1. 1 Qinghua Xu, (LBNL) EIC workshop, July 19, 206 Introduction Spin transfer of (anti)Lambda in pp collisions (anti)Lambda polarization in lp collisions Summary Spin transfer of Lambda in polarized ep collider

2. 2 With its “self-analyzing” decay  ->p  + (Br~64%), the Lambda polarization can be measured from the angular distribution of decay proton: decay parameter 0.642(PDG) Unit vector along proton momentum in  rest frame.  polarization vector  polarization palys an important role in spin physics: 1. Well-known transverse polarization in unpolarized pp, pA ( G. Bunce et al 1976 ). 2. Study pol. fragmentation function and spin content of hyperon. 3. A tool to study spin structure of nucleon. Why do we study Lambda?

3. 3 Transverse  polarization with pol. beam: fixed Target pp: E704 (PRL’97), DISTO(PRL’99)… lepton-nucleon : COMPASS pp collider : RHIC Experiment overview on Lambda polarization Longitudinal  polarization: e+e-: ALEPH(PLB’96), OPAL(EPJC’98); Polarized lepton-nucleon DIS: E665(EPJC’00), HERMES(PRD’01), NOMAD(NPB’01), COMPASS Polarized pp collider: RHIC

4. 4 Study polarized fragmentation function with  polarization in pp : Lambda polarization in pp collisions QM DIS equal contr. (D.de Florian, M.Stratmann, W.Vogelsang, PRL’98)

5. 5 Q. Xu, E. Sichtermann, Z. Liang, PRD’06 Anti-Lambda polarization at high pT are sensitive to strange quark polarization, more so than the spin transfer models in fragmentation. Anti_ Lambda polarization in pp collisions Q. Xu, E. Sichtermann, Z. Liang, PRD 73, 077503(2006) discardkeep

6. 6 Inclusive (anti)Lambda with STAR AGS Heclical Partial Snake 4 spin orientations : ++,+-,-+,-- Stable polarization direction - transverse Longitudinal polarization at STAR/Phenix

7. 7 primary vertex p V0_vertex V0_DCA  The cross-section of inclusive  has been measured with STAR, and reasonably described by NLO calculation. TPC PANIC05: M.Heinz for the STAR collaboration Inclusive (anti)Lambda with STAR

8. 8 Extracting pol. from the asymmetry Momentum distribution of decay proton: Assuming 2  sample with opposite pol., consider a small bin in  : [  1,  2 ]: A(cos  ): detector acceptance (acceptance is cancelled!) Symmetry relations Extraction of Lambda polarization: N +(-) : number of  with beam positively (negativly) polarized

9. 9 D_LL with data of 0.8 pb -1 in 2003 and 2004: No. of events: ~30 K for Lambda ~27 K for anti-lambda Kinematics : | |~0.008 ~1.5GeV Stat. error ~0.05 With data of 2005 (~3 pb -1 ) and 2006 (~8 pb -1 ), a stat. error of 0.03 with pT>4GeV can be reached. --- ~100 pb -1 data needed to get stat. error of ~0.01 at pT>8 GeV! PANIC05: Q.Xu for the STAR (anti)Lambda polarization with STAR This is essentially the only way in which RHIC can access strangeness, since the charm-associated W production will be luminosity hungry.

10. 10 Transverse polarization of hyperons in pp and  q(x) P H in transversely polarized pp collisions: transversity distribution :  f(x) = f  (x) - f  (x) pQCD Information on  T D(z) or  q(x) can be accessed via transverse Lambda polarization in pp collisions. ---  T D(z) is one of the few quantities can decouple  q(x) as well as the Collins frag. function, Drell-Yan process…

11. 11 Transverse polarization of hyperon in pp J.Collins et al, NPB420 (1995)565 Transverse polarization direction of the parton may be changed in the hard subprocess! Spin transfer factor in hard scattering can be obtained with pQCD. Magnitude of transverse polarization:  01 Q. Xu, Z. Liang, PRD 70, (2004) q in q out (J.Soffer) (B.Q.Ma et al)

12. 12 Longitudinal  polarization in letpon-nucleon reactions P N =0, P l  0: current fragmentation region Polarization of scattered quark : clean measurement of pol. fragmentation function polarized p.d.f Depolarization factor Lar ge y needed to have big D(y)! P N  0, P l =0: (P l, P N : pol. of lepton and nucleon)

