1. Spin of the proton and its transverse spin structure at RHIC HERMES seminar at Tokyo Tech November 9, 2005 Yuji Goto (RIKEN)

2. November 9, 2005Yuji Goto (RIKEN)2 RHIC – QCD collider

3. November 9, 2005Yuji Goto (RIKEN)3 RHIC polarized-proton collision Luminosity 1  10 31 cm -2 sec -1 at  s = 200 GeV achieved –8  10 31 cm -2 sec -1 at 200 GeV and 2  10 32 cm -2 sec -1 at 500 GeV in the future Polarization 50% achieved – 70% in the future installed and commissioned during in 2004 run installed in 2005 and to be commissioned to be commissioned

4. November 9, 2005Yuji Goto (RIKEN)4 STAR and PHENIX STAR detector 2  coverage for jet measurement barrel TPC and EMC endcap EMC PHENIX detector limited acceptance high resolution central EMCal high-rate trigger and DAQ forward muon detectors

5. November 9, 2005Yuji Goto (RIKEN)5 RHIC/PHENIX polarized-proton runs  s = 200 GeV P recorded L recorded LP 4 data volume 2001-2002 transverse-spin run 15% 0.15 pb -1 20 TB first polarized proton collisions 2003 longitudinal-spin run 27% 0.35 pb -1 1.5 nb -1 35 TB spin rotators commissioned, AGS p-C CNI polarimeter 2004 commissioning run (longitudinal spin) 40% 0.12 pb -1 3.3 nb -1 35 TB AGS warm snake commissioned, gas-jet absolute polarimeter 2005 longitudinal-spin run 49.5/44.5% 3.8 pb - 1 205 nb -1 262 TB AGS cold snake installed 2005 – First long longitudinal-spin polarized-proton run Figure of merit (LP 4 ) more than 40 times larger than that of previous runs

6. November 9, 2005Yuji Goto (RIKEN)6 Where is the proton spin ? Origin of the nucleon spin 1/2 –polarized DIS experiments showed the quark contribution is only 10-30% –gluon contribution ? Scaling violation in polarized DIS Semi-inclusive DIS –high-p T hadron pairs –open charm production B. Adeva et al., PRD 58, 112002 (1998). P.L. Anthony et al., PLB 493, 19 (2000). lepton beam  or  nucleon target ** gluon heavy flavor

7. November 9, 2005Yuji Goto (RIKEN)7 Gluon contribution ? Polarized hadron collision –leading-order gluon measurement A LL of  0 proton beam  or  gluon photon proton beam  or  gluon heavy flavor direct photon productionheavy-flavor production gg + qg dominant sensitive to the gluon reaction

8. November 9, 2005Yuji Goto (RIKEN)8 PHENIX A LL of  0 Theory modelC.L. (%) GRSV-std17.1-21.7 *GRSV-max (  g=g) 0.0-0.0 *GRSV  g=0 16.7-18.4 *GRSV  g=−g 0.0-0.7 * at input scale Q 2 = 0.4 GeV - Run5 conclusively excludes GRSV maximal scenarios. - Data consistent with GRSV standard and GRSV  G = 0. GRSV-max:  g = 1.84 GRSV-std:  g = 0.42 at Q 2 =1(GeV/c) 2 best fit to DIS data

9. November 9, 2005Yuji Goto (RIKEN)9 Single transverse-spin asymmetry Left-right asymmetry Forward-rapidity –Fermilab-E704 fixed-target experiment at  s = 19.4 GeV left right

10. November 9, 2005Yuji Goto (RIKEN)10 STAR forward pion Run2 results –In agreement with several models including different dynamics:  Sivers: spin and k  correlation in initial state (related to orbital angular momentum?)  Collins: Transversity distribution function & spin-dependent fragmentation function  suppressed? (hep- ph/0408356)  Qiu and Sterman (initial-state) / Koike (final-state) twist-3 pQCD calculations STAR collaboration, hep-ex/0310058, Phys. Rev. Lett. 92 (2004) 171801STAR

11. November 9, 2005Yuji Goto (RIKEN)11 STAR forward pion Run3 results –Positive A N at large positive x F has been confirmed Larger significance to be non-zero & positive than published data –The first measurement of negative x F A N has been done, and is consistent with zero Sensitive to twist-3 gluon- gluon correlation Statistical error only for =4.1

12. November 9, 2005Yuji Goto (RIKEN)12 STAR outlook Disentangling the dynamics of A N via –Higher precision A N measurement vs x F and p T –A N with mid rapidity correlation –Forward jet Proposal for forward calorimeter upgrade –Heavy mesons and direct photons –Low x gluons in nuclei Mid rapidity jets –Di-jet k T balance  gluon Sivers function –Inside jet particle correlation  Collins function * Transversity ~2.4m square ~1500 cells  =4.2  =3.2  =2.5 Current FPD

