Spin Structure of Nucleon and Spin Transfer in High Energy Fragmentation Processes

1. Spin Structure of Nucleon and Spin Transfer in High Energy Fragmentation Processes 梁作堂 (Liang Zuo-tang) 山东大学(Shandong University) • What is the problem ? • How to study the problem ? • Results and discussions References Boros & Liang, PRD 57, 4491 (1998); Liu & Liang, PRD62, 0904001(2000); Liu, Xu & Liang, PRD64, 073004 (2001); Xu, Liu and Liang, PRD65, 114008 (2002) ; Liang & Liu, PRDD66, 057302 (2002); Xu and Liang, PRD70, 034015 (2004). 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

2. Introduction Two different pictures for the quark spin composition of nucleon: • The SU(6) quark model • The DIS picture Question: Extending to other baryons? 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

3. Extracting  from Inclusive DIS data Quark Parton Model: Integrated over x: Operator expression: SUf(3) Symmetry in Hyperon Decay Wigner-Eckart Theorem: The 8-dimensional representation of the SUf(3) group. E.g.: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

4. Further Implications (1) Flavor decomposition: (2) Quark spin compostion for other baryons in the JP=(1/2)+ octet All these results are as reliable as those for proton! 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

5. Question: Which should be used for fragmentation? Before 1998, no discussion was made. One simply uses: SU(6) picturein describing hyperon polarization in pp/pA collisions: E.g.: Andersson, Gustafson,Ingelman, Phys. Lett. 85B(1979); DeGrand & Miettinen, Phys. Rev. D24 (1981); Pondrom, Phys. Rep. 122 (1985); Liang & Boros, Phys. Rev. Lett. 79 (1997); … … … … … DIS picture in describing hyperon polarization in deeply inelastic lepton-nucleon scattering: E.g.: Jaffe, PRD54 (1996); Artru & Mekhfi, Z. Phys. C45(1990); Burkardt, Jaffe, Phys. Rev. Lett. 70 (1993); … … … … … Test by experiments (Boros & Liang, PRD 1998). 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

6. Spin transfer can be studied produce a polarized quark beam, measure the polarization of h. To study the spin transfer, we need to:  Hyperon production in the following reactions is ideal to study this problem, since, Quark polarization can easily be calculated. Hyperon polarization can easily be measured. fragmentation E.g., at the Z0 pole, <Pf(q)>=-0.94 for qf=s,d,b; <Pf(q)>=-0.67 for qf=u,c. current fragmentation region 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

7. Boros, Liang, PRD(98). Calculation method ofPHin q0fH+X flavor We divide the produced Hinto the following 4 groups: (a) Directly produced and contain q0f . (polarized) (b) Decay products of heavier Hj which contain q0f . (polarized) (c) Directly produced but do not contain q0f . (unpolarized) (d) Decay products of heavier Hjwhich do not contain q0f . (unpolarized) Independent of spin, calculable using fragmentation models (e.g. JETSET). Pf(q): polarization ofq0f, calculable (electro-weak interaction; pQCD). t FH,f =Qf /nf : fragmentation polarizationtransfer factor, different in SU(6) or DIS. t DH,Hj : decay polarization transfer factor. (Data and/or simple model estimations). 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

8. P in Boros,Liang, PRD(98) SU(6) agrees with the data not worse than DIS! Max of |P| SU(6) • A systematic study of hyperon polarization in: DIS 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

9. Further predictions on hyperon polarization in e+e- annihilations (a) Energy dependence:P at LEP II energy.  is the leading in one direction, K + is the leading in the opposite. (b) Flavor separation: E.g. P in events where: (c) Other hyperons: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

10. Hyperon polarization in Starting point:At sufficiently high Q2 and W, hadrons in the current fragmentation regions are pure results of struck quark fragmentation. Advantages: Longitudinal and transverse.  Automatic flavor separation. Pf(q) for the outgoing qf in e-qfe-qf . Longitudinal : Transverse: For qf from qf-qf : Pf(q) = -1. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

11. Longitudinal Lambda polarization in 4 different combinations of beam and target polarizations PL(l) and PL(N). Liu, Xu,Liang, PRD(02) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

12. Transverse Lambda polarization in A rough estimation by taking: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

13. Brief summary for  polarization in (1) Longitudinal: Significantly high in the cases when the electron is longitudinally polarized, but very small in case of unpolarized electron. Influence of heavier hyperon decay is high. in u-quark jet Fraction of events  decay * decay directly produced (2) Transverse: Only if the target is transversely polarized. Very small. Influence of heavier hyperon decay is high. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

14. Polarization of other H’s in (1) Longitudinal polarization: • Significantly higher than |P|. • Decay influence is neglegible. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

15. Polarization of + in (2) Transversal polarization: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

16. Hyperon polarization in (1) 100% polarization of the struck quark. (2) Flavor separation are more suitable to study spin transfer! 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

17. at NOMAD energies  polarization in at E=40~ 60 GeV NOMAD experiments: A characteristic feature: Data: The magnitude of the polarization increases with decreasing xF, also when xF across zero! Theory: The polarization goes to 0 when when xF goes to zero! A question: Does this imply that none of the pictures discussed above is suitable to describe the spin transfer in fragmentation processes? 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

18. at NOMAD energies  polarization in Observation: C.M. energy of the hadronic system at NOMAD: • Dominance of the contribution from the fragmentation of the target remnant to baryon production. • No separation between the contribution from the fragmentation of the struck quark and that of the remnant of the target! Containing at least one valence quark from the remnant of the target Number of Lambda’s Results from LEPTO: Liang, Liu, PRD(02) Containing the struck quark 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

19. at NOMAD energies  polarization in Results of a rough estimation by taking the remnant contribution into account Liang, Liu, PRD(02) Without remnant contribution With remnant contribution Conclusion: the remnant contribution has to be taken into account at such energies! Similarly at HERMES etc. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

20. Hyperon polarization in high pjets in polarized pp collisions Contributions from different hard processes: Much more complicated than that in lepton-induced reactions Gluon fragmentation (even less known than quark). Question:Is it possible to separate different contributions by choosing events in different kinematical regions ? From quark Jets From gluon Jets Number of jets Number of Lambda’s From PYTHIA 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

21. Hyperon polarization in high pjets in polarized pp collisions Results for Hyperon polarization P • |P| is small • Diference is small • Decay contribution is large  polarization is better to differentiate SU(6) or DIS. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

22. Summary and Outlook Spin transfer in fragmentation processes can be studied by measuring hyperon polarization in • SU(6) seems to agree better with the data for • Decay contribution to  is usually large, • Fragmentation of the rest of the target at low energies is important, •  production is more suitable to differentiate different pictures. Thank you for your attention ! 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)