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Qinghua Xu, ( LBNL) EIC workshop, July 19, 206

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

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Qinghua Xu, ( LBNL) EIC workshop, July 19, 206

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

  2. Why do we study Lambda? • With its “self-analyzing” decay ->p+(Br~64%), the Lambda polarization • can be measured from the angular distribution of decay proton: Unit vector along proton momentum in rest frame. polarization vector decay parameter 0.642(PDG) •  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 .

  3. 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 • Transverse  polarization with pol. beam: • fixed Target pp: E704 (PRL’97), DISTO(PRL’99)… • lepton-nucleon:COMPASS • pp collider : RHIC

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

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

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

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

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

  9. (anti)Lambda polarization with STAR • 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 Stat. error ~0.05 • Kinematics : • |<xF>|~0.008 • <pT>~1.5GeV PANIC05: Q.Xu for the STAR • 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! • This is essentially the only way in which RHIC can access strangeness, • since the charm-associated W production will be luminosity hungry.

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

  11. Transverse polarization of hyperon in pp Transverse polarization direction of the parton may be changed in the hard subprocess! Spin transfer factor in hard scattering can be obtained with pQCD. qout qin J.Collins et al, NPB420 (1995)565 Magnitude of transverse polarization: Q. Xu, Z. Liang, PRD 70, (2004) (J.Soffer) (B.Q.Ma et al) -1 0 1 

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

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

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

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

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

  17. 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: Df/ Df ~ Qf () : average polarization of qf in 

  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 : (M.Burkardt, R.Jaffe, 1993) DIS data Neutron, hyperon beta decay data A feeling of possible difference among Du,Dd ,Ds!

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

  20. Relative contribution of different flavors Lambda Anti_Lambda Ee=10 GeV Ep=250 GeV PYTHIA • Anti_Lambda is dominated by s_bar frag. at large xF ! • --- good measurement of Ds_bar(z)/Ds_bar(z) • Anti_Lambda pol. will be larger than  at large xF if Du(d) is small! • Different , anti_Lambda pol. at xF<0.4 will indicates sizable Du ! ---effects from decay contribution and target remnant not included.

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

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

  23. Summary • 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 Ds-bar(z) at large xF from anti_Lambda pol. • Information s_bar(x) can be accessed with anti_Lambda polarization in case Pl=0, PN0! • Transverse  polarization can give an access to transversity distribution of nucleon!

  24. Backup slides

  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 : (M.Burkardt, R.Jaffe, 1993) DIS data Neutron, hyperon beta decay data SU6 Agree with available data on small Du ! DIS (C.Boros, Z.Liang, 1998)

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