1. Spin physics with STAR at RHIC
Qinghua Xu（徐庆华)
Shandong University(山东大学物理学院)
Introduction - spin structure of nucleon
STAR longitudinal spin program: results and status
STAR transverse spin program: results and status
Summary and Outlook

2. Spin of nucleon Proton Spin
Spin, as a fundamental degree of freedom, was discovered in 1925 by Uhlenbeck and Goudsmit, and plays a paramount role in studies of fundamental interactions, particle property and hadron structure.
Each particle has its spin,
integer or half-integer.
Important application- NMRI
G.Uhlenbeck
S.Goudsmit
Nucleons (proton& neutron), the
most abundant particles around us,
is spin 1/2, and it has a internal structure of quarks and gluons,
How is the proton spin 1/2 carried by its internal partons: quarks and gluons ?
Proton Spin

3. Spin structure of nucleon
In the naive Quark Model, the nucleon is made of three quarks - p(uud)
The quark spins make up the nucleon spin, since the quarks are in the s-orbit:
 =1
European Muon Collaboration (polarized Deep Inelastic Scattering)
“Spin Crisis”--- proton spin carried by quark spin is rather small:  ~ 0.2
In the Naïve QM, nucleon is made of three quarks and nothing else. So its spin is completely carried by 3 quarks’ spin, since it is in ground state.
Now we known that nucleon has a more complicated structure than just 3 constitute quark, but also contains a number of sea quarks and gluons. Then the natural question is, how is the spin structure now? To answer this, we first need to know and understand How large the contribution from quark spin is?
In 1988, EMC found that, the contribution from quark spin is rather small,
It is called spin crisis at that time, people are asking :” where are the rest of the proton spin?”
EMC results has forced us to rethink the nucleon spin structure and we currently think in terms of quark and gluon spins, and orbital momenta.. Even so, the expectation for strange quark polarization remains that it is negative. ~

4. Spin structure of nucleon
Spin sum rule (longitudinal case): (X.D. Ji 1997)
Quark spin,
Best known (~30%)
Gluon spin,
Poorly known
Orbital Angular Momenta
Little known (DVCS)
Polarized parton densities:
Now it is known that nucleon has a more complicated structure than just 3 constitute quark, but also contains a number of sea quarks and gluons. The nucleon’s spin is 1/2, a natural question is, how is the nucleon’s spin carried by its components?
The spin sum rule shows the 3 parts: quark’s spin, gluon’s spin and the OAM(although it is ground state). Among them, OAM is little known, gluon part is poorly known, which is being changed by RHIC. And the best known part is quark spin’s contribution, summed over all flavor. Today we will focus on strangeness part. In 1998, EMC first found quark part is suprisingly small than expected from QM. You may wonder the role of sea quark here.
The consequence of this assumption is DS is ~60%. We may conclude from this difference, this should be negative and play an important role.

5. World data on pol. and unpol. deep-inelastic scattering

6. Detailed knowledge on ∆q from global fit before RHICx
De Florian, Navarro, and Sassot, 2005

7. World efforts for spin physics
Current running
Lepton-nucleon scattering HERMES, COMPASS,
JLAB
Polarized proton-proton scattering, RHIC
Future facilities
eRHIC (BNL)
JPARC (Japan)
GSI-FAIR (Germany)
DESY
SLAC E 
Jefferson Lab
All these experiments have their unique coverage on
q, g, Lq,g, and they are complementary as well

8. RHIC- also the first polarized pp collider
pp Run Year
2002
2003
2004
2005
2006
2008
< Polarization> % 15 30
40-45
45-50 60 45
Lmax [ 1030 s-1cm-2 ] 2 6 16 35
Lint [pb-1 ] at STAR
(Longitudinal/Transverse)
0 / 0.3
0.3 / 0.25
0.4 / 0
3.1 / 0.1
8.5 / 3.4
0/3.1

