability for a set of charm and bottomhadron yields

θ = (θcθb) (3)

given the values of the measured electron data pointsx Since we are only interested in the parameters whichmaximize p(θ|x) we can dispense with the calculation ofP (x) as it serves only as an overall normalization

Here θ comprises 17 bins of both charm and bottomhadron pT yielding a 34-dimensional space which mustbe sampled from in order to evaluate p(θ|x) To ac-complish this we employ a Markov Chain Monte Carlo(MCMC) algorithm to draw samples of θ in proportionto p(θ|x) This makes accurate sampling of multidimen-sional distributions far more efficient than uniform sam-pling In implementation it is in fact the right handside of Eq 2 that is sampled The MCMC variant usedhere is an affine-invariant ensemble sampler described inRef [55] and implemented as described in Ref [56] Itis well suited to distributions that are highly anisotropicsuch as spectra which often vary over many orders ofmagnitude

3 Modeling the likelihood function

This analysis is based on 21 data points of total heavyflavor electron invariant yield Ydata in the range 10ndash90 GeVc from the 2004 data set [12] and five electronDCAT distributions Ddata

j where j indexes each electronpT interval within the range 15ndash50 GeVc from the 2011data set Therefore

x = (YdataDdata0 Ddata

1 Ddata2 Ddata

3 Ddata4 ) (4)

in Eq 2Our ultimate goal is to accurately approximate the

posterior distribution over the parent hadron invariantyields θ by sampling from it For each trial set of hadronyields the prediction in electron pT Y(θ) and DCAT Dj(θ) is calculated by

Y(θ) = M(Y)θc + M(Y)θb (5)

Dj(θ) = M(D)j θc + M

(D)j θb (6)

where M(Y) and M(D)j are decay matrices discussed in

Section III G 4 We then evaluate the likelihood betweenthe prediction and each measurement in the data setsYdata and Ddata

j 4j=0 As is customary the logarithm ofthe likelihood function is used in practice The combined(log) likelihood for the data is explicitly

lnP (x|θ) = lnP (Ydata|Y(θ)) +

4sumj=0

lnP (Ddataj |Dj(θ)) (7)

The Ydata dataset is assigned statistical uncertaintiesthat are assumed to be normally distributed and uncorre-lated Thus the likelihood lnP (Ydata|Y(θ)) is modeledas a multivariate Gaussian with diagonal covariance Thesystematic uncertainties on the Ydata dataset and theireffect on the unfolding result are discussed in Sec III H

The DCAT data sets in contrast each comprise a his-togrammed distribution of integer-valued entries and thelikelihood lnP (Ddata

j |Dj(θ)) is thus more appropriatelydescribed by a multivariate Poisson distribution How-ever the likelihood calculation for the DCAT data setsrequires three additional considerations First there aresignificant background contributions from a variety ofsources as discussed in Section III E Secondly detec-tor acceptance and efficiency effects are not explicitly ac-counted for in the DCAT distributions This implies thatthe total measured yield of signal electrons in each DCAT

histogram is below what was actually produced and con-sequently the measured Ddata

j distributions do not matchthe predictions in normalization Lastly because of thehigh number of counts in the region near DCAT = 0 thisregion will dominate the likelihood and be very sensitiveto systematic uncertainties in the DCAT shape thereeven though the main source of discrimination betweencharm and bottom electrons is at larger DCAT

To deal with the first issue the relatively normalizedbackground described in Sec III E is added to each pre-diction of the DCAT distribution for summed electronsfrom charm and bottom hadrons so that the shape andrelative normalization of the background component ofthe measurement is accounted for

To handle the second each prediction plus the back-ground is scaled to exactly match the normalization ofDdataj In this way only the shape of the prediction is a

constraining factorTo deal with the third a 5 uncertainty is added in

quadrature to the statistical uncertainty when the num-ber of counts in a given DCAT bin is greater than areasonable threshold (which we set at 100 counts) Thisaccounts for the systematic uncertainty in the detailedDCAT shape by effectively de-weighting the importanceof the region DCAT asymp0 while maintaining the overallelectron yield normalization (as opposed to removing thedata entirely) This additional uncertainty also necessi-tates changing the modeling of lnP (Ddata

j |Dj(θ)) from aPoisson to a Gaussian distribution We have checked thatvarying both the additional uncertainty and the thresh-old at which it is added has little effect on the results

4 Decay model and matrix normalization

The pythia-6 [57] generator with heavy flavor pro-duction process included via the parameter MSEL=4(5)is used to generate parent charm (bottom) hadrons andtheir decays to electrons Electrons within |η| lt 035decayed from the ground state charm hadrons (Dplusmn D0Ds and Λc) or bottom hadrons (Bplusmn B0 Bs and Λb)

are used to create a decay matrix between hadron pT (phT representing charm hadron pT pcT or bottom hadron pT pbT ) and electron pT (peT ) and DCAT Here we treat thefeed down decay B rarr D rarr e as a bottom hadron decayand exclude it from charm hadron decays

0 5 10 15 20pc

T [GeVc]

0 5 10 15 20pc

T [GeVc]

eplusmn

15ltpeT [GeVc]lt20(b)

FIG 9 (Color Online) (a) The decay matrix M(Y) encod-ing the probability for charmed hadrons decaying to electronswithin |η| lt 035 as a function of both electron pT (peT ) and

charm hadron pT (pcT ) (b) An example decay matrix M(D)j

encoding the probability for charmed hadrons decaying toelectrons within |η| lt 035 and 15 lt peT [ GeVc] lt 20 as afunction of both electron DCAT and charm hadron pT (pcT )In both cases the color intensity represents the probability ofdecay in the given bin

The probability for a charm or bottom hadron at agiven phT to decay to an electron at a given peT and DCAT

is encoded in the multidimensional matrices M(Y) andM

(D)j An example decay matrix for charmed hadrons

is shown in Fig 9 Note that the 17 bins in pcT corre-spond to the same bins shown along the x-axis in Fig 15and that the binning in peT and DCAT seen in Fig 9 isthe same as that shown in Fig 12 and Fig 13 respec-tively Furthermore note that the marginal probabili-ties do not integrate to unity in these matrices Thisis because the decay probabilities are normalized to thenumber of hadrons that are generated at all momenta inall directions and over all decay channels The probabil-ity distribution for a hadron integrated over all rapiditiesand decay channels within a given phT range to decay toan electron at |y| lt 035 with a given peT (integrated overDCAT ) is shown in Fig 10 for an example set of phT bins

P(crarr

(a) 05 lt pcT lt 10

25 lt pcT lt 30

40 lt pcT lt 45

70 lt pcT lt 80

120 lt pcT lt 150

1 2 3 4 5 6 7 8 9pe

T [GeVc]

P(brarr

(b) 05 lt pbT lt 10

25 lt pbT lt 30

40 lt pbT lt 45

70 lt pbT lt 80

120 lt pbT lt 150

FIG 10 (Color Online) The probability for (a) charm and(b) bottom hadrons in a given range of hadron pT (pcT andpbT for charm and bottom hadrons respectively) to decay toelectrons at midrapidity as a function of electron pT (peT )

In principle this decay matrix introduces a model de-pendence to the result In the creation of the decay ma-trix we are integrating over all hadron rapidities as wellas combining a number of hadron species and their de-cay kinematics to electrons This involves two assump-tions The first is that the rapidity distributions of the

hadrons are unmodified BRAHMS found that the pionand proton RAA did not depend strongly on rapidity upto y asymp 3 [58] justifying the assumption This assumptionwill further lead us to quote charm and bottom hadronyields as a function of pT integrated over all rapidity Thesecond assumption is that all ground state charm hadronsexperience the same modification as a function of pcT While different than the charm suppression all bottomhadrons are assumed to experience the same modifica-tion

