M. Grosse Perdekamp, UIUC
Transverse Spin Measurements at RHIC
Workshop on Transverse Spin and the Transverse Structure of the Nucleon
3rd Joint Meeting of the DNP and the JPS in Waikola, Hawaii,
October 13h -17th , 2009 STARSTAR
M. Grosse Perdekamp, UIUC
Transverse Spin Measurements at RHIC
Inclusive Single Spin Asymmetries AN
in Hadron
Introduction RHIC Measurements Interpretation
Measurements to Isolate different Mechanisms Tansversity & Collins Sivers
Future Measurements Drell Yan & Jet-Photon
STARSTAR
Single Spin Asymmetries (SSA) in Hadron Collisions
Introduction
4
Single Spin Asymmetries (SSA) AN in Polarized Proton-Proton Scattering
sp
π
pp
π spp
p
= 0 ? AN =
NL - NR
NL + NR
NL : pions to the left
NR : pions to the right
Xpp Example:Inclusive π productionin polarized p-p
Correlation proton spin Sp vs pπ⊥ π transverse momentum
Single transversespin asymmetries AN
October 13th Transverse Spin Measurements at RHIC
5
Scaling Limit: AN 0 , QCD Test !?
4q 10, 20,3m example, N
qN AGeVsMeV
s
mA
October 13th Transverse Spin Measurements at RHIC
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Experiment: Sizeable SSA Observed over Large Range of Scales !
Experiment: AN >> 10-4 for 4 GeV < √s < 200 GeV for charged pions !
from Christine Aidala, Spin 2008 andDon Crabb & Alan Krisch in then Spin 2008 Summary, CERN Courier, 6-2009
ZGS √s=4.7 GeV AGS √s=6.5 GeV FNAL √s = 20 GeV RHIC √s = 200 GeV
π+
π-
October 13th Transverse Spin Measurements at RHIC
Soft effects due to QCD dynamics in hadronsremain relevant up to scales where pQCD canbe used to describe the scattering process!
7
NLO pQCD Cross Sections vs RHIC data for Different √s and Rapidity Intervals
√s = 200 GeV
∆ PHENIX π0, η = 0∙ Brahms π+ ,η = 2.95 ⌷ STAR π0 ,η = 0
- - - - - NLO pQCD
√s = 62.4 GeV
See analysis in De Florian, Vogelsang, Wagner PRD 76,094021 (2007) and Bourrely and Soffer Eur.Phys.J.C36:371-374 (2004)
o PHENIX π0, η = 0-------- NLO pQCD
Good agreement between inclusivehadron cross sections from RHIC data and pQCD calculations !
pT [GeV]pT [GeV]
October 13th Transverse Spin Measurements at RHIC
8
Origin of Large SSA Inspect Factorized Cross Section at Hard Scales!
2P
)( 1xqi
)( 2xG
11Px
22PxijLLa
1ps
Jet
proton structure
hard scattering reaction
fragmentationprocess
),(
)(ˆ)(),( ,
21
3
2,121
3
. Thqlkji
Tqi pzFFdxdx
qqqqdxGkxq
dzdxdx
Xppdlk
Final state – hadron fragmentation
pQCD
Initial state – proton structure
Kane, Pumplin, Repko aLL~10-4)
Can initial and/or final state effects generate large transverse spin asymmetries? (AN ~10
-1)
October 13th Transverse Spin Measurements at RHIC
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Origin of Large SSA for Hard Scattering --Two Solutions: Final State vs Initial State
(I) “Transversity” quark-distributions and Collins fragmentation
Correlation between proton- und quark-spin and spin dependent fragmentation
),()( 221
kzHxq
(II) Sivers quark-distribution+
Correlation between proton-spin and transverse quark momentum
)(),( 21 zDkxf h
T
Collins FFQuark transversespin distribution
Sivers distribution
(III) Initial or final state twist-3+
Qiu/Sterman and Koike
STAR, PRL-92:171801, 2004
+ unified picture: Ji, Qiu, Vogelsang and Yuan in PRL-97:082002, 2006
October 13th Transverse Spin Measurements at RHIC
First measurement atRHIC √s = 200 GeV
RHIC Measurements of AN
for Inclusive Hadrons
11
BRAHMS: AN for Charged Pions vs pT and xF at √s=62.4 GeV and √s=200 GeV
200 GeV
√s=200 GeV
√s=62.4 GeV
0.4<pT<0.6 GeV/c 0.5 pT<0.6 GeV/c 0.6 pT<0.8 GeV/c 0.8 pT<1.0 GeV/c 1.0 pT<1.2 GeV/c
0.5<pT<0.75 GeV/c1.0<pT<1.25 GeV/c 1.25<pT<1.5 GeV/c 1.5<pT<2.0 GeV/c 2.0<pT<2.5 GeV/c
AN increases withxF (valence quarks)
AN increases with pT (?)