13. November 9, 2005Yuji Goto (RIKEN)13 Mid-rapidity at PHENIX Different kinematic region –forward-rapidity at STAR (x F > 0.3) quark-gluon reaction dominant large contribution from x ~ 0.6 quark polarization/transversity –mid-rapidity at PHENIX (x F ~ 0) contribution from both gluon-gluon and quark-gluon reactions x = 0.03 – 0.1 small quark polarization/transversity no gluon transversity in leading twist negligible transversity & Collins effect contribution

14. November 9, 2005Yuji Goto (RIKEN)14 Mid-rapidity at PHENIX Run2 results –A N for both  0 and charged hadrons consistent with zero at mid- rapidity –~5 times smaller asymmetry than STAR forward-rapidity data (~10%) –comparable data with Fermilab-E704 for  0 and charged hadrons Fermilab-E704

15. November 9, 2005Yuji Goto (RIKEN)15 Forward neutron asymmetry PHENIX local polarimeter R&D at IP12 EM Cal Base PbWO 4 Charge Veto Neutron VetoHadron Cal Base Pb Scintillator W+Fiber Cal Post-shower

16. November 9, 2005Yuji Goto (RIKEN)16 Forward neutron asymmetry Hadron CalEM Cal A N =  0.126  0.008  0.041A N =  0.116  0.018  0.020 preliminary very forward neutron A N ~ -12% x F > 0.2 p T < 0.3 GeV/c

17. November 9, 2005Yuji Goto (RIKEN)17 Local polarimeter at PHENIX Longitudinal component of the proton polarization at PHENIX 410 GeV run in 2005 –analyzing power of local polarimeter roughly the same despite doubling of energy 2005 run

18. November 9, 2005Yuji Goto (RIKEN)18 Back-to-back jet at PHENIX Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the  distribution of back-to-back jets Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets STST j1 j2 00 22  h Boer and Vogelsang, Phys.Rev.D69:094025,2004  N g =  N d (E704)

19. November 9, 2005Yuji Goto (RIKEN)19 Back-to-back jet at PHENIX Measurement of the gluon Sivers function via A N for di-hadron angular correlations –Sivers distribution is a transverse parton momentum distribution correlated with the nucleon’s spin axis, which could arise from orbital angular momentum –Error bars: Expected sensitivity with P=60% and 7 pb -1

20. November 9, 2005Yuji Goto (RIKEN)20 Back-to-back jet at STAR

21. November 9, 2005Yuji Goto (RIKEN)21 Spin dependence of k T of jets Possible helicity effect –We may observe net effect (after averaging over impact factor) k T larger k T smaller Same helicity Opposite helicity

22. November 9, 2005Yuji Goto (RIKEN)22 Spin dependence of k T of jets Run3 result: hint of helicity dependence ? –not yet sure Run5 data should yield a definite answer.

23. November 9, 2005Yuji Goto (RIKEN)23 Summary RHIC data began to provide restriction to the gluon- spin contribution to the proton spin –We need to know contribution of the orbital angular momentum as the final piece RHIC has potential measurements of the orbital angular momentum and/or transverse spin structure of the proton –single transverse-spin asymmetries –Sivers effect/function measurements –… We will have some transverse-spin run in 2006

24. Backup slides

25. November 9, 2005Yuji Goto (RIKEN)25 Naohito’s analysis

26. November 9, 2005Yuji Goto (RIKEN)26 Vertical vs radial run in 2006 Boer and Vogelsang, PRD69:094025,2004 STST STST  1 = 0  1 =  /2  1 = 0 :  1 =  /2 : private communication, Boer and Vogelsang

27. November 9, 2005Yuji Goto (RIKEN)27 Spin dependence of k T of jets Back-to-back nature of jets is broken by initial/final state transverse momentum k T （ e.g., intrinsic k T, soft gluon radiation ） Orbital angular momentum: k T × r introduces intrinsic k T in the initial state  measurement of jet k T gives an access to parton orbital angular momentum

28. November 9, 2005Yuji Goto (RIKEN)28 Transversity at PHENIX Transversity throught  +  - interference FF –non-vanishing “support” only in the  mass region Jet Proton Structure Hard Scattering Process Interference Fragmentation ,, 200 GeV 500 GeV Maximum Asymmetry

29. November 9, 2005Yuji Goto (RIKEN)29 Transversity throught  +  - interference FF Projected asymmetry Small aymmetry below 5% but good rate! For 32pb -1 (1 week of running) 5.2 Million events in 32 pb -1 15% with pair after cuts