Spin Alignment of Vector Mesons in Polarized and Unpolarized High Energy Reactions

1. Spin Alignment of Vector Mesons in Polarized and Unpolarized High Energy Reactions Liang Zuo-tang Department of Physics Shandong University Jinan, Shandong, China References: Xu Q.-h, Liu C.-x, and Liang Z.-t, Phys. Rev. D63, R111301(2001); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D66, 017301 (2002); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D67, 114013 (2003); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D68, 034023 (2003). 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

2. Spin Alignment of Vector Mesons in Polarized High Energy Reactions Outline 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

3. Definition of the Spin Alignment mm:the diagonal element of spin density matrix of vector meson V . 11:the probability to be in m=1 state, similar for -1-1 and00 . For V1+2, where 1 and 2 are two pseudoscalar mesons, 00 can be obtained from the angular distribution of the decay products. • 00 = 11=-1-1 = 1/3, if the vector meson is unpolarized. • If 00  1/3, V has a spin alignment along the quantization axis. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

4. Spin alignment of vector meson in Experimental results PLB (1997). unpolarized 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

5. Spin alignment of vector meson in Experimental results 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

6. Lesson directly from the data Since: • the initial quark and anti-quark are longitudinally polarized • mesons with large xp contain the initial quark/anti-quark. fragmentation There exists a significant spin alignment of vector mesons produced in the fragmentation of longitudinally polarized quark with the fragmenting quark. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

7. Previous theoretical approaches The simple statistical model: A QCD inspired model: A fast moving quark combines with a soft anti-quark to for the meson, where soft antiquark preferentially has the same helicity as the quark. Another model:V is produced via qq’V, where the vector meson couples to the quark like a vector current. None of them is consistent with the data! 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

8. A Theoretical Study 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) donot 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., (ii) V(A,f) is calculated according to the assumption: Spin of V(qf0q-bar) = Spin of qf0 + Spin of q-bar 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

9. Calculation of V(A,f) We build the direct product: We transform it to the coupled basis and obtain: Hence: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

10. Results and conclusions To get a V(A,f ) which is larger than 1/3, one has to take Pz<0 if Pf>0! Fitting the data, we obtained that: Xu, Liu & Liang, PRD63,111301 (2001) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

11. For other mesons Xu, Liu & Liang, PRD63,111301 (2001) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

12. Question: Is the relation PZ=-Pf indeed true? • Independent of the processes in which the fragmenting quark is produced? • Longitudinally v.s. transversely polarized cases? • … … Further studies in other reactions such as: current fragmentation region 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

13. Deeply inelastic scattering  - p - VX Xu & Liang, PRD66,017301 (2002) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

14. Deeply inelastic scattering  p -VX Xu & Liang, PRD66,017301 (2002) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

15. p()+pV+X with high pT Xu & Liang, PRD67,114013 (2003) 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

16. Spin Alignment of Vector Mesons in Unpolarized Hadron-Hadron Collisions Outline • Experimental indications • Qualitative Arguments for a Close Relation between the Spin Alignment of Vector Meson in unpolarized hadron-hadron collisions and the Single-spin Left-right Asymmetry • A rough quantitative estimation 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

17. Spin alignment of vector meson in Experimental results: Excharm Collab., PLB485, 334 (2000) Quantization axis: normal of the production plane Quite similar to hyperon polarization in 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

18. Qualitative Arguments Close relation between 00V and AN?! 00V (n+CK*++X )>1/3 in the large xF region uv-quark was polarized transversely to the production plane. Extension of the lesson from 00V (e++e-Z0 V+X ) to transversely polarized case. there exist a spin-correlation of the form in hadron-hadron collisions AN[p()+p ++X ]>0 in the large xF region There exist a spin-correlation of the form at the hadron level in the reaction. 00V and AN are two manifestations of the existence of the spin-correlation in hadron-hadron collisions 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

19. Qualitative Arguments In another word: the existence of a spin-correlation of the form in hadron-hadron collisions AN[p()+p ++X ]>0 in the large xF region uv-quark was polarized transversely to the production plane. Extension of the lesson from 00V (e++e-Z0 V+X ) to transversely polarized case. 00V (n+CK*++X )>1/3 in the large xF region 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

20. Qualitative Arguments Similarity to hyperon polarization in p(0)+A(0)H+X (Liang & Boros, PRL’97). the existence of a spin-correlation of the form in hadron-hadron collisions AN[p()+p ++X ]>0 in the large xF region qv-quark was polarized transversely to the production plane. SU(6) wavefunctions for hyperons Hyperon polarization transversely to the production in unpolarized hh-collisions in the large xF region The same origin for AN, PH and 00V in unpolarized hh-collisions 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

21. A Rough Quantitative Estimations Determining the polarization of the valence quark before hadronization AN[p()+p ++X ]>0 in the large xF region the existence of a spin-correlation of the form in hadron-hadron collisions The polarization of the valence-quark transverse to the production plane. Number density of M from the rest. Number density of M from Difference of the probability for M from to go left and that to go right 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

22. A Rough Quantitative Estimations Calculation of 00V in h(0)+h(0)V+X Similar to e+e- Z0 V+X: 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

23. Results Xu & Liang, PRD68,035023 (2003) Two classes of vector mesons: Class 1: Having a valence quark of the same flavor as that of the incident hadron. E.g.: +, -, 0, K*+,K*0 in pp-collisions. Class 2: Having no valence quark of the same flavor as that of the incident hadron. E.g.: K*-, K*0-bar in pp-collisions. N0 dominates for all xF, thus 00V =1/3 for all xF. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

24. Conclusion • To explain the spin alignment of vector meson observed in e+e- annihilation, we need: Pz=-Pf. • Extending to other polarized reactions, we obtain the spin alignments of vector mesons in all these reactions. • Spin alignment of vector mesons in unpolarized hh-collisions is closely related to the single-spin left-right asymmetries. 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)