Spin effects in fragmentation processes at RHIC

1. Spin effects in fragmentation processes at RHIC Qinghua Xu (徐庆华) Physics department, Shandong University References: Xu Q.H., Liu C.X., and Liang Z.T., Phys. Rev. D65, 114008 (2002); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D67, 114013 (2003); Xu Qing-hua, and Liang Zuo-tang, hep-ph/0406119. Qinghua Xu, Shandong University

2. Introduction • Spin-dependent fragmentation function(spin effect in frag.): • (study the polarization and/or momentum distribution of hadrons • produced in the fragmentation of a polarized quark.) • hadronization mechanism; • to study spin structure of nucleon, as filters for exoticp.d.f, e.g., g(x) andq(x)! • Hyperon polarizations (, +) are widely used to study • polarized fragmentation function, since their polarization • can be measured through their self-analyzing decay. Qinghua Xu, Shandong University

3. Previous study of polarized fragmentation function SU(6) fragmentation (Boros, Liang,PRD’98) DIS E.g., at the Z0 pole, <Pf>= -0.94 for f=s,d,b; <Pf>= -0.67 for f=u,c. Qinghua Xu, Shandong University

4. The DIS data available: • HERMES(PRD01), E665(EPC00) ----- large error ! • NOMAD(NPB00), better statistics, but energy too low ! • RHIC spin program (pp collision) is promising: • (a) high statistics (high luminosity) • (b) high energy (200-500GeV). • Available theoretical studies in pp collisions: • D.de Florian,M.Stratmann, W.Vogelsang, Phys. Rev. Lett. 81(1998); • C. Boros, J.T.Londergan, A.W.Thomas, Phys. Rev. D62 (2000); • B.Q. Ma, I.Schmidt, J.Soffer, J.J.Yang, Nucl. Phys. A703 (2002); • Xu Q.H., Liu C.X, Liang Z.T., Phys. Rev. D65, 114008 (2002). Qinghua Xu, Shandong University

5. PH in high pT jets at RHIC • Hyperon production with high pT: helicity distribution function longitudinally polarized fragmentation function Qinghua Xu, Shandong University

6. Contribution of gluon and quark jet(s) to  production • Different subprocess: qqqq, qgqg, gggg……, but : From quark fragmentation From gluon fragmentation PYTHIA • Quark jets dominate the Hyperon production with high PT ! Qinghua Xu, Shandong University

7. polarized fragmentation function • We divide the produced Hi’s in into four groups: (a) directly produced and contain the qf ; (b) decay products of polarized heavier hyperons ; (c) directly produced but don’t contain the qf ; (d) decay products of unpolarized heavier hyperons. • Those from (a) and (b) can be polarized, (c) and (d) are not! • Hence : can be obtained from generator (e.g.PYTHIA) : spin transfer factor • : fraction of spin carried by qf in Hi (qf….) SU(6), DIS • for (b) qf Hj +X decay spin transfer factor inHjHi +X’. Qinghua Xu, Shandong University

8. Results of hyperonpolarization • The decay contribution of  is very large, while origin of + is much cleaner! SU(6), set I(GRSV00) SU(6), set I SU(6), set II DIS, set I DIS, set I DIS, set II DIS, set II(GRSV96) SU(6), set II (1)Pis very small . (2) Difference between results of SU(6) and DIS is small. (3)Phas a strong dependence of different sets of f (x) ! • P+ is large . • Difference between results • of SU(6) and DIS is large. • P+ has a weak dependence • of different sets of f (x) !

9. Characteristic of + production in pp+X • Contribution of directly produced • and contain a fragmenting u play • the dominant role! • In the limiting case that there is • only this contribution in : containing fragmenting u containing fragmenting s decay contribution Polarization of fragmenting u, related to polarizedp.d.f. • Different models only differ in the constant , • Hence , we can study p.d.f. from P+in pp reactions. Qinghua Xu, Shandong University

10. P+ in and g(x) • Subprocesses involved, (dominant) (negligible) • P+ in Qinghua Xu, Shandong University

11. P+ in at BB02 g AAC g GRSV00 g Qinghua Xu, Shandong University

12. Transverse polarization of hyperons with high pT and q(x) • PH in transversely polarized pp collisions: • For , similar as the longitudinally polarized case, Qinghua Xu, Shandong University

13. Numerical results for + polarization (J.Soffer) (B.Q.Ma et al) take for a simple assumption! P+ with pT>13 GeV in at Qinghua Xu, Shandong University

14. Spin alignment of vector meson • Polarization of V: 00: Prob. of being in h= 0 state. • The data at LEP: • K*0 Spin alignment exists in fragmentation of a longitudinally polarized quark !

15. To study what the data tell us, we made the following calculations (1) We divided the produced vector mesons into two groups: (A) contain the initial quark qf0 ; (B) do not contain the qf0 . n(z|A,f),n(z|A): number density of V from (A) and (B), calculable using a MC event generator such as JETSET; V(A,f) and V(B): spin density matrix of V from (A) and (B). (2) We calculate V(A,f) and V(B) in the following way: (i) Vector mesons in group (B) are taken as unpolarized, i.e., 00(B)=1/3 (ii)V(A,f) is calculated according to the assumption: Spin of V(qf0q-bar) = Spin of qf0+Spin of q-bar Qinghua Xu, Shandong University

16. Calculation of V(A,f) • The spin density matrix of V can be obtained from the product: Pf is the polarization of qf0 , • transforming it to the coupled basis and obtain: To get V00(A,f ) > 1/3, signs of Pf and Pz should be opposite! • Hence: Qinghua Xu, Shandong University

17. Fitting the data, we obtained that: Qinghua Xu, Shandong University

18. Qinghua Xu, Shandong University

19. Spin alignment of V in pp-->VX • Is this relation universal • for the fragmentation of • a longitudinally polarized • quark ? • Applying it to other process • to make further tests ! • DIS, pp collisions… (a) spin alignment of V in at s=500 GeV and pT>13 GeV. Qinghua Xu, Shandong University

20. Spin alignment in transversely polarized pp collisions • Further extents to the transversely polarized case! Soffer inequality Light cone model (a) in transversity frame (b) in helicity frame Fig: Spin alignment of V in pp reaction at s=500 GeV and pT>13 GeV. Qinghua Xu, Shandong University

21. Summary • Spin dependent fragmentation function is studied from • PH in high pT jets in polarized pp collisions. We find that, • + is more suitable than  for this purpose. • + polarization in can provide important • information on g(x). • + polarization in can provide useful • information on q(x). Numerical results are given. • Spin alignment of vector meson in polarized pp collisions • are studied at RHIC energy. Qinghua Xu, Shandong University

22. Thank you!

23. Polarization of h(q0x) from • Fraction of spin carried by q0 in a hadron h Qinghua Xu, Shandong University

24. z-distribution of type (a) + Qinghua Xu, Shandong University

25. For hyperons of group (b),qf Hj +X Hi +X ’ : decay spin transfer factor in HjHi +X’. • Hyperon polarization can be given by: • :independent of polarization properties, and can be obtained by hadronization model or event generator (PYTHIA …)! Qinghua Xu, Shandong University

26. P+ in BB02 AAC00 GRSV00 Qinghua Xu, Shandong University

27. Fig: P+ with 0<<1.5 in at Qinghua Xu, Shandong University