Measurement of absolute branching fractions of inclusive semileptonic decays of charmand charmed-strange mesons
D.M. Asner,1 K.W. Edwards,1 J. Reed,1 A.N. Robichaud,1 G. Tatishvili,1 E. J. White,1 R. A. Briere,2 H. Vogel,2
P. U. E. Onyisi,3 J. L. Rosner,3 J. P. Alexander,4 D.G. Cassel,4 S. Das,4 R. Ehrlich,4 L. Fields,4 L. Gibbons,4 S.W. Gray,4
D. L. Hartill,4 B. K. Heltsley,4 J.M. Hunt,4 D. L. Kreinick,4 V. E. Kuznetsov,4 J. Ledoux,4 J. R. Patterson,4 D. Peterson,4
D. Riley,4 A. Ryd,4 A. J. Sadoff,4 X. Shi,4 S. Stroiney,4 W.M. Sun,4 J. Yelton,5 P. Rubin,6 N. Lowrey,7 S. Mehrabyan,7
M. Selen,7 J. Wiss,7 M. Kornicer,8 R. E. Mitchell,8 M. R. Shepherd,8 C.M. Tarbert,8 D. Besson,9 T. K. Pedlar,10 J. Xavier,10
D. Cronin-Hennessy,11 K.Y. Gao,11 J. Hietala,11 R. Poling,11 P. Zweber,11 S. Dobbs,12 Z. Metreveli,12 K.K. Seth,12
B. J. Y. Tan,12 A. Tomaradze,12 S. Brisbane,13 J. Libby,13 L. Martin,13 A. Powell,13 P. Spradlin,13 G. Wilkinson,13
H. Mendez,14 J. Y. Ge,15 D.H. Miller,15 I. P. J. Shipsey,15 B. Xin,15 G. S. Adams,16 D. Hu,16 B. Moziak,16 J. Napolitano,16
K.M. Ecklund,17 J. Insler,18 H. Muramatsu,18 C. S. Park,18 E. H. Thorndike,18 F. Yang,18 S. Ricciardi,19 C. Thomas,13,19
M. Artuso,20 S. Blusk,20 S. Khalil,20 R. Mountain,20 K. Randrianarivony,20 T. Skwarnicki,20 S. Stone,20 J. C. Wang,20
L.M. Zhang,20 G. Bonvicini,21 D. Cinabro,21 A. Lincoln,21 M. J. Smith,21 P. Zhou,21 J. Zhu,21
P. Naik,22 and J. Rademacker22
1Carleton University, Ottawa, Ontario, Canada K1S 5B62Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
3University of Chicago, Chicago, Illinois 60637, USA4Cornell University, Ithaca, New York 14853, USA
5University of Florida, Gainesville, Florida 32611, USA6George Mason University, Fairfax, Virginia 22030, USA
7University of Illinois, Urbana-Champaign, Illinois 61801, USA8Indiana University, Bloomington, Indiana 47405, USA9University of Kansas, Lawrence, Kansas 66045, USA
10Luther College, Decorah, Iowa 52101, USA11University of Minnesota, Minneapolis, Minnesota 55455, USA
12Northwestern University, Evanston, Illinois 60208, USA13University of Oxford, Oxford OX1 3RH, United Kingdom14University of Puerto Rico, Mayaguez, Puerto Rico 0068115Purdue University, West Lafayette, Indiana 47907, USA
16Rensselaer Polytechnic Institute, Troy, New York 12180, USA17Rice University, Houston, Texas 77005, USA
18University of Rochester, Rochester, New York 14627, USA19STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom
20Syracuse University, Syracuse, New York 13244, USA21Wayne State University, Detroit, Michigan 48202, USA22University of Bristol, Bristol BS8 1TL, United Kingdom
(Received 21 December 2009; revised manuscript received 22 February 2010; published 16 March 2010)
We have measured the inclusive semileptonic branching fractions ofD0,D, andDs mesons. For thesemeasurements, we have used the full CLEO-c open-charm data samples, 818 pb1 at ECM 3:774 GeV,giving D0 D0 and DD events, and 602 pb1 at ECM 4:170 GeV, giving Ds Ds events. Weobtain BD0 ! Xee 6:46 0:09 0:11%, BD ! Xee 16:13 0:10 0:29%, andBDs ! Xee 6:52 0:39 0:15%, where the first uncertainties are statistical and the secondare systematic. From these and lifetimes obtained elsewhere, we obtain the ratios of semileptonic decay
widths D ! Xee=D0 ! Xee 0:985 0:015 0:024 and Ds ! Xee=D0 !Xee 0:828 0:051 0:025. The ratio of D and D0 is consistent with the isospin symmetryprediction of unity, and the ratio of Ds and D0 differs from unity, as expected.