Possibly constantfrom pT =1.5 GeV/c ?
October 13th Transverse Spin Measurements at RHIC
PHENIX: AN vs XF for 0’s at √s=62.4 GeV
AN = 0 for xF < 0 no sizeableasymmetries at small x!
Larger forward asymmetries at higher pseudo-rapidity, η ?
Limited by statistics and correlations between xF, pT and η !
October 13th Transverse Spin Measurements at RHIC
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STAR Run 2006: pT Dependence of AN at √s=200 GeV PRL 101,222001
For given η strong correlation between xF and pT:
AN(pT)integratedover xF
AN(pT, xF)
AN increases with pT up topT ~ 3 GeV/c -- Models: AN ~ 1/pT
October 13th Transverse Spin Measurements at RHIC
Decrease as ~1/pT expected from initial state effects is not observed.AN constant from pT>2.5 GeV. Need more statistics to extend measurement to pT > 4 GeV !
Positive xF Negative xF
Consistent with zero for all pT
STAR Run 2008: pT Dependence of AN at √s=200 GeV Ogawa at CIPANP 2009
October 13th Transverse Spin Measurements at RHIC
K p
Large AN for K- significant Sivers asymmetries for sea quarks ?!
Large AN for anti-Proton unexplained.
BRAHMS: AN for Charged Pions ,Kaons and Protons at √s=200 GeV
October 13th Transverse Spin Measurements at RHIC
Another Surprise: AN for Eta Mesons larger than for Pions !
STARSTAR0.361 0.064NA
0.078 0.018NA
GeV 200
s
Xpp
AN(η) > AN(π0) for 0.55 < xF < 0.75
Does this point to large effectsin the fragmentation?
STAR arXiv:0905.2840 (Heppelmann, DIS08)
October 13th Transverse Spin Measurements at RHIC
17
Understanding of AN in terms of Collins and Sivers Effect:
Work in Progress! Future goal: Extract Sivers and transversity quark distributions from global anlaysis to all SIDIS, pp and e+e- data!
Present work: Extract Sivers + transversity from SIDIS and e+e- and predict AN in pp
Presently: Poor agreement with many problems to solve! Universality, evolution, pdf and fragmentation functions not sufficiently known.
For example, note the impact of un-polarized FFs thick line DSS thin line Kretzer
October 13th Transverse Spin Measurements at RHIC
STAR π0
BRAHMS π+,-
Global analysis of SIDIS & e+e-
Anselmino, Boglione, D’Alesio,Kotzinian, Murgia, Prokudin, TurkPhys. Rev. D75:05032,2007
AN calculation from D’Alesio
18
A RHIC and US-Japan Contribution to Transverse SpinAnalysis: Measurement of the Collins Effect in e+e- Annihilation into Quarks at Belle BNL-Illinois-RBRC-RIKEN
q1
quark-1 spin
electron
positron
q2quark-2
spin
e++e- π+ + π- + X
~ Collins(z1) x Collins (z2)
October 13th Transverse Spin Measurements at RHIC
Belle Collinsasymmetries & global fit
Collins FF extracted from Belle data.
Measurement of the Collinseffect in e+e- at Belle:
SSA in Very Forward Neutron Production
neutron
Large negative SSA observed for xF>0
Diffractive physics Highly useful as local polarimeter at PHENIX
October 13th Transverse Spin Measurements at RHIC
Measurements to Isolate Different Mechanisms o Transversity & Collins o Sivers
21
Ideas for Measurements of Transversity Observables
at RHIC
][
][
Xpp
Xhjetpp
Xpp
Xllpp
hemisphere
hemisphere
Drell Yan:Required luminosity not available at RHIC.
Spin dependent Lambda-FF unknown.Measure Λ-FF in e+e- ?