An enhancement in the baryon to meson productionratios in both nonstrange and strange hadrons has beenmeasured at RHIC [59] which may carry over into theheavy quark sector invalidating the second assumptionWhile there are some models [60] that attempt to in-corporate this anomalous enhancement into the charmhadrons to help explain the measured heavy flavor elec-tron RAA there are few measurements to help con-strain this proposed enhancement Following Ref [61]we have tested the effect of this assumption by apply-ing the observed baryonmeson enhancement to both theΛcD and ΛbB ratios As in Ref [61] we assume thatthe modification asymptotically approaches 1 for hadronpT gt 8 GeVc We find that including the enhance-ment gives a lower charm hadron yield at high-pT and alarger bottom hadron yield at high-pT but the modifi-cations are within the systematic uncertainties discussedin Sec III H and shown in Fig 15 We also find a largerbottom electron fraction which is again within the sys-tematic uncertainties shown in Fig 17 While we havenot used other particle generators to create alternate de-cay matrices we find that the D0 and Dplusmn meson pT andrapidity distributions from pythia are similar to thosegiven by Fixed Order + Next-to-Leading Log (fonll)calculations [33] We have not included any systematicuncertainty due to this model dependence in the finalresult

5 Regularizationprior

To penalize discontinuities in the unfolded distribu-tions of charm and bottom hadrons we include a regu-larization term to the right hand side of equation 7 Inthis analysis we included a squared-exponential function

lnπ(θ) = minusα2(|LRc|2 + |LRb|2

where Rc and Rb are ratios of the charm and bottomcomponents of the parent hadron pT vector to the corre-sponding 17 components of the prior θprior and L is a17-by-17 second-order finite-difference matrix of the form

minus1 1

1 minus2 1

1 minus1

Thus the addition of this term encodes the assumptionthat departures from θprior should be smooth by penaliz-ing total curvature as measured by the second derivative

Here α is a regularization parameter set to α = 10 inthis analysis We determine α by repeating the unfold-ing procedure scanning over α and choosing the valueof α which maximizes the resulting sum of Eq 7 andminus(|LRc|2 + |LRb|2

)(Eq 8 dropping α2) In this way

we can directly compare log likelihood values for unfold-ing results with different α values We include variationson α in the systematic uncertainty as described in Sec-tion III H

We set θprior to pythia charm and bottom hadronpT distributions scaled by a modified blast wave calcu-lation [29] which asymptotically approaches RAA valuesof 02(03) for D(B) mesons at high-pT We have testedthe sensitivity of the result to θprior by alternatively usingunmodified pythia charm and bottom hadron pT distri-butions We find that the result is sensitive to the choiceof θprior dominantly in the lowest charm hadron pT binswhere there is minimal constraint from the data We haveincluded this sensitivity in the systematic uncertainty asdiscussed in Section III H

6 Parent charm and bottom hadron yield and theirstatistical uncertainty

The outcome of the sampling process is a distributionof θ vectors which is 34-dimensional in this case In prin-ciple the distribution of θ vectors contains the full proba-bility including correlations between the different param-eters The 2-D correlations are shown in Fig 11 Whileit is difficult to distinguish fine details in the 34times34-dimensional grid of correlation plots we can see a fewgross features A circular contour in the 2-D panels rep-resents no correlation between the corresponding hadronpT bins An oval shape with a positive slope indicatesa positive correlation between corresponding bins andan oval shape with a negative slope represents an anti-correlation between corresponding bins A large positivecorrelation is seen for adjacent bins for high-pT charmhadrons and low-pT bottom hadrons This is a conse-quence of the regularization which requires a smooth pTdistribution and is stronger at the higher and lower pTregions where there is less constraint from the data We

also see that while there is little correlation between themajority of nonadjacent pT bins there does seem to be aregion of negative correlation between the mid to high pTcharm hadrons and the low to mid pT bottom hadronsCharm and bottom hadrons in these regions contributedecay electrons in the same pT region and appear tocompensate for each other to some extent An exam-ple of this is shown between 35 lt pcT GeVc lt 40 and25 lt pbT GeVc lt 30 in Fig 11(b)-(d)

To summarize p(θ|x) we take the mean of themarginalized posterior distributions (the diagonal plotsin Fig 11) for each hadron pT bin as the most likelyvalues and the 16th and 84th quantiles to represent theplusmn1σ uncertainty in those values due to the statisticaluncertainty in the data modified by the regularizationconstraint

7 Re-folded comparisons to data

The vector of most likely hadron yields with uncer-tainties can be multiplied by the decay matrix to checkthe consistency of the result with the measured data(here referred to as re-folding) Figure 12 shows the mea-sured heavy flavor electron invariant yield in Au+Au col-lisions [12] compared with the re-folded electron spectrafrom charm and bottom hadrons We find good agree-ment between the measured data and the electron spec-trum from the re-folded charm and bottom hadron yieldsFigure 13 shows the comparison in electron DCAT spacefor each bin in electron pT Shown in each panel is themeasured DCAT distribution for electrons the sum ofthe background contributions discussed in Section III Ethe DCAT distribution of electrons from charm hadrondecays and the DCAT distribution of electrons from bot-tom hadron decays Note that the sum of the backgroundcontributions is fixed in the unfolding procedure andonly the relative contribution of charm and bottom elec-trons within |DCAT | lt 01 cm as well as their DCAT

shape vary For convenience the region of the DCAT

distribution considered in the unfolding procedure is alsoshown as discussed in Section III D 6 The sum of thebackground contributions charm and bottom electronsis shown for a direct comparison with the data

The summed log likelihood values for each of theDCAT distributions and the electron invariant yield aregiven in Table II To aid in the interpretation of the like-lihood values we use a Monte-Carlo method to calcu-late the expected likelihood from statistical fluctuationsaround the re-folded result We draw samples from there-folded result based on the data statistics and calcu-late the distribution of resulting likelihood values Thenumber of standard deviations from the expected valueis also shown in Table II We find that the log likelihoodvalues are large compared to expectations in the heavyflavor electron invariant yield as well as the lowest twoDCAT pT bins We note that the likelihood values donot incorporate the systematic uncertainties on the data

0003 0007yield

25ltpbT lt30

(d)002 003yield

35ltpcT lt40

002 00335ltpc

T lt40

pb Tlt

30 (c)

pcT pb

FIG 11 (Color Online) The joint probability distributions for the vector of hadron yields θ showing the 2-D correlationsbetween parameters The diagonal plots show the marginalized probability distributions for each hadron pT bin (ie the1-dimensional projection over all other parameters) Along the Y-axis the plots are organized from top to bottom as the 17charm hadron pT (pcT ) bins from low to high pcT followed by the 17 bottom hadron pT (pbT ) bins from low to high pbT TheX-axis is organized similarly from left to right The pcT and pbT binning follows that shown in Fig 15 The region of green plots(top left quadrant) shows the charm hadron yields and the correlations between charm hadron yields The region of blue plots(bottom right quadrant) shows the bottom hadron yields and correlations between bottom hadron yields The region of orangeplots (bottom left quadrant) shows the correlations between charm and bottom hadron yields Sub-panels (b)-(d) show a setof example distributions (b) The 1-D probability distribution of charm hadron yield in 35 lt pcT GeVc lt 40 (d) The 1-Dprobability distribution of bottom hadron yield in 25 lt pbT GeVc lt 30 (c) The correlation between (b) and (d)

which are handled separately as described in Sec III HIn particular the statistical uncertainties on the heavy

flavor electron invariant yield are much smaller than thesystematics at low-pT making the likelihood value not

surprising We find reasonable agreement within uncer-tainties between the remaining DCAT pT bins

1 2 3 4 5 6 7 8 9

)minus2]

|y|lt035Au+Au MB

radicsNN =200 GeV

PHENIX Run 4 + Run 11

(a) crarre+brarre

crarre

brarre

Phys Rev C 84 044905 (2011)