DOI: 10.1103/PhysRevD.81.052007 PACS numbers: 13.20.Fc
PHYSICAL REVIEW D 81, 052007 (2010)
1550-7998=2010=81(5)=052007(10) 052007-1 2010 The American Physical Society
As part of the CLEO-c analyses of exclusive  andinclusive semileptonic decays , this article presentsmeasurements of D0, D, and Ds inclusive semileptonicbranching fractions using the complete CLEO-c data sets.Using these results and known lifetimes, we also report theratios of the widths D ! Xee=D0 ! Xee(which is expected to be unity due to isospin symmetry)and Ds ! Xee=D0 ! Xee (which is not ex-pected to be unity [9,10], though with poor theoreticalprecision). These measurements are important in theirown right, and, due to similarities between the D and Bsectors, will also improve understanding of B semileptonicdecays. In particular, knowledge of the previously unmeas-ured ratio Ds ! Xee=D0 ! Xee enables amore reliable prediction of the difference of the inclusivedecay rates between B0 and B mesons in b ! udecays, thereby reducing theoretical uncertainty  indetermination of weak mixing parameter Vub.
Two sets of open-charm data samples are used to studythe semileptonic decays of charm and charmed-strangemesons. In ee collisions provided by the CornellElectron Storage Ring (CESR), the CLEO-c detector hascollected integrated luminosities of 818 pb1 at the center-of-mass energy ECM 3:774 GeV near the peak of thec 3770 resonance which decays to D D pairs, and602 pb1 at ECM 4:170 GeV near the peak productionof Ds Ds pairs. The former data set contains 3:0 106D0 D0 and 2:4 106 DD pairs, and is used to study D0and D semileptonic decays. The latter data set contains0:6 106 Ds Ds pairs, and is used to study Ds semi-leptonic decays. We have previously reported  measure-ments of inclusive semileptonic decay branching fractionsof D0 and D mesons with a subsample of the former dataset.
The remainder of this article is organized as follows. TheCLEO-c detector is described in Sec. II. Event reconstruc-tion and selection criteria are described in Sec. III. Theanalysis procedure to extract semileptonic decay rates iscovered in Sec. IV. Results for inclusive spectra are pre-sented in Sec. V. Systematic uncertainty in our measure-ments is evaluated in Sec. VI. Finally, in Sec. VII asummary of our results is provided.
II. THE CLEO-C DETECTOR
The CLEO-c detector  is a general-purpose so-lenoidal detector equipped with four concentric compo-nents: a six-layer vertex drift chamber, a 47-layer maindrift chamber, a ring-imaging Cherenkov (RICH) detector,and a cesium iodide electromagnetic calorimeter. The de-tector provides acceptance of 93% of the full 4 solidangle for both charged particles and photons. The maindrift chamber provides specific-ionization (dE=dx) mea-surements that discriminate between charged pions and
kaons. The RICH detector covers approximately 80% of4 and provides additional separation of pions and kaonsat high momentum ( 700 MeV). Electron identificationis based on a likelihood variable that combines the infor-mation from the RICH detector, dE=dx, and the ratio ofelectromagnetic shower energy to track momentum (E=p).A GEANT-based  Monte Carlo (MC) simulation is usedto study efficiencies of signal and background events.Physics events are generated by EVTGEN , tuned withimproved knowledge of charm decays , and final-state radiation (FSR) is modeled by PHOTOS .