Collins effect in jets:Forward calorimeter upgrade in PHENIX
Di-hadron intereference fragmentation function. IFF data available from e+e- Belle !
October 13th Transverse Spin Measurements at RHIC
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Interference Fragmentation –IFF- for Di-Hadrons at Mid-Rapidity in
PHENIX
AUT compatible ~0
Dilution from gg processes!
Future:
Update with more statistics Study possibility of forward measurements: enhance qg fraction and higher x.
October 13th Transverse Spin Measurements at RHIC
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IFF Measurement in e+e- at BELLE
1 2( ) ( )jet jete e X
Artru and Collins,
Z. Phys. C69, 277 (1996)
Boer, Jakob, and Radici,
PRD67, 094003 (2003)
Vossen, Spin Conference in Dubna
October 13th Transverse Spin Measurements at RHIC
q1
quark-1 spin
electron
positron
q2
quark-2 spinzpair-1
zpair-1
z1,2 relative pion-pair momenta
ϕpair-1ϕpair-21
1 2
2 θ
22 2
12 1 1 1 1 2 22
sin~ ( , ) ( , )
1 cos pair pair pair paira H z M H z M
PreliminaryPreliminary
Preliminary
Preliminary
PreliminaryPreliminary
Preliminary
Preliminary
Preliminary
Belle IFF- Asymmetries vs Hadron Pair Momentum Fraction zi
9x9 z1 z2 binning
z1
a12
BNL-Illinois-RBRC-RIKEN
October 13th Transverse Spin Measurements at RHIC
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Ideas for Measurements of Sivers Observables at RHIC
llpp
Xjetpp
Xpp
Xjetpp
Xflavorheavypp
Xjetjetpp
Xhpp
0
Precision measurement of AN at mid-rapidity.
Back-to-back correlations for jets.
AN for inclusive jets.
AN for heavy flavor.
AN for direct photons.
AN in jet-photon production.
AN in Drell Yan.
significant improve-ments from upgrades: forward calorimeters+ silicon vertex detectors
October 13th Transverse Spin Measurements at RHIC
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AN from 0 and h+/- at Central Rapidity
PRL 95, 202001 (2005)
Analysis with high statistics 2006+2008 data in progress Statistical uncertainties will reduce by factor 7.
PHENIX AN(η=0), Run 2002 PHENIX AN(η=0), Run 2005Anselmino et al, Phys. Rev. D 74, 094011
Constrain gluon Sivers effect with PHENIX 2002 0 data !
October 13th Transverse Spin Measurements at RHIC
Process Contribution to 0, η=0, s=200 GeV
27
AN in Di-Jet Production in STAR
zx
y
180º
proton spin
1S
Di-jet pT
Additional kT kick to jet axis from Sivers effect Boer & Vogelsang, PRD 69, 094025 (2004)
parton
kK
Gluon radiation
Di-jet pT
STAR: PRL-99:142003,2007
Di-jet AN consistent with 0 and consistent with DIS
October 13th Transverse Spin Measurements at RHIC
Sivers Effect in Heavy Flavor Production
Heavy flavor production gives sensitivity to gluon Sivers effect . Significant improvement with vertex detector upgrades. Work needed to connect theory and experimental observable.
Anselmino et al, PRD 70, 074025 (2004)
Gluon Sivers=0
Gluon Sivers=Max
Calculations for D mesons
Measurement for -
Future Measurements ofSivers Asymmetries in the
Drell Yan and Jet-Photon Channels
30
Transverse Spin Drell Yan at RHIC vs π-Sivers Asymmetry in Deep Inelastic
Scattering
• Important test at RHIC of the fundamental QCD prediction using gauge link formalism of the non-universality of the Sivers effect!
• Requires very high luminosity (~ 250pb-1)
October 13th Transverse Spin Measurements at RHIC
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Soft Gluon Interaction in the Initial and Final State of Hard Scattering Processes
...
22/
||)(1
~...
pOpQCQ
...ndtt
Integrate initial state gluon radiation: gauge linkand insert gauge link in hard scattering matrix element
Integrate final state gluon radiation: gauge link and insert gauge link in hard scattering matrix element
October 13th Transverse Spin Measurements at RHIC
Unique predictions forprocess dependence:SIDIS vs Drell Yanor direct photon at RHIC!