13. 13 Current fragmentation & target remnant effects HERMES: E e = 27 GeV (CME=3.6 GeV) NOMAD: E nu = 44 GeV (CME=4.5 GeV) COMPASS: E mu = 160 GeV (CME=8.7GeV) E665: E mu = 500 GeV (CME=15GeV), limited by statistics Containing at least one valence quark from the target Containing the struck quark H.Dong et al, PRD 72, 033006(2005) EIC collider: much better with sqrt(s)=22 ~100 GeV E e = 27 GeV  Low CME : there is some contribution from target remnant fragmentation at x F >0 other than from current quark.( x F =p l /p lmax in hadronic frame) Target remnant contri. J. Ellis et al, EPJC 25, 603(2002) HERMES NOMAD COMPASS LEPTO

14. 14 NOMAD  With remnant contribution Without remnant contribution Z. Liang, C.Liu, PRD 66(2002) Example of target remnant effects   The scattered quark is polarized with pol.=-1 with nutrino CC reaction Data of  pol. at NOMAD:

15. 15 The measured quantity at HERMES and COMPASS: S(y) is determined by  D f (z)/ D f (z) and their relative contributions of each flavor! Data with P N =0, P l  0: M.G.Sapozhnikov et al, hep-ex/0503009

16. 16 hep-ex/0607004 Data with P N =0, P l  0: HERMES, hep-ex/0607004 relative contributions of each flavor u quark dominate  production Measured small spin transfer  D u (z) is small (within stat. error)!

17. 17  D f / D f ~  Q f (  ) : average polarization of q f in  The spin transfer in fragmentation is expected to be related to the spin content of Lambda. G.Gustafson, J.Hakkinen, 1993 C.Boros, Z.Liang,1998 D.Ashery, H.J. Lipkin,1999 B.Q.Ma, J.J.Yang, I. Schmidt, 2000 For those Lambdas directly produced and contains the struck quark, assuming its helicity is preserved during the fragmentation process:

18. 18 Spin content of Lambda  SU(6) : SU(6) wave function of (Quark Model)  DIS : obtained from DIS data for proton and SU(3) flavor symmetry : Neutron, hyperon beta decay data DIS data (M.Burkardt, R.Jaffe, 1993) A feeling of possible difference among  D u,  D d,  D s !

19. 19 SPIN2005 M.G.Sapozhnikov et al, hep-ex/0602002 Pb= -0.76 What does it mean if they are different or same? Different polarization for Lambda and anti_Lambda?

20. 20 Relative contribution of different flavors Anti_LambdaLambda E e =10 GeV E p =250 GeV PYTHIA Anti_Lambda is dominated by s_bar frag. at large x F ! --- good measurement of  D s_bar (z)/ D s_bar (z) Anti_Lambda pol. will be larger than  at large x F if  D u(d) is small ! Different , anti _Lambda pol. at x F <0.4 will indicates sizable  D u ! ---effects from decay contribution and target remnant not included.

21. 21 There is no contamination from gluon at leading order! Longitudinal Lambda pol. with P N  0, P l =0:  polarization related with helicity distribution of quark in nucleon: Information of  s_bar(x) can be accessed with anti_Lambda polarization with P N =0, P l  0 ! N  D s_bar (z)/ D s_bar (z) can be extracted from anti_Lambda polarization at large x F with P N =0, P l  0 ! Anti_Lambda

22. 22 Transverse Lambda polarization in ep collier Information on  q(x) or  T D(z) can be accessed via transverse polarization of Lambda in ep and pp! Polarization of scattered quark: P q is independent of lepton polarization, and small y is required ! transversity (Artru, Mekhfi 1991)

23. 23 Spin transfer of Lambda and anti-Lambda in polarized pp collisions being measured with STAR at RHIC (Anti)Lambda polarization with high precision at ep collider  give new insights into spin transfer in fragmentation process, especially access of  D s-bar (z) at large x F from anti_Lambda pol.  Information  s_bar(x) can be accessed with anti_Lambda polarization in case P l =0, P N  0!  Transverse  polarization can give an access to transversity distribution of nucleon! Summary

24. 24 Backup slides

25. 25 Spin content of Lambda  SU(6) : SU(6) wave function of (Quark Model)  DIS : obtained from DIS data for proton and SU(3) flavor symmetry : Neutron, hyperon beta decay data DIS data (M.Burkardt, R.Jaffe, 1993) Agree with available data on small  D u ! SU6 DIS (C.Boros, Z.Liang, 1998)