III. EVENT SELECTION
Charm or charmed-strange mesons are always producedin pairs in our open-charm data samples. Since the data aretaken just above threshold, the mesons are produced in avery clean environment with no additional particles except,in the case of theDsD
s , a photon or a neutral pion from the
Ds decay. The analysis proceeds by first defining a singletag (ST) sample, in which one of theD (orDs) mesons in aD D (or DsD
s) event is reconstructed in a chosen hadronic
decay mode, and a further double tag (DT) subsample inwhich an additional recoiling electron (or positron) isrequired as a signature of the signal semileptonic decay.Absolute semileptonic branching fractions for charm orcharmed-strange mesons can then be obtained from thefraction of the ST sample that is DT, without requiring anyknowledge of the integrated luminosity or how many me-sons are produced.
A. Tag selection
To minimize the combinatorial backgrounds and sys-tematic uncertainties, three very clean tag modes com-posed of only charged particles are used: D0 ! K,D ! K, and Ds ! . Here, the notationDs ! is a shorthand label for Ds ! KKevents within a 10 MeV mass window of the mesonpeak in KK invariant mass. The inclusion of chargeconjugate modes is implied throughout this article unlessotherwise stated.We identify a ST in the c 3770 data sample using the
energy difference E ED Ebeam and the beam-constrained mass difference Mbc E2beam p2D1=2 mD, where ED is the energy of the tag, Ebeam is the beamenergy, pD is the three momentum of the tag, andmD is thenominal mass  of the neutral or charged charm meson.We require the D0 ! K and D ! K tags tohave Mbc within a 4 MeV mass window around thenominal D mass.For data collected at the center-of-mass energy of
4170 MeV, we identify a ST by using the invariant massof the tag MDs and recoil mass against the tagMrecoilDs. The recoil mass is defined as MrecoilDs Eee EDs2 pee pDs21=2, where Eee;pee is the
D.M. ASNER et al. PHYSICAL REVIEW D 81, 052007 (2010)
net four-momentum of the ee beam taking the finitebeam crossing angle into account, and EDs;pDs is thefour-momentum of the tag, with EDs computed from pDsand the nominal mass  of theDs meson. We require therecoil mass to be within 55 MeVof the Ds mass . Thisloose window allows both primary and secondary (fromDs ! Ds or Ds ! Ds 0) Ds tags to be selected. Weveto tag candidates with track momenta below 100 MeVto reduce the background from D D decays (throughD ! D).
The E and M distributions obtained from data areshown in Fig. 1. To estimate the backgrounds from thewrong tag combinations, we use the sidebands of the Edistribution or the tag mass difference M MDs
mDs distribution, where mDs is the nominal mass  of
theDs meson. We define the signal and sideband regions inTable I. We fit the distributions to a sum of a double-Gaussian function (for signal) and a second orderChebyshev polynomial function (for background) to deter-mine the tag sideband scaling factor stag, which is the ratio
of areas in the signal and sideband regions described by thebackground polynomial function. Obtained ST yields andtag sideband scaling factors are listed in Table II.
B. Signal selection
We form DT candidates from ST candidates by adding arecoiling charged track that is consistent with coming fromthe nominal interaction point. Specifically, the recoilingtracks point of closest approach to the origin must bewithin 5 cm of the interaction point along the beam lineand within 5 mm of the interaction point in the planetransverse to the beam line. We require the momentum ofthe track to be p 200 MeV and the angle with respect tothe beam to be j cosj< 0:80 so that all charged-particleidentification (PID) information (dE=dx, RICH, and E=p)is available. The signal track in the DT candidate is alsorequired to be identified as an electron, a charged pion, or acharged kaon, for further analysis. This is discussed in thenext section.