1 2 3 4 5 6 7 8 9pe

T [GeVc]

000510152025

ld (b)

FIG 12 (Color Online) The heavy flavor electron invariantyield as a function of pT from measured data [12] compared toelectrons from the re-folded charm and bottom hadron yieldsThe boxes represent the point-to-point correlated uncertain-ties on the measured heavy flavor electron invariant yieldwhile the error bars on the points represent the point-to-point uncorrelated uncertainties The label ldquoPHENIX Run4 + Run 11rdquo on this and all subsequent plots indicates thatthe unfolding result uses the heavy flavor electron invariantyield as a function of pT from data taken in 2004 (Run 4)combined with DCAT measurements from data taken in 2011(Run 11)

H Systematic uncertainties

When performing the unfolding procedure only thestatistical uncertainties on the electron DCAT and pTspectra are included In this section we describe how weconsider the systematic uncertainties on both the mea-sured data and the unfolding procedure We take thefollowing uncertainties into account as uncorrelated un-certainties

TABLE II The log likelihood values (LL) summed over eachDCAT distribution and for the comparison to the heavy flavorelectron invariant yield Also quoted is the number of datapoints (Np) and the deviation from the log likelihood valueexpected from statistical fluctuations (∆LL) as discussed inthe text for each comparison

Data set Np LL ∆LL [σ]

e DCAT 15 lt peT lt 20 50 -1955 -38

e DCAT 20 lt peT lt 25 50 -1565 -29

e DCAT 25 lt peT lt 30 50 -1158 -06

e DCAT 30 lt peT lt 40 50 -1041 -18

e DCAT 40 lt peT lt 50 50 -532 00

e Inv Yield 10 lt peT lt 90 21 -459 -35

Total Sum 271 -6738

1 Systematic uncertainty in the heavy flavor electronpT invariant yield

2 Uncertainty in the high-multiplicity background

3 Uncertainty in the fraction of nonphotonic elec-trons (FNP)

4 Uncertainty in Ke3 normalization

5 Regularization hyperparameter α

6 Uncertainty in the form of θprior

The uncertainty in FNP (See Sec VI A) and Ke3 arepropagated to the unfolded hadron yields by varying eachindependently byplusmn1σ and performing the unfolding pro-cedure with the modified background template The dif-ference between the resulting hadron yields and the cen-tral values is taken as the systematic uncertainty Thesame procedure is used to determine the uncertainty inthe result due to the regularization parameter which isvaried by +060

minus025 based on where the summed likelihoodfrom both the data and regularization drops by 1 fromthe maximum value

The uncertainty in the high-multiplicity backgroundincludes two components The first is the uncertaintyon the normalization of the high-multiplicity backgroundDCAT distribution as determined in Sec III E 2 andshown in Fig 5 This is propagated to the unfoldedhadron yields by varying the normalization by plusmn1σ andperforming the unfolding procedure with the modifiedbackground template as with the FNP and Ke3 uncer-tainties The second component addresses the small ex-cess in the embedded primary electron distribution ob-served in Fig 6 and not accounted for by using the DCAT

distribution for large DCAL We parametrize the excesswhich is more than two orders of magnitude below thepeak and apply it to the background components re-performing the unfolding procedure to find its effect onthe hadron yield Both effects combined are small rela-tive to the dominant uncertainties

015 010 005 000 005 010 015

15-20 GeVcb(b+c)=0115

Au+Au MBradicsNN =200 GeV

PHENIXRun 4 + Run 11

015 010 005 000 005 010 015DCAT [cm]

0510152025

015 010 005 000 005 010 015

20-25 GeVcb(b+c)=0264

015 010 005 000 005 010 015DCAT [cm]

0510152025

015 010 005 000 005 010 015

25-30 GeVcb(b+c)=0427

015 010 005 000 005 010 015DCAT [cm]

0510152025

015 010 005 000 005 010 015

30-40 GeVcb(b+c)=0520

015 010 005 000 005 010 015DCAT [cm]

0510152025

015 010 005 000 005 010 015

40-50 GeVcb(b+c)=0488

015 010 005 000 005 010 015DCAT [cm]

0510152025

DataBackground + charm + bottomTotal BackgroundUnfolded bottomUnfolded charm

FIG 13 (Color Online) The DCAT distribution for measured electrons compared to the decomposed DCAT distributionsfor background components electrons from charm decays and electrons from bottom decays The sum of the backgroundcomponents electrons from charm and bottom decays is shown as the red (upper) curve for direct comparison to the data Thegray band indicates the region in DCAT considered in the unfolding procedure Also quoted in the figure is the bottom electronfraction for |DCAT | lt 01 cm integrated over the given pT range The legend follows the same order from top to bottom aspanel (b) at DCAT = minus01 cm

Incorporating the pT correlated systematic uncertaintyon the heavy flavor electron invariant yield is more dif-

ficult Ideally one would include a full covariance ma-

trix encoding the pT correlations into the unfolding pro-cedure In practice the methodology employed in [12]does not provide a convenient description of the pT cor-relations needed to shape the covariance matrix Insteadwe take a conservative approach by considering the caseswhich we believe represent the maximum pT correlationsWe modify the heavy flavor electron invariant yield by ei-ther tilting or kinking the spectrum about a given pointTilting simply pivots the spectra about the given pointso that for instance the first point goes up by a fractionof the systematic uncertainty while the last point goesdown by the same fraction of its systematic uncertaintywith a linear interpolation in between Kinking simplyfolds the spectra about the given point so that that thespectrum is deformed in the form of a V We implementthe following modifications and re-perform the unfoldingprocedure

1 Tilt the spectra about pT = 18 GeVc by plusmn1σ ofthe systematic uncertainty

3 Kink the spectra about pT = 18 GeVc by plusmn1σ ofthe systematic uncertainty

The pT points about which the spectra were modifiedwere motivated by the points in pT at which analysismethods and details changed as discussed in [12] Wethen take the RMS of the resulting deviations on thehadron yield from the central value as the propagatedsystematic uncertainty due to the systematic uncertaintyon the heavy flavor electron invariant yield

The effect of our choice of θprior on the charm andbottom hadron yields is taken into account by varyingθprior as discussed in Section III G 5 The differencesbetween each case and the central value are added inquadrature to account for the bias introduced by θprior

The uncertainties on the unfolded hadron yields due tothe six components described above and the uncertaintydetermined from the posterior probability distributionsare added in quadrature to give the uncertainty shown inFig 15

Due to the correlations between charm and bottomyields the relative contributions from the different un-certainties depend on the variable being plotted To givesome intuition for this we have plotted the relative con-tributions from the different uncertainties to the fractionof electrons from bottom hadron decays as a function ofpT (discussed in Sec IV A) in Fig 14 One can see thatthe dominant uncertainties come from the statistical un-certainty on the DCAT and heavy flavor electron invari-ant yield the systematic uncertainty on the heavy flavorelectron invariant yield and FNP We remind the reader

1 2 3 4 5 6 7 8 9

04020002040608 (a)Unfold Uncertainty

Spectra Systematic Uncertainty

1 2 3 4 5 6 7 8 9

04020002040608

inty (b)High-mult Bkg Uncertainty

FNP UncertaintyKe3 Uncertainty

1 2 3 4 5 6 7 8 9pe

T [GeVc]

04020002040608 (c)α Uncertainty

θprior Uncertainty

FIG 14 (Color Online) The relative contributions from thedifferent components to the uncertainty on the fraction ofelectrons from bottom hadron decays as a function of pT The shaded red band in each panel is the total uncertainty

that for pT gt 5 GeVc we no longer have DCAT infor-mation to directly constrain the unfolding and all infor-mation comes dominantly from the heavy flavor electroninvariant yield leading to the growth in the uncertaintyband in this region

