1. 2004-8-13, CCASTQinghua Xu, Shandong University1 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.

2. 2004-8-13, CCASTQinghua Xu, Shandong University2 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 exotic p.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.

3. 2004-8-13, CCASTQinghua Xu, Shandong University3 Previous study of polarized fragmentation function SU(6) DIS (Boros, Liang,PRD’98) fragmentation E.g., at the Z 0 pole, = -0.94 for f=s,d,b; = -0.67 for f=u,c.

4. 2004-8-13, CCASTQinghua Xu, Shandong University4 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).

5. 2004-8-13, CCASTQinghua Xu, Shandong University5 P H in high p T jets at RHIC Hyperon production with high p T : helicity distribution function longitudinally polarized fragmentation function

6. 2004-8-13, CCASTQinghua Xu, Shandong University6 Contribution of gluon and quark jet(s) to  production  Quark jets dominate the Hyperon production with high P T ! From gluon fragmentation From quark fragmentation PYTHIA Different subprocess : qq  qq, qg  qg, gg  gg ……, but :

7. 2004-8-13, CCASTQinghua Xu, Shandong University7 polarized fragmentation function  We divide the produced H i ’s in into four groups: (a) directly produced and contain the q f ; (b) decay products of polarized heavier hyperons ; (c) directly produced but don’t contain the q f ; (d) decay products of unpolarized heavier hyperons.  Those from (a) and (b) can be polarized, (c) and (d) are not !  Hence : : spin transfer factor : fraction of spin carried by q f in H i (q f ….)  SU(6), DIS for (b) q f  H j +X decay spin transfer factor in H j  H i +X’. can be obtained from generator (e.g.PYTHIA)

8. Results of hyperon polarization SU(6), set II SU(6), set I( GRSV00) DIS, set I DIS, set II(GRSV96) SU(6), set I DIS, set I SU(6), set II DIS, set II The decay contribution of  is very large, while origin of  + is much cleaner! (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. 2004-8-13, CCASTQinghua Xu, Shandong University9 containing fragmenting u containing fragmenting s decay contribution  Contribution of directly produced and contain a fragmenting u play the dominant role!  In the limiting case that there is only this contribution in :  Different models only differ in the constant, è Hence, we can study p.d.f. from P  + in pp reactions. Characteristic of  + production in pp  + X Polarization of fragmenting u, related to polarized p.d.f.

10. 2004-8-13, CCASTQinghua Xu, Shandong University10 P  + in and  g(x) Subprocesses involved, P  + in (dominant) (negligible)

11. 2004-8-13, CCASTQinghua Xu, Shandong University11 P  + in at BB02  g GRSV00  g AAC  g

12. 2004-8-13, CCASTQinghua Xu, Shandong University12 Transverse polarization of hyperons with high p T and  q(x) P H in transversely polarized pp collisions: For, similar as the longitudinally polarized case,

13. 2004-8-13, CCASTQinghua Xu, Shandong University13 P  + with p T >13 GeV in at Numerical results for  + polarization (J.Soffer) (B.Q.Ma et al) take for a simple assumption!

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

15. 2004-8-13, CCASTQinghua Xu, Shandong University15 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 q f 0 ; (B) do not contain the q f 0.  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(q f 0 q-bar) = Spin of q f 0 + Spin of q-bar

16. 2004-8-13, CCASTQinghua Xu, Shandong University16 transforming it to the coupled basis and obtain: Hence: The spin density matrix of V can be obtained from the product: Calculation of  V ( A,f) To get  V 00 (A,f ) > 1/3, signs of P f and P z should be opposite! P f is the polarization of q f 0,

17. 2004-8-13, CCASTQinghua Xu, Shandong University17 Fitting the data, we obtained that:

18. 2004-8-13, CCASTQinghua Xu, Shandong University18

19. 2004-8-13, CCASTQinghua Xu, Shandong University19 Spin alignment of V in pp-->VX (a) spin alignment of V in at  s=500 GeV and p T >13 GeV. Is this relation universal for the fragmentation of a longitudinally polarized quark ? Applying it to other process to make further tests ! DIS, pp collisions…

20. 2004-8-13, CCASTQinghua Xu, Shandong University20 Fig: Spin alignment of V in pp reaction at  s=500 GeV and p T >13 GeV. (b) in helicity frame Spin alignment in transversely polarized pp collisions (a) in transversity frame Light cone model Soffer inequality Further extents to the transversely polarized case!

21. 2004-8-13, CCASTQinghua Xu, Shandong University21 Summary Spin dependent fragmentation function is studied from P H in high p T 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.

22. Thank you!

23. 2004-8-13, CCASTQinghua Xu, Shandong University23 Polarization of h(q 0 x) from Fraction of spin carried by q 0 in a hadron h

24. 2004-8-13, CCASTQinghua Xu, Shandong University24 z-distribution of type (a)  +

25. 2004-8-13, CCASTQinghua Xu, Shandong University25 : independent of polarization properties, and can be obtained by hadronization model or event generator ( PYTHIA … )! Hyperon polarization can be given by: : decay spin transfer factor in H j  H i +X’. For hyperons of group (b), q f  H j +X H i +X ’

26. 2004-8-13, CCASTQinghua Xu, Shandong University26 P  + in BB02 GRSV00 AAC00

27. 2004-8-13, CCASTQinghua Xu, Shandong University27 Fig : P  + with 0<  <1.5 in at