9. STAR Detector TPC Barrel EMC BBC East BBC West  = -ln[tan(/2)]
EndCap
EMC
Barrel EMC
TPC
||<1.4
Charged particle momentum
BEMC
||<1.0
Neutral Energy
High pT Trigger
EEMC
1<<2
BBC
3.4<||<5
MinBias Trigger
Relative Lumi.
(also ZDC)
TPC
BBC
East
BBC
West
 = -ln[tan(/2)]
Blue beam
Yellow beam

10. The RHIC spin program
Helicity structure: determination of the parton distribution functions
Gluon polarization ∆g(x) in the nucleon
-- results and status (inclusive jet, hadrons)
-- future plan (di-jets, +jet, hadrons)
Flavor separation: sea quark polarization
-- RHIC 500 GeV program (W prodction)
Transverse spin effects:
Single spin asymmetry AN (SSA)
-- recent results on SSA of 0 from RHIC
QCD mechanisms (Sivers, Collins, high-twist)
-- recent results of di-jets production on Sivers effects at STAR

11. Accessing ∆g(x) at a proton collider
Longitudinal spin asymmetry:
f1
f2

12. Results on jet X-section and spin asymmetry
Experimental cross section agrees with
NLO pQCD over 7 orders of magnitude
PRL 100, (2008)
2005
PRL 97, (2006)
2006

13. Impact of RHIC early results on g(x)
de Florian, Sassot, Stratmann, Vogelsang, arXiv:
RHIC constraints
Early RHIC data (2005, 2006) included in a global analysis along with DIS and SIDIS data.
Evidence for a small gluon polarization over a limited region of momentum fraction (0.05<x<0.2)

14. Future inclusive jet measurements: Increasing Precision

15. Longitudinal asymmetry ALL with inclusive hadrons - complementary measurement for g

16. Future probes for g
Upcoming Correlation Measurements :

17. Sensitivity of di-Jets measurements

18. Direct Photon - Jet Correlations
Direct +jet dominated by qg-Compton process: 90% from qg x2
W.Vogelsang x1
Reconstruction of partonic kinematics
--> x-dependence of g !

19. Flavor separation of proton spin
Quark polarimetry with W-bosons:
Spin measurements:

20. Sensitivity of W measurements
Large asymmetries
dominated by quark
polarization: Consistency
check with DIS data.
With 300 pb-1 a strong
impact constraining the
unknown sea quark
polarizations.

21. Strange quark polarization
S~ from inclusive DIS
under SU(3)_f symmetry
D. de Florian et al, arXiv:
SDIS results at HERMES:
arXiv:
Let come back to DS, the strange sea part, here is a sign change around ~0.02 driven the Hermes SDIS data. But integration remains negative.
The uncertainty is still large, so more measurement are needed, but not seen in the RHIC main program. We asked, are there any opportunities at RHIC for DS?
Clear need to measure.
Can we do it with hyperons at RHIC?
- hyperons contain at least one strange quark and
their polarization can be determined via their weak decay.

22. DLL-Longitudinal spin transfer at RHIC
Expectations at LO show sensitivity of DLL for anti-Lambda to :
GRSV00-M.Gluck et al, Phys.Rev.D63(2001)094005
Pol. frag. func. models
Typ. range at RHIC
Q. X, E. Sichtermann, Z. Liang, PRD 73(2006)077503
We made predictions using 2 models for polarized fragmentation functions and 2 parameterizations for \delta s_bar versus \eta at large pT>8 GeV.
As we see, the anti_Lambda polarization is more sensitive to \delta s_bar models than to polarized fragmentation function, due to the dominance of s_bar quark.
The right plot shows the 2 parameterizations for \delta s_bar of GRSV So, this is a promising measurements, since neither the role of anti-strange polarization nor the fragmentation is well-understood. and effects are large enough to be observed.
The Lambda will be ….
Xi will be a bit more sensitive, since it contains two valence s_bar, but..
- Promising measurements---effects potentially large enough to be observed.
- DLL of  is less sensitive to s, due to larger u and d quark frag. contributions.