IV RESULTS

The final result of the unfolding procedure applied si-multaneously to the heavy flavor electron invariant yieldvs pT (shown in Fig 12) and the five electron DCAT

distributions (shown in Fig 13) is the invariant yield ofcharm and bottom hadrons integrated over all rapidityas a function of pT As a reminder the hadron yieldsare integrated over all rapidity by assuming the rapid-ity distribution within pythia is accurate and that it isunmodified in Au+Au as detailed in Sec III G 4 Theunfolded results for MB (0ndash96) Au+Au collisions atradicsNN

=200 GeV are shown in Fig 15 The central pointrepresents the most likely value and the shaded bandrepresents the 1σ limits on the combination of the un-

certainty in the unfolding procedure and the systematicuncertainties on the data as described in Sec III H Theuncertainty band represents point-to-point correlated un-certainties typically termed Type B in PHENIX publi-cations There are no point-to-point uncorrelated (TypeA) or global scale uncertainties (Type C) from this pro-cedure

The uncertainties on the hadron invariant yields shownin Fig 15 grow rapidly for charm and bottom hadronswith pT gt 6 GeVc This is due to the lack of DCAT in-formation for peT gt 5 GeVc Above peT gt 5 GeVc theunfolding is constrained by the heavy flavor electron in-variant yield only This provides an important constrainton the shape of the hadron pT distributions but theDCAT distributions provide the dominant source of dis-criminating power between the charm and bottom How-ever due to the decay kinematics even high pT hadronscontribute electrons in the range 15 lt peT [ GeVc] lt50 We find that charm(bottom) hadrons in the range7 lt phT [ GeVc] lt 20 contribute 182(03) of the to-tal electron yield in the region 15 lt peT [ GeVc] lt 50This explains the larger uncertainties in the bottomhadron yield compared to the charm hadron yield at highphT

The yield of D0 mesons over |y| lt 1 as a function ofpT has been previously published in Au+Au collisionsatradicsNN

=200 GeV by STAR [14] In order to com-pare our unfolded charm hadron results over all rapidityto the STAR measurement we use pythia to calculatethe fraction of D0 mesons within |y| lt 1 compared tocharm hadrons over all rapidity Since the measurementby STAR is over a narrower centrality region (0ndash80vs 0-96) we scale the STAR result by the ratio of theNcoll values This comparison is shown in Fig 16 Foradded clarity we have fit the STAR measurement with aLevy function modified by a blast wave calculation givenby

f(pT ) = p0

(1minus (1minus p1)pT

)1(1minusp1)

times(

13radic

2πp24G(pT p3 p4) +p5

1 + eminuspT+3

where G(pT p3 p4) is a standard Gaussian function andpi are the parameters of the fit The ratio of the data tothe fit is shown in the bottom panel of Fig 16 We findthat within uncertainties the unfolded D0 yield agreeswith that measured by STAR over the complementarypT range The unfolded yield hints at a different trendthan the STAR data for pT gt 5 GeVc However wenote that the 〈pT 〉 of charm(bottom) hadrons which con-tribute electrons in the range 40 lt pT [ GeVc] lt 50is 72(64) GeVc This means that the yields of charmand bottom hadrons have minimal constraint from theDCAT measurements in the high-pT regions which isrepresented by an increase in the uncertainties

A The bottom electron fraction

The fraction of heavy flavor electrons from bottomhadrons ( brarre

brarre+crarre ) is computed by re-folding the charmand bottom hadron yields shown in Fig 15 to get the in-variant yield of electrons from charm and bottom decaysat midrapidity (|y| lt 035) Here the electrons from bot-tom hadron decays include the cascade decay brarr crarr eThe resulting bottom electron fraction is shown as a func-tion of pT in Fig 17 The central values integrated overthe pT range of each DCAT distribution are also quotedin Fig 13 As in the hadron yields the band representsthe 1σ limits of the point-to-point correlated (Type B)uncertainties

Also shown in Fig 17 is the bottom electron fractionpredictions from fonll [33] for p+p collisions at

radicsNN

=200 GeV We find a bottom electron fraction whichis encompassed by the fonll calculation uncertaintiesThe shape of the resulting bottom electron fraction showsa steeper rise in the region 20 lt pT [GeVc] lt 40 with apossible peak in the distribution compared to the centralfonll calculation

The fraction of electrons from bottom decays hasbeen previously measured in p+p collisions at

radicsNN

=200 GeV by both PHENIX [34] and STAR [35]These measurements are made through electron-hadronor electron-D meson correlations These are very differ-ent analyses than the one presented here and have theirown model dependencies In Fig 18 we compare thebottom electron fraction between our unfolded Au+Auresult and the electron-hadron correlation measurementsin p+p For pT gt 4 GeVc we find agreement betweenAu+Au and p+p within the large uncertainties on bothmeasurements This implies that electrons from bottomhadron decays are similarly suppressed to those fromcharm For reference included in Fig 18 is the centralfonll calculation which within the large uncertaintiesis consistent with the p+p measurements

With the additional constraints on the bottom elec-tron fraction in p+p from the correlation measurementsand the measured nuclear modification of heavy flavorelectrons we can calculate the nuclear modification ofelectrons from charm and bottom hadron decays sepa-rately The nuclear modifications RcrarreAA and RbrarreAA forcharm and bottom hadron decays respectively are calcu-lated using

RcrarreAA = (1minusFAuAu)(1minusFpp) RHF

AA (11)

RbrarreAA = FAuAu

FppRHFAA (12)

where FAuAu and Fpp are the fractions of heavy flavorelectrons from bottom hadron decays in Au+Au and p+prespectively and RHF

AA is the nuclear modification of heavyflavor electrons (combined charm and bottom) Ratherthan combining all measurements for the bottom electronfraction in p+p which introduces a further extraction un-certainty we have chosen to calculate RcrarreAA and RbrarreAA us-

0 5 10 15pc

T [GeVc]

(12πp

c)minus

Au+Au MB radic

sNN =200 GeVPHENIX Run 4 + Run 11

0 5 10 15pb

T [GeVc]

Unfolded charmUnfolded bottom

FIG 15 (Color Online) Unfolded (a) charm and (b) bottom hadron invariant yield as a function of pT integrated over allrapidities as constrained by electron yield vs DCAT in 5 peT bins and previously published heavy flavor electron invariant yieldvs peT [12]

ing only the six STAR electron-hadron Fpp values Whenperforming the calculation we determine the full proba-bility distributions assuming Gaussian uncertainties onFAuAu Fpp and RHF

AA As when determining the charmand bottom hadron yields we take the median of the dis-tribution as the central value and the 16 and 84 ofthe distribution as the lower and upper 1σ uncertaintiesThe resulting values are shown in Fig 19(a) We findthat the electrons from bottom hadron decays are lesssuppressed than electrons from charm hadron decays for3 lt pT GeVc lt 4 To further clarify this statement wecalculate the ratio of RbrarreAA RcrarreAA shown in Fig 19(b)In this ratio the uncertainty on RHF

AA cancels Here againwe calculate the full probability distributions and use thesame procedure as above to determine the central valuesand uncertainties We find that the probability distri-butions for RbrarreAA RcrarreAA are highly nonGaussian whichleads to the large asymmetric uncertainty band shownin Fig 19(b) It is clear from the ratio that b rarr e isless suppressed than c rarr e at the 1σ level up to pT sim 4GeVc

V DISCUSSION

There are a number of theoretical calculations in theliterature for the interaction of charm and bottom quarkswith the QGP Many of these models have predictions for

the nuclear modification factor RAA for electrons fromcharm decays and separately RAA for electrons frombottom decays For consistency we have assumed thefonll [33] yields for electrons from charm (bottom) de-cays calculated for p+p at

radicsNN

=200 GeV and thenscaled them by the heavy-ion model results for the RAAof electrons from charm (bottom)