The D (or Ds) semileptonic inclusive spectrum (ordifferential decay rate) can be expressed as
where nD is the number of D mesons produced, ne is thenumber of produced primary electrons in bins of momen-tum p, nST is the number of ST, nDT is the electroncandidate yield in bins of momentum, and SL is the(momentum-dependent) electron detection efficiency.
FIG. 1 (color online). Tag E and M distributions in data (histograms) with fits (solid curves) and background contributions(dashed lines).
TABLE I. Signal and sideband regions of E andM for eachtag mode.
Tag mode Signal (MeV) Sideband (MeV)
D0 ! K 30 E
The D semileptonic branching fraction can be obtained byintegrating the differential spectrum and correcting for the200 MeV momentum cutoff by extrapolating the spectrumbelow the cutoff. If we had a perfect MC modeling of thesemileptonic decays, a simple momentum bin-by-bin cor-rection factor could be used for SL. Instead, we use a moregeneral unfolding  approach to minimize MC modeldependence.
The observed laboratory momentum spectrum yb; itrackof a particle identified as type b ( e, , or K) in bins ofmeasured track momentum bin itrack can be modeled as afolded distribution. It is related to the true laboratorymomentum na; j via detector-response matrices that ac-count for resolution and efficiency:
yb; itrack X
Atrackitrackja; jna; j;
where a ( e, , , or K) is the true particle speciesindex, na; j is the true laboratory momentum spectrum inbins of true laboratory momentum bin index j of a particletype a, Atrackitrackja; j is the tracking efficiency matrix,which describes the probability of a particle of type a withmomentum in bin j to be reconstructed in track momentumbin itrack, and APIDbja; itrack is the PID efficiency matrix,which describes the probability of a particle of type a withmeasured momentum in bin itrack to be identified as PIDtype b. We unfold  Eq. (2) to obtain the true momen-tum spectrum
na e; j Xitrack
A1trackitrackja e; j
A1PIDbja; itrackyb; itrack
where the A1s are the unfolded inverses of each effi-ciency matrix. Because we are interested in the primaryelectron laboratory momentum spectrum (to obtain thebranching fraction) we use the electron solution after PIDunfolding (a e).
In addition to finite resolution and efficiency, modeledby detector-response matrices, we have to consider pos-sible backgrounds in our observed spectrum. We removecombinatorial wrong-tag background contribution by E(or M) sideband subtraction. Charge symmetric nonpri-mary true electron backgrounds (from conversion and0
Dalitz decay) are subtracted by using the wrong-sign (WS,opposite to the expected primary electron charge) electronsample. In the following subsections, we break the analysisdescribed above into discrete steps.
A. PID yield
From a set of signal candidate tracks, we measure thePID yield yb; i in bins of PID type b, track momentumbin itrack, E (or M) signal and sideband regions iSB, and
right-sign (RS) or wrong-sign (WS) bin iRW depending onthe charge of the track and the flavor of the tag, where i is acollective index for itrack; iSB; iRW. The charge of thedaughter kaon defines the flavor of the D0 ! K tag,and the charge of the tag defines D ! K andDs ! tags. The RS track is defined to be the trackwith the same charge as the tagged D0 daughter kaon or tobe the opposite charge of the charged tags, and the WStrack is defined the other way around.
B. PID unfolding
We correct for PID efficiency and mis-PID crossfeedbackgrounds using
ya; i A1PIDbja; iyb; i; (4)where i is a collective index for itrack; iSB; iRW. The PIDmatrix APIDbja used in the unfolding is shown in Fig. 2.PID matrix elements associated with the charged pion areobtained from K0S ! events, the charged kaon ele-ments are obtained from D ! K events, and theelectron elements are obtained from radiative Bhabhaevents (ee) embedded in hadronic events. Here...