23. Spin transfer for Lambda hyperons

24. Transverse spin program
Single transverse-spin asymmetry
Basic QCD calculations (leading-
twist, zero quark mass) predict
AN~0
---AN~0.4 for + in pp at E704 (1991)
Understanding transverse spin effect:
Qiu and Sterman (initial-state) / Koike (final-state) twist-3 pQCD calculations
Sivers: spin and k correlation in initial state (related to orbital angular momentum)
Collins: spin and k correlation in fragmentation process (related to transversity)
STAR, Phys. Rev. Lett. 92 (2004)171801

25. Recent results on SSA X-section reproduced with pQCD
PRL97,152302(2006)
hep-ex/
X-section reproduced with pQCD
AN increase with xF, in agreement
with pQCD model calculation.

26. Recent results on SSA X-section reproduced with pQCD
STAR, PRL97,152302(2006)
X-section reproduced with pQCD
AN increase with xF, in agreement
with pQCD model calculation.
pQCD based models predicted
decreasing AN with pT , which
Is not consistent with data.
hep-ex/

27. AN results with di-jet production
Idea: directly measure kT by observing momentum imbalance of a pair of jets produced in p+p collision and attempt to measure Sivers distribution if kT is correlated with incoming proton spin
Boer & Vogelsang, PRD 69 (2004)
jet
AN pbeam  (kT  ST)
pbeam
into page
STAR 27

28. VY 1, VY 2 are calculations by
AN results with di-jet production
Emphasizes (50%+ )
quark Sivers
AN consistent with zero , different as the model predictions with Sivers fit from SDIS.
Sivers distribution, k -dependent distribution is not universal,
VY 1, VY 2 are calculations by
Vogelsang & Yuan, PRD 72 (2005)
STAR, PRL99,142003(2007)
STAR
Both effects occur in pp di-jets production, may cancel each other. 28

29. Future plan for transverse spin physics
Extend measurements of transverse single spin asymmetries from hadron production to prompt photon+jet production, to verify the theoretical understanding of Sivers distribution.
Develop RHIC experiments for a future measurement of transverse single spin asymmetries for Drell-Yan production of dilepton pairs.
A.Bacchetta et al., PRL99,2007

30. Summary STAR longitudinal spin program:
STAR ALL measurements via inclusive jets/hadron production: Important contribution to understanding of G!
Upcoming results on correlation measurements: Di-jets
Future measurements:
---Prompt photons and Flavor decomposition through W production
STAR transverse spin program:
Precise AN measurement of forward 0 production, pQCD model
calculation agree with the xF dependence, but not the pT dependence.
Di-jet AN measurement are found to be zero, in disagreement with
calculations based on quark Sivers functions from SDIS data.

31. Outlook Projected integrated luminosity through 2013 at RHIC:
Goal of beam polarization: 70%.
200 GeV has been achieved in 2006
500 GeV development achieved 45%

32. Backup slides

33. Measurements of longitudinal spin asymmetry
Ingredients:
Polarization P1,P2: measured by RHIC polarimeters
Relative Luminosity R measured with the STAR BBC & scaler system
Spin dependent yields N++,, N+- : number of detected jets/particles
for a given combination of beam polarization directions

34. Jet Finding in STAR

35.  from polarized inclusive DIS
How  is determined in inclusive DIS?
Now let’s see how DS is determined in DIS? Here, the lepton beam and the proton or deuteron target both need to be polarized and the polarized structure function can be measured from asymmetry of spin dependent cross section. This plot shows different measurement covering a wide range of bjorken x - the momentum fraction of proton carried by struck quark.
Then from the first moment of g1, actually the combination of DU,DD, and DS. 3 unknowns. Luckly, under the assumption of SU3 symmetry, the neutron decay and hyperon beta decay can also give information on 3 unknows.
Now data give DQ~30%, and DS minum indeed negative, no x dependence information.
--together with neutron, hyperon  decay data using SU(3)_f symmetry,
U~ 0.84,
D~ 0.43,
S~ 0.08
 = 0.33 0.030.010.03: (HERMES,Q2=5 GeV2)
Where are the rest of proton spin?