Figure 20(a) compares the bottom electron fractionfrom one class of calculations modeling only energy lossof these heavy quarks in medium In an early pQCD cal-culation by Djordjevic Gyulassy Vogt and Wicks [62]the authors apply the DGLV theory of radiative energyloss They find that even for extreme opacities with gluonrapidity densities up to 3500 the bottom quark decayelectrons dominate at high-pT and that limits the singleelectron RAA to the range 05ndash06 for pT gt 5 GeVcAlthough this result is known to be higher than thePHENIX measured heavy flavor electron RAA [12] weshow the b rarr e(b rarr e + c rarr e) predictions for gluonrapidity densities of 1000 and 3500 in Fig 20(a) How-ever we do note that the calculations are for 0ndash10central collisions compared to the MB data althoughthe calculations span a factor of 35 range in the gluondensity We find that the calculations for both gluon ra-pidity densities are in good agreement with our resultsfor pT lt 4 GeVc but are slightly above and outsidethe uncertainty band on the unfolded result at higherpT More recent calculations in the same framework but

0 1 2 3 4 5 6 7

100(12πp

c)minus

D0 |y|lt1Au+Au at

radicsNN =200 GeV

(a) PHENIX Run 4 + Run 11 MBSTAR 0-80 times 2578

Levy fit times modified blast wave

0 1 2 3 4 5 6 7pT [GeVc]

000510152025

FIG 16 (Color Online) The invariant yield of D0 mesonsas a function of pT for |y| lt 1 inferred from the unfoldedyield of charm hadrons integrated over all rapidity comparedto measurements from STAR [14] See the text for detailson the calculation of the D0 yield inferred from the unfoldedresult To match the centrality intervals the STAR result hasbeen scaled by the ratio of Ncoll values The bottom panelshows the ratio of the data to a fit of the STAR D0 yield

with the inclusion of collisional energy loss [31] result ina heavy flavor electron high-pT RAA closer to 03 and inreasonable agreement with previous PHENIX publishedresults [12] This updated prediction for the bottom elec-tron fraction also shown in Fig 20 gives a similar valueto their previous result but is only published for pT gt 5GeVc

Figure 20(b) compares the bottom electron fractionfrom a calculation using a T-matrix approach by vanHees Mannarelli Greco and Rapp [63] The authorsprovided us with different results for 0ndash10 centralAu+Au collisions depending on the coupling of theheavy-quark to the medium The coupling is encapsu-lated in the diffusion parameter D where smaller valuesyield a stronger coupling Shown in Fig 20(b) are threeresults corresponding to three values of the parameterD(2πT ) = 4 6 30 The largest D value correspond-ing to the weakest coupling yields almost no deviation

1 2 3 4 5 6 7 8 9pe

T [GeVc]

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLUnfold Result

FIG 17 (Color Online) The fraction of heavy flavor electronsfrom bottom hadron decays as a function of pT from this workand from fonll p+p calculations [33]

1 2 3 4 5 6 7 8 9pe

T [GeVc]

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLUnfold ResultSTAR e-h correlation in p+p

STAR e-D0 correlation in p+p

PHENIX e-h correlation in p+p

FIG 18 (Color Online) bottom electron fraction as a func-tion of pT compared to measurements in p+p collisions at

radics

=200 GeV from PHENIX [34] and STAR [35] Also shown arethe central values for fonll [33] for p+p collisions at

radicsNN

=200 GeV

from the p+p reference fonll result and the successivelystronger coupling pushes the bottom fraction contribu-tion higher and higher We find that the calculationswith D(2πT ) = 4 6 are in good agreement with our re-sult for pT lt 4 GeVc but begin to diverge where thecalculation stops at 5 GeVc

Figure 20(c) compares the bottom electron fractionfrom another class of calculations which employ a combi-nation of Langevin or transport type modeling of heavy-quarks in the bulk QGP with energy loss mechanismsthat dominate at higher pT In Ref [64] Alberico et alemploy a Langevin calculation where a good match tothe PHENIX heavy flavor electrons is found It is no-

(a) crarre

brarre

(c+b)rarrePhys Rev C 84 044905 (2011)

1 2 3 4 5 6 7 8 9pe

T [GeVc]00

Rbrarr

|y|lt035Au+Au MB

radicsNN =200 GeV

Au+Au from Unfoldp+p from e-h correlations

PhysRevLett 105 (2010)

FIG 19 (Color Online) (a) The RAA for c rarr e b rarr e andcombined heavy flavor [12] as a function of peT The crarr e andbrarr e RAA is calculated using Eq 11-12 where FAuAu uses theunfolded result determined in this work and Fpp determinedfrom STAR eminush correlations [35] (b) The ratio RbrarreAA RcrarreAA

as a function of peT

table that this calculation has a very strong suppressionof charm decay electrons such that bottom contributionsdominate even at modest pT ge 2 GeVc The calcu-lations are consistent with the data for pT lt 4 GeVcand over-predict the bottom contribution for higher pTvalues

Figure 20(c) also compares the bottom electron frac-tion from another variant of the Langevin calculation byCao et al as detailed in Ref [65] For this calculationwe show two results corresponding to two different inputvalues D(2πT ) = 15 and 6 For the lower parameteragain stronger heavy-quark to medium coupling thereis a sharp rise in the bottom contribution which thenflattens out This feature is due to the increased colli-sional energy loss which has a larger effect on the charmquarks coupled with the strong radial flow effects en-abling the heavier bottom quarks to dominate even atpT sim 2 GeVc These calculations use an impact pa-rameter of b = 65 fm which should roughly correspondto MB collisions We find that the calculation using the

larger value of D(2πT ) = 60 is in reasonable agreementwith the data across the calculated pT range

Lastly Fig 20(d) shows a more recent calculation byHe et al employing a T-matrix approach similar to thatshown in Fig 20(b) but with a number of updates asdescribed in Ref [66] In this case the authors provideda calculation of the bottom electron fraction in both p+pand Au+Au at

radicsNN

=200 GeV and we therefore do notcalculate the bottom fraction using fonll as a baselineThe calculation is performed for the 20ndash40 centralitybin which the authors find well represents MB We findthat the calculation under-predicts the bottom fractionfor pT lt 3 GeVc although it is worth noting that thecalculation in p+p is also below the fonll curve acrossthe full pT range Above pT sim 3 GeVc the calculationis in agreement with the measurement It is also worthnoting that of the models presented here this is the onlyone that shows in Au+Au a slight decrease in the bottomfraction at high pT

There are numerous other calculations in the litera-ture [67ndash69] that require mapping charm and bottomhadrons to electrons at midrapidity to make direct datacomparisons We look forward to soon being able to testthese calculations with analysis of new PHENIX datasets

VI SUMMARY AND CONCLUSIONS

This article has detailed the measurements of electronsas a function of DCAT and pT from Au+Au data takenatradicsNN

=200 GeV in 2011 with the enhanced vertexingcapabilities provided by the VTX detector In conjunc-tion with previous PHENIX results for the heavy flavorelectron invariant yield as a function of pT [12] we per-form an unfolding procedure to infer the parent charmand bottom hadron yields as a function of pT We findthat this procedure yields consistent agreement betweenthe heavy flavor electron invariant yield and the newlymeasured electron DCAT distributions

We find that the extracted D0 yield vs pT is in goodagreement with that measured by STAR [14] over thecomplimentary pT region Without a proper p+p base-line extracted from a similar analysis it is difficult tomake any quantitative statements about the charm orbottom hadron modification

We compare the extracted bottom electron fraction tomeasurements in p+p collisions and find agreement be-tween Au+Au and p+p for pT gt 4 GeVc within thelarge uncertainties on both measurements The agree-ment between Au+Au and p+p coupled with the mea-sured heavy flavor electron RAA strongly implies thatelectrons from charm and bottom hadron decays aresuppressed Using these components we calculate thenuclear modification for electrons from charm and bot-tom hadron decays and find that electrons from bottomhadron decays are less suppressed than those from charmhadron decays in the range 3 lt pT GeVc lt 4 We fur-