32
Drell Yan at RHIC
ϒ-states
J/Ψ
Drell Yan
Ψ’
charm
bottom
FVTX enables DY measurement byrejecting heavy flavor background:Measurement: 4 GeV < Q < 10 GeV
yie
ld in
arb
itra
ry
un
its
October 13th Transverse Spin Measurements at RHIC
Bland et al. “Transverse Spin Drell-Yan Physics at RHIC”http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf
33
0.1 0.2 0.3 x
Siv
ers
Am
plitu
de
0
Experiment SIDIS vs Drell Yan: Sivers|DIS= − Sivers|DY
Test Unique Prediction of Gauge Theory
HERMES Sivers Results
Markus DiefenthalerDIS WorkshopMűnchen, April 2007
0
RHIC Drell Yan Projections
October 13th Transverse Spin Measurements at RHIC
Bland et al. “Transverse Spin Drell-Yan Physics at RHIC”http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf
34
ANphoton+Jet : An Alternative Test of the
Process Dependence of the Sivers Effect at RHIC
Bachhetta, Bomhof, D’Alesio, Mulders, MurgiaPhys.Rev.Lett.99:212002,2007.
Weig
hte
d m
om
en
t of
AN
ph
oto
n+
Jet
no process dependence
Correct process dependence
Measurement: AN in jet-photon productionforward photon η > 2jet -1 < η < 0
Much less luminosity hungry …
NSAC milestone for transverse spin (HP-13, 2015) ! Reachable at STAR. Requires FOCAL upgrade in PHENIX.
October 13th Transverse Spin Measurements at RHIC
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Summary
Single spin asymmetries found in the past at low center of massenergies persist at the highest center of mass energies at RHIC.
Precise AN data for inclusive hadrons are available from RHIC. Morestatistics is still needed to characterize the kinematic dependence ofAN at high pT. The theoretical analysis of AN into Collins and Sivers contributions continues to be challenging.
SSA in forward neutron production discovered at RHIC, are sizeable at all center of mass energies and used for local polarimetery at RHIC.
Several observables exist that will permit to isolate Sivers and Collins effects at RHIC. These measurement will benefit from detector and luminosity upgrades in progress at RHIC.
The newly developed gauge link formalism makes uniquepredictions for the process dependence of Sivers asymmetries that can be tested at RHIC in Drell Yan or Jet-Photon production.
October 13th Transverse Spin Measurements at RHIC
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Backup
October 13th Transverse Spin Measurements at RHIC
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Simple QEDexample:
DIS: attractive Drell-Yan: repulsiveSame in QCD:
As a result:
Non-universality of Sivers Asymmetries:Unique Prediction of Gauge Theory !
October 13th Transverse Spin Measurements at RHIC
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Collins Effect in Quark FragmentationJ.C. Collins, Nucl. Phys. B396, 161(1993)
q
momentum hadron relative : 2
z
momentum hadron e transvers:
momentum hadron :
spinquark :
momentumquark :
h
sE
EE
p
p
s
k
h
qh
h
h
q
qs
k
hph
,
Collins Effect:Fragmentation of a transversely polarizedquark q into spin-less hadron h carries anazimuthal dependence:
hp
sin
qh spk
October 13th Transverse Spin Measurements at RHIC
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General Form of Fragmentation Functions
h
qhh
hqhqh
h
q zM
spkpzHzDpzD
ˆ ),()(),( 2,
1,
1
Number density for finding hadron h from a transversely polarized quark, q:
unpolarized FF Collins FF
October 13th Transverse Spin Measurements at RHIC
IFF- a12 vs Invariant Mass8x8 m1 m2 binning
40
PreliminaryPreliminary
Preliminary
Preliminary
Preliminary Preliminary
Preliminary
PreliminarySystematic errors shown.a12 increases with m1 and m2
reaches |a12 | ~ 0.1 at large mi.
m1 [GeV/c2]
a12
41
The Sivers Effect
proton
Sp
Sp
proton
Sivers function:D. Sivers 1990
Sivers:
Correlation between the transverse spin of theproton and the transverse momentum kT of quarks and gluons in the proton (link to orbitalangular momentum?)
M
SkPkxfxqA PTq
TN
)ˆ(
),()( 2211Observed asymmetry:
October 13th Transverse Spin Measurements at RHIC