Spin Alignment of Vector Mesons in Polarized and

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. D 63, R 111301(2001); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D 66, 017301 (2002); Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D 67, 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 1

Spin Alignment of Vector Mesons in Polarized High Energy Reactions Outline 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 2

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. 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 3

Spin alignment of vector meson in Experimental results PLB (1997). unpolariz ed 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 4

Experimental results Spin alignment of vector meson in 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 5

Lesson directly from the data Since: q the initial quark and anti-quark are fragmentati on longitudinally polarized q mesons with large xp contain the initial quark/anti-quark. There exists a significant spin alignment of vector mesons produced in the fragmentation of longitudinally polarized quark with the fragmenting quark. 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 6

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! 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 7

A Theoretical Study To study what the data tell us, we made the following calculations (1) We divided the produced vector mesons into two (A)groups: contain the initial quark q 0 ; (B) donot contain the qf 0. f 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 (i) Vectorway: mesons in group (B) are taken as unpolarized, i. e. , V (ii) (A, f) is calculated according to the assumption: 0 Spin of V(qf q-bar) = Spin of qf 0 + Spin of qbar 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 8

Calculation of V(A, f) We build the direct product: We transform it to the coupled basis and obtain: Hence: 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 9

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: g, n a i &L 1 u i L Xu, 3, 11130 6 PRD ) 1 (200 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 10

For other mesons g, n a i L & u i 1 L Xu, 3, 11130 6 PRD ) 1 (200 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 11

Question: Is the relation PZ=- Pf indeed true? v Independent of the processes in which the fragmenting quark is produced? v Longitudinally v. s. transversely polarized cases? v … …studies in other reactions Further such as: current fragmentation region 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 12

- VX g, n a i L 1 Xu & 6, 01730 6 PRD ) 2 (200 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 13

Deeply inelastic scattering p -VX g, n a i L 1 Xu & 6, 01730 6 PRD ) 2 (200 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 14

p( )+p V+X with high p. T g, n a i L 3 Xu & 7, 11401 6 PRD ) 3 (200 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 15

Spin Alignment of Vector Mesons in Unpolarized Hadron-Hadron Collisions Outline Ø Experimental indications Ø Qualitative Arguments for a Close Relation between the Spin Alignment of Vector Meson in unpolarized hadron collisions and the Single-spin Left-right Asymmetry Ø A rough quantitative estimation 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 16

Spin alignment of vector meson in Experimental results: Excharm Collab. , PLB 485, 334 (2000) Quantization axis: normal of the production plane Quite similar to hyperon polarization in 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 17

Qualitative Arguments 00 Close relation between 00 V and AKN*++X ? ! V (n+C u -quark was polarized )>1/3 in the large x. F region Extension of the lesson from 00 V (e++e- Z 0 V+X ) to transversely polarized case. AN [p( )+p ++X ]>0 in the large x. F region V and v transversely to the production plane. there exist a spin-correlation of the form in hadron collisions AN are two existence of the 00 2003年 9月16日-20日，JINR Dubna There exist a spin-correlation of the form at the hadron level in the reaction. manifestations of the spin-correlation in 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 18

Qualitative Arguments In another word: [p( )+p +X the existence of + AN ]>0 in the large x. F region a spincorrelation of the form hadron-hadron collisions in uv-quark was polarized transversely to the production plane. Extension of the lesson from 00 V (e++e- Z 0 V+X ) to transversely polarized case. 2003年 9月16日-20日，JINR Dubna 00 V (n+C K*++X )>1/3 in the large x. F region 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 19

Qualitative Arguments Similarity to hyperon p(0)+A(0) H+X AN [p( )+p Boros, ]>0 in the large x. F region ++X PRL’ 97). polarization in (Liang & the existence of a spincorrelation of the form hadron-hadron collisions in 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 x. F region The same origin for AN, PH and 00 V in unpolarized hh -collisions 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 20

A Rough Quantitative Estimations Determining the polarization of the valence quark before hadronization AN [p( )+p ++X ]>0 in the large x. F 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 Number density of M rest. from Difference of the probability for M from to go left and that to go right 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 21

A Rough Quantitative Estimations Calculation of 00 V h(0)+h(0) V+X Similar to e+e- Z 0 V+X: 2003年 9月16日-20日，JINR Dubna in 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 22

Results g, n a i L 3 Xu & 8, 03502 6 PRD ) Two classes of vector mesons: 3 (200 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. K*-, K*0 -bar in xpp-collisions. N E. g. : dominates for all , thus V =1/3 for all x. 0 2003年 9月16日-20日，JINR Dubna F 00 F 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 23

Conclusion n 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. 2003年 9月16日-20日，JINR Dubna 梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 24