1 2 3 4 5 6 7 8 9pe

T [GeVc]

12brarr

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLDjordjevic et al dNdy=1000 (0-10)Djordjevic et al dNdy=3500 (0-10)Djordjevic et al (0-10)Unfold Result

1 2 3 4 5 6 7 8 9pe

T [GeVc]

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLD(2 π T)=30 van Hees et al (0-10)D(2 π T)=6 van Hees et al (0-10)D(2 π T)=4 van Hees et al (0-10)Unfold Result

1 2 3 4 5 6 7 8 9pe

T [GeVc]

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLAlberico et alD(2 π T)=6 Cao et alD(2 π T)=15 Cao et alUnfold Result

1 2 3 4 5 6 7 8 9pe

T [GeVc]

e(brarr

crarre)

|y|lt035Au+Au MB

radicsNN =200 GeV

FONLLHe et al Au+AuHe et al p+p

Unfold Result

FIG 20 (Color Online) Bottom electron fraction as a function of pT compared to a series of model predictions detailed in thetext

ther compare the bottom electron fraction to a varietyof model calculations employing variously energy lossLangevin transport and T-matrix approaches We findthat there are a number of models which are in reasonableagreement with the extracted bottom electron fractionwithin the relatively large uncertainties

We note that a significantly larger data set of Au+Aucollisions at

radicsNN

=200 GeV was collected in 2014 withan improved performance of the VTX detector The 2014Au+Au data coupled with the p+p data taken in 2015should yield both an important baseline measurement ofthe bottom electron fraction and a more precise measure-ment in Au+Au

ACKNOWLEDGMENTS

We thank the staff of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the staff of the other PHENIX participating

institutions for their vital contributions We acknowl-edge support from the Office of Nuclear Physics in theOffice of Science of the Department of Energy the Na-tional Science Foundation Abilene Christian UniversityResearch Council Research Foundation of SUNY andDean of the College of Arts and Sciences Vanderbilt Uni-versity (USA) Ministry of Education Culture SportsScience and Technology and the Japan Society for thePromotion of Science (Japan) Conselho Nacional de De-senvolvimento Cientıfico e Tecnologico and Fundacao deAmparo a Pesquisa do Estado de Sao Paulo (Brazil) Nat-ural Science Foundation of China (P R China) Croa-tian Science Foundation and Ministry of Science Ed-ucation and Sports (Croatia) Ministry of EducationYouth and Sports (Czech Republic) Centre National

de la Recherche Scientifique Commissariat a lrsquoEnergieAtomique and Institut National de Physique Nucleaireet de Physique des Particules (France) Bundesminis-terium fur Bildung und Forschung Deutscher Akademis-

cher Austausch Dienst and Alexander von HumboldtStiftung (Germany) National Science Fund OTKAKaroly Robert University College and the Ch SimonyiFund (Hungary) Department of Atomic Energy and De-partment of Science and Technology (India) Israel Sci-ence Foundation (Israel) Basic Science Research Pro-gram through NRF of the Ministry of Education (Korea)Physics Department Lahore University of ManagementSciences (Pakistan) Ministry of Education and ScienceRussian Academy of Sciences Federal Agency of AtomicEnergy (Russia) VR and Wallenberg Foundation (Swe-den) the US Civilian Research and Development Foun-dation for the Independent States of the Former SovietUnion the Hungarian American Enterprise ScholarshipFund and the US-Israel Binational Science Foundation

APPENDIX DETAILED NORMALIZATION OFELECTRON BACKGROUND COMPONENTS

This appendix details the calculation of the normaliza-tions for the background components

bull Photonic electrons

bull Kaon decay electrons

bull Heavy quarkonia decay electrons

using the bootstrap method described in Sec III F Wefirst determine the fraction of nonphotonic electronsFNP We then calculate the normalization of Dalitz andconversion components followed by the normalization ofKe3 and quarkonia components

A Fraction of nonphotonic electrons FNP

We first determine FNP the fraction of nonphotonicelectrons to inclusive electrons after the application ofall analysis cuts including the conversion veto cut Notethat nonphotonic electrons include contributions fromheavy flavor semi-leptonic decays quarkonia decays andkaon decays Photonic electrons are from π0 and η Dalitzdecays and photon conversionsFNP in the 2011 data can be determined using the pub-

lished 2004 result [12] as follows Let YNP be the yield ofnonphotonic electrons and YDalitz the yield of electronsfrom Dalitz decays Note that both YNP and YDalitz areindependent of the year of data taking In the PHENIX2004 Au+Au data run the ratio of the nonphotonic elec-tron yield to the photonic electron yield (R2004

NP ) was mea-sured The relation of YNP and YDalitz is as follows

YNP = R2004NP (1 +R2004

CD )times YDalitz (13)

where R2004CD represents the ratio of conversion electron

yield to Dalitz electron yield in the 2004 PHENIX detec-tor It is calculated as

R2004CD =

sumi=π0ηγ

R2004CD (i) middot rDalitz(i)) (14)

Here R2004CD (i) is the ratio of conversion electrons to elec-

trons from Dalitz decays in the 2004 PHENIX detectorcalculated by a full geant3 simulation The factors

bull rDalitz(π0)

bull rDalitz(η)

bull rDalitz(γ)

are the fractional contributions of π0 η and direct pho-ton contribution to the total Dalitz decays respectively1We only consider the contributions of π0 η and γdir (di-rect photon) since the sum of other contributions is small(5 or less) Thus they are normalized such that

rDalitz(i) = 1 (15)

Figure 21 shows rDalitz for π0 η and direct photonas a function of transverse momentum of the electronsfor MB Au+Au collisions at 200 GeV The ratios arecalculated from the invariant yield of π0[49] η[50] anddirect photons[3 51]

[GeVc]eT

p0 05 1 15 2 25 3 35 4 45 5

1 = 200 GeVNNsAu+Au MB

γ-e+ erarr 0π γ-e+ erarr η

-e+ erarr γDirect

FIG 21 (Color Online) The fraction of π0 η and directphoton Dalitz decay electrons in all Dalitz electrons as a func-tion of electron pT (peT )

In the 2011 data set the observed electron yields fromconversion and Dalitz decays are modified by the elec-tron survival probability after the conversion veto cut is

1 Here we include internal conversion of direct photon in Dalitzdecays Note that the Dalitz decay of π0 (η) is caused by internalconversion of one of two decay photons in π0(η) rarr γγ

applied The yield of photonic electrons which pass theconversion veto (Y 2011

P ) is

Y 2011P = R2011

PD times YDalitz (16)

R2011PD =

sumi=π0ηγ

(SD(i) + SC middotR2011

CD (i))rDalitz(i)(17)

where SC is the survival probability of conversion elec-trons SD(π0) SD(η) SD(γ) are survival probabilities ofDalitz decay electrons from π0 η and direct photonsrespectively as shown in Fig 8 R2011

CD (i) (i = π0 η γ)isthe ratio of conversion electrons to Dalitz electrons forparticle i in the 2011 PHENIX detector after the addi-tion of the VTX and the replacement of the beam pipeIt is determined to be R2011

CD (i) asymp 110 from full geant3simulations

[GeVc]eT

p0 05 1 15 2 25 3 35 4 45 5

PHENIX 2011

FIG 22 (Color Online) The fraction of nonphotonic elec-trons to inclusive electrons as a function of electron pT (peT )

The fraction of nonphotonic electrons to inclusive elec-trons can then be calculated as

FNP =YNP

YNP + Y 2011P

=R2004

NP (1 +R2004CD )

R2004NP (1 +R2004

CD ) +R2011PD

The resulting FNP as a function of peT and the calcu-lated systematic uncertainties due to the uncertainties onthe input yields is shown in Fig 22 With FNP in handwe obtain the number of photonic electrons Ne

P and thenumber of nonphotonic electrons Ne

NeP = Ne(1minus FNP) (20)

NeNP = NeFNP (21)

[GeVc]eT

p0 05 1 15 2 25 3 35 4 45 5

1Au+Au MB

= 200 GeVNNsPHENIX 2011

γDirect

FIG 23 (Color Online) The fraction of π0 η and directphoton electrons in all photonic electrons as a function ofelectron pT (peT )

where Ne is the number of electrons with conversion vetoafter the subtraction of the hadronic contamination andrandom background

B Normalization of Dalitz and conversioncomponents

In the previous section we obtained NeP the number of

photonic electrons in the data after the conversion vetocut There are two components in the photonic electrons(Ne

1 Electrons from Dalitz decays (π0 + η + γ)

2 Electrons from conversions in the beam pipe andB0

In the next step we determine the normalization ofDalitz and conversions separately This is needed sincethe shape of DCAT distribution of Dalitz and conversionsare different

After application of the conversion veto cut we have

NeC(i) = SCR

2011CD (i)(1minus δrandom)εAYDalitz (22)

NeD(i) = SD(i)(1minus δrandom)εAYDalitz (23)

(i = π0 η γ) (24)

where NeC(i) and Ne

D(i) are the number of electrons fromconversions and Dalitz from particle i after the conver-sion veto cut respectively δrandom is the common reduc-tion factor of tracks due to random hits in the windows

of the conversion veto cut and εA is the efficiency andacceptance without the conversion veto cut Since thenumber of photonic electron is Ne

P (i) = NeD(i) + Ne

C(i)the fraction of conversions and Dalitz decays in the pho-tonic electrons are

NeC(i)

NeP (i)

=SCRCD(i)

SD(i) + SCR2011CD (i)

NeD(i)

NeP (i)

=SD(i)

The fraction of electrons from conversions (NeCN

and Dalitz (NeDN

eP ) is the average of these fractions

NeC = Ne

sumi=π0ηγ

rph(i)SCR

2011CD (i)

NeD = Ne

sumi=π0ηγ

rph(i)SD(i)

where rph(i) (i = π0 η γ) is the relative contribution ofelectrons from (conversion + Dalitz decay) for particle iafter application of conversion veto cut Figure 23 showsrph(i) (i = π0 η γ) as a function of peT The conversioncontributions are nearly the same for π0 η and γ andeffectively cancel when calculating the ratio Thereforerph (Fig 23) is almost identical with rDalitz (Fig 21)

C Normalization of Ke3 and quarkonia components

The ratio of electrons from kaons to all nonphotonicelectrons before the application of the conversion vetocut δK is calculated from the ratio of the nonphotonicelectron yield to the electron yield from kaons [12] Com-pared to Ref [12] we find that sim 50 of electrons fromkaon decays are removed by DCAT and DCAL cuts aswell as the method used to subtract random backgroundwhich contains some real electrons from kaon decays

The ratio of electrons from Jψ decays to all nonpho-tonic electrons before the application of the conversionveto cut δJψ is taken from Ref [12] The survival ratefor electrons from Jψ decays SJψ is taken to be unitywhile the survival rate for Ke3 decays SK is taken tobe the same value as that for electrons from charm andbottom decays (namely SHF) See Sec III E 3 for details

After application of conversion veto cut the normal-izations of these two nonphotonic electron componentsare described by

NeJψ = Ne

δJψSJψδJψSJψ+δKSK+(1minusδJψminusδK)SHF

NeK = Ne

NPδKSK

δJψSJψ+δKSK+(1minusδJψminusδK)SHF(30)

[1] K Adcox et al (PHENIX Collaboration) ldquoFormation ofdense partonic matter in relativistic nucleus-nucleus colli-sions at RHIC Experimental evaluation by the PHENIXCollaborationrdquo Nucl Phys A 757 184 (2005)

[2] J Adams et al (STAR Collaboration) ldquoExperimentaland theoretical challenges in the search for the quarkgluon plasma The STAR Collaborationrsquos critical assess-ment of the evidence from RHIC collisionsrdquo Nucl PhysA 757 102 (2005)

[3] A Adare et al (PHENIX Collaboration) ldquoEnhancedproduction of direct photons in Au+Au collisions atradicsNN=200 GeV and implications for the initial temper-

aturerdquo Phys Rev Lett 104 132301 (2010)[4] P Romatschke ldquoNew Developments in Relativistic Vis-

cous Hydrodynamicsrdquo Int J Mod Phys E 19 1 (2010)[5] U Heinz and R Snellings ldquoCollective flow and viscosity

in relativistic heavy-ion collisionsrdquo Ann Rev Nucl PartSci 63 123 (2013)

[6] A Bazavov et al (HotQCD) ldquoEquation of state in ( 2+1)-flavor QCDrdquo Phys Rev D 90 094503 (2014)

[7] P K Kovtun Dan T Son and A O Starinets ldquoVis-cosity in strongly interacting quantum field theories fromblack hole physicsrdquo Phys Rev Lett 94 111601 (2005)

[8] M Gyulassy and L McLerran ldquoNew forms of QCDmatter discovered at RHICrdquo Quark gluon plasmaNew discoveries at RHIC A case of strongly interact-

ing quark gluon plasma Proceedings RBRC WorkshopBrookhaven Upton USA May 14-15 2004 Nucl PhysA 750 30 (2005)

[9] U W Heinz ldquoRHIC serves the perfect fluid Hydrody-namic flow of the QGPrdquo in Proceedings Workshop onExtreme QCD p 3 (2005)

[10] S S Adler et al (PHENIX Collaboration) ldquoCentral-ity dependence of charm production from single elec-trons measurement in Au + Au collisions at

radicsNN =

200 GeVrdquo Phys Rev Lett 94 082301 (2005)[11] K Adcox et al (PHENIX Collaboration) ldquoMeasurement

of single electrons and implications for charm productionin Au+Au collisions at

radics(NN) = 130 GeVrdquo Phys Rev

Lett 88 192303 (2002)[12] A Adare et al (PHENIX Collaboration) ldquoHeavy Quark

Production in p+ p and Energy Loss and Flow of HeavyQuarks in Au+Au Collisions at

radicsNN=200 GeVrdquo Phys

Rev C 84 044905 (2011)[13] A Adare et al (PHENIX Collaboration) ldquoEnergy Loss

and Flow of Heavy Quarks in Au+Au Collisions atradicsNN

= 200 GeVrdquo Phys Rev Lett 98 172301 (2007)[14] L Adamczyk et al (STAR Collaboration) ldquoObserva-

tion of D0 Meson Nuclear Modifications in Au+Au Colli-sions at

radicsNN=200 GeVrdquo Phys Rev Lett 113 142301

(2014)[15] B B Abelev et al (ALICE Collaboration) ldquoAzimuthal

anisotropy of D meson production in Pb-Pb collisions atradicsNN=276 TeVrdquo Phys Rev C 90 034904 (2014)

[16] B Abelev et al (ALICE Collaboration) ldquoSuppression ofhigh transverse momentum D mesons in central Pb-Pbcollisions at

radicsNN=276 TeVrdquo J High Energy Phys 09

(2012) 112[17] S Chatrchyan et al (CMS Collaboration) ldquoSuppression

of nonprompt Jψ prompt Jψ and Y(1S) in PbPb col-lisions at

(2012) 063[18] S Chatrchyan et al (CMS Collaboration) ldquoEvidence

of b-Jet Quenching in PbPb Collisions atradicsNN=276

TeVrdquo Phys Rev Lett 113 132301 (2014) [ErratumPhys Rev Lett 115 029903 (2015)]

[19] A Adare et al (PHENIX Collaboration) ldquoSystem-sizedependence of open-heavy-flavor production in nucleus-nucleus collisions at

radicsNN=200 GeVrdquo Phys Rev C 90

034903 (2014)[20] A Adare et al (PHENIX Collaboration) ldquoCold-nuclear-

matter effects on heavy-quark production in d+Au colli-sions at

(2012)[21] D Antreasyan J W Cronin H J Frisch M J Shochet

L Kluberg P A Piroue and R L Sumner ldquoProductionof hadrons at large transverse momentum in 200-GeV300-GeV and 400-GeV pp and pn collisionsrdquo Phys RevD 19 764 (1979)

[22] A Adare et al (PHENIX Collaboration) ldquoHeavy-quarkproduction and elliptic flow in Au+Au collisions atradicsNN = 624 GeVrdquo Phys Rev C 91 044907 (2015)

[23] S Batsouli S Kelly M Gyulassy and J L Nagle ldquoDoesthe charm flow at RHICrdquo Phys Lett B 557 26 (2003)

[24] G D Moore and D Teaney ldquoHow much do heavy quarksthermalize in a heavy ion collisionrdquo Phys Rev C 71064904 (2005)

[25] S Cao G-Y Qin and S A Bass ldquoHeavy-quark dy-namics and hadronization in ultrarelativistic heavy-ioncollisions Collisional versus radiative energy lossrdquo PhysRev C 88 044907 (2013)

[26] R Rapp and H van Hees R C Hwa X-N Wang (Ed)Quark Gluon Plasma 4 111 (2010) (World Scientific)

[27] H van Hees M Mannarelli V Greco and R RappldquoNonperturbative heavy-quark diffusion in the quark-gluon plasmardquo Phys Rev Lett 100 192301 (2008)

[28] P B Gossiaux J Aichelin T Gousset and V GuiholdquoCompetition of Heavy Quark Radiative and Colli-sional Energy Loss in Deconfined Matterrdquo Strangenessin quark matter Proceedings 14th International Confer-ence SQM 2009 Buzios Rio de Janeiro Brazil Septem-ber 27-October 2 2009 J Phys G 37 094019 (2010)

[29] A M Adare M P McCumber James L Nagle andP Romatschke ldquoExamination whether heavy quarkscarry information on the early-time coupling of thequark-gluon plasmardquo Phys Rev C 90 024911 (2014)

[30] Y L Dokshitzer and D E Kharzeev ldquoHeavy quark col-orimetry of QCD matterrdquo Phys Lett B 519 199 (2001)

[31] M Djordjevic and M Djordjevic ldquoHeavy flavor puzzlefrom data measured at the BNL Relativistic Heavy IonCollider Analysis of the underlying effectsrdquo Phys RevC 90 034910 (2014)

[32] M Djordjevic ldquoAn Overview of heavy quark energyloss puzzle at RHICrdquo International Conference onStrangeness in Quark Matter (SQM2006) Los AngelesCalifornia March 26-31 2006 J Phys G 32 S333

(2006)[33] M Cacciari P Nason and R Vogt ldquoQCD predictions

for charm and bottom production at RHICrdquo Phys RevLett 95 122001 (2005)

[34] A Adare et al (PHENIX Collaboration) ldquoMeasurementof Bottom versus Charm as a Function of Transverse Mo-mentum with Electron-Hadron Correlations in p+p Col-lisions at

radics = 200 GeVrdquo Phys Rev Lett 103 082002

(2009)[35] M M Aggarwal et al (STAR Collaboration) ldquoMeasure-

ment of the Bottom contribution to nonphotonic electronproduction in p + p collisions at

radics=200 GeVrdquo Phys

Rev Lett 105 202301 (2010)[36] K Adcox et al (PHENIX Collaboration) ldquoPHENIX de-

tector overviewrdquo Nucl Instrum Methods Phys ResSec A 499 469 (2003)

[37] M L Miller K Reygers S J Sanders and P Stein-berg ldquoGlauber modeling in high energy nuclear colli-sionsrdquo Ann Rev Nucl Part Sci 57 205 (2007)

[38] M Baker et al (PHENIX Collaboration) ldquoProposal fora Silicon Vertex Tracker (VTX) for the PHENIX Exper-imentrdquo BNL internal report 72204

[39] Rachid Nouicer (PHENIX Collaboration) ldquoProbing Hotand Dense Matter with Charm and Bottom Measure-ments with PHENIX VTX Trackerrdquo Proceedings 23rdInternational Conference on Ultrarelativistic Nucleus-Nucleus Collisions Quark Matter 2012 (QM 2012)Nucl Phys A 904-905 647c (2013)

[40] M Kurosawa (PHENIX Collaboration) ldquoHigher har-monics flow measurement of charged hadrons and elec-trons in wide kinematic range with PHENIX VTXtrackerrdquo Proceedings 23rd International Conference onUltrarelativistic Nucleus-Nucleus Collisions QuarkMatter 2012 (QM 2012) Nucl Phys A 904-905 397c(2013)

[41] R Ichimiya et al (PHENIX Collaboration) ldquoStatus andoverview of development of the Silicon Pixel Detector forthe PHENIX experiment at the BNL RHICrdquo J Inst 4P05001 (2009) and references therein

[42] W Snoeys et al ldquoPixel readout chips in deep submi-cron CMOS for ALICE and LHCb tolerant to 10-Mradand beyondrdquo in Development and application of semicon-ductor tracking detectors Proceedings 4th InternationalSymposium Hiroshima Japan March 22-25 2000 Vol466 (2001) p 366

[43] Z Li et al ldquoNovel silicon stripixel detector for PHENIXupgraderdquo Frontier detectors for frontier physics Pro-ceedings 9th Pisa Meeting on advanced detectors LaBiodola Italy May 25-31 2003 Nucl Instrum Meth-ods Phys Res Sec A 518 300 (2004)

[44] R Nouicer et al (PHENIX Collaboration) ldquoStatus andPerformance of New Silicon Stripixel Detector for thePHENIX Experiment at RHIC Beta Source Cosmic-rays and Proton Beam at 120 GeVrdquo J Inst 4 P04011(2009) and references therein

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[50] A Adare et al (PHENIX Collaboration) ldquoTransversemomentum dependence of meson suppression η suppres-sion in Au+Au collisions at

radicsNN = 200 GeVrdquo Phys

Rev C 82 011902 (2010)[51] S Afanasiev et al (PHENIX Collaboration) ldquoMea-

surement of Direct Photons in Au+Au Collisions atradicsNN=200 GeVrdquo Phys Rev Lett 109 152302 (2012)

[52] A Adare et al (PHENIX Collaboration) ldquoJψ Produc-tion vs Centrality Transverse Momentum and Rapidityin Au+Au Collisions at

radicsNN=200 GeVrdquo Phys Rev

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cle physicsrdquo Advanced statistical techniques in particlephysics Proceedings Conference Durham UK March18-22 2002 Conf Proc C 0203181 248 (2002)

[54] G Choudalakis ldquoFully Bayesian UnfoldingrdquoArXiv12014612

[55] Goodman J and Weare J ldquoEnsemble samplers withaffine invariancerdquo Comm App Math Comp Sci 5 65(2010)

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Single electron yields from semileptonic charm and bottom hadron decays in Au+Au collisions at sNN=200 GeV

Abstract

I Introduction

II PHENIX Detector


B The central arms

C The VTX detector

III Analysis

A Overview

B Event selection







1 VTX alignment




5 DCAT and DCAL

6 DCA measurement





4 Ke3

5 Quarkonia

F Normalization of electron background components

G Unfolding

1 Introduction

2 Unfolding method




6 Parent charm and bottom hadron yield and their statistical uncertainty



IV Results


V Discussion

VI Summary and Conclusions

ACKNOWLEDGMENTS

APPENDIX Detailed Normalization of electron background components


B Normalization of Dalitz and conversion components


References