hyperon polarization in hh/ha collisions and related problems

2004年8月梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 1

Hyperon polarization in hh/hA collisions and related problems

梁作堂 (Liang Zuo-tang)山东大学 (Shandong University)

Introduction The physical picture Results for single-spin left-right asymmetries Results for hyperon polarizations in hh/hA collisions Further tests.


Single-spin left-right asymmetries in e.g. p()+p(0)+X Hyperon polarization in unpolarized h+h or h+A collisions

IntroductionTwo classes of puzzling spin effects in inclusive h-h reactions

,)()( tindependen spin33 nsppd

dpd

d

||/)( hinhin ppppn

For p()+p+X, protonincident ss

tindependen spin3

2/13

2/13

2/13

2/13

)/()(

|)/(|)/(|)/(|)/(

pddp

pddpddpddpdd

Ansns

nsnsN

For p+pH+X, Hss

tindependen spin3

2/13

2/13

2/13

2/13

)/()(

|)/(|)/(|)/(|)/(

pddp

pddpddpddpdd

Pnsns

nsnsH

Question: Relation between PH and AN?


Single Spin Left-Right AsymmetryExperimental Results:

AN is non-zero for large xF and moderate p.

AN depends on the flavor of the produced hadron.

AN depends on the flavor of the polarized incident hadron.


Hyperon Polarization in Unpolarized h-h Collisions

-P in K- +p+X, compared with P in p+p+X.

The same characteristics as those for AN!

P in - +p+X, compared with P in p+p+X.Experimental Results


A Physical Picture(i) Hadrons in fragmentation regions are products of direct fusions of

valence quark(s) with sea- or anti-sea-quark(s), i.e.

(ii) In the direct fusion processes (a) and (b), i.e. in qv+(..)h(qv..), there exists a spin-dependent interaction so the cross section can be written as,

(iii) The direct fusion process is accompanied by , and the associatively produced M and B move in opposite transverse direction.

(iv) SU(6) wave-function is used to related the spin of qv and that of B which contains this qv.

(v) Spins of qs and qs-bar in the associated direct-fusion processes and are anti-aligned.

, )( Mqqa sv ,)( )( Bqqqb ssv . )( Bqqqc svv

),(10 vqsn

||/)( ppppn incinc

Bqqqc svv )(

Mqqa sv )(

Bqqqc svv )(Mqqa sv )(


A simple working model for AN in p()+ph+XFirst, take h=meson as an example. In this case, points (i) and (ii) are relevant.

),()(),( 0 sxDxNsxN FFF

p+p+X includes Direct Fusion: , contributing to AN sv qqOthers: no contribution to AN

)( )( ),( Ts

PvF xqxqsxD

Energy-momentum conservation demands smxxxxxx FT

FP / ,/ , 2

00

)( )( ),( Ts

PvF xqxqCsxD ),,(),( sxDsxN FF

)( )( )()( )( ),(

0T

sP

vF

Ts

Pv

FN xqxqxNxqxqC

sxA

The number density:

6.02)()(

)()(

0

1)(

CRLRLA D

N

.2/1 : ;2/1 : nsRnsL qq

)(10 vqsn

For , sv qq

c.m.s. energy squared


Results for AN

Liang & Meng, Z. Phys.A (1992).Boros, Liang & Meng, Phys.Rev.Lett. (1993).

AN for lepton-pair production: clear test of the picture!

)()( )(

)( )( ),( 2

2

TPxqxqe

xqxqeCsxA T

sP

vq

q

Ts

Pv

qq

FllN


Energy dependence

Dong and Liang, PRD (2004)

GeVs 200GeVs 200

BNL E925Pinc=22GeV

FNAL E704Pinc=200GeV


Results for AN in p()+p+XTwo contributing direct fusion processes:

Test of point (iii).,)( ,)( )( ssvssv sudsdub , )( svv sduc

FNAL E704Pinc=200GeV

Boros and Liang, PRD (1996)


Results for PH in h+hH+XClass I: only (b) qv+qsqsH is contributing, i.e. the produced hyperon

has one common valence quark with the projectile.

),.(10 ns

C

nsnsnsns

Pvv

vv

vqq

qqq

)//()//()//()//(

The existence of PH in h+h/AH+X.

E.g.: p+p-+X dominated by : ,)( ssv sdd 0P

p+p+X dominated by : ,)( 0 ssv ssu )( ssv ssd

0P

K-+p+X dominated by : ,)( ssv dus 0P

Points (i), (ii) and (iv) are relevant.

2004年8月梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 11Dong and Liang, PRD (2004).


Results for PH in h+hH+XClass II: both (b) qv+qsqsH and (c) qvqv+qsH are contributing. The produced hyperon has two common valence quark with the projectile.

svv sdu )( Ksu s

av

)(

nsq

type of correlation CPnP av

av uu

)()( ,//

CPnPss ss ,//

(Spin of K+)= 0 CPnPss ss ,//

(v): anti-alignment of the spins of ss and ss-bar

CP

0,0)( vvuu

)()( avu

K

)()(

)(

Points (i), (ii), (iii), (iv) and (v) are relevant.

E.g.: p+p+X.

are contributing.

(ii):

2004年8月梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 13Liang and Boros, PRL (1997).

2004年8月梁作堂(Liang Zuo-tang)，山东大学(Shandong University) 14Dong and Liang, PRD (2004).


Tests of (V): spins of qs and qs-bar are anti-aligned

(1) Lambda polarization in pp pK+

Ksu sa

v)(

svv sdu )(

|P| in pppK+ takes the maximum among different channels of pp X, and P=-C=-0.6.

Liang and Boros, PRD (2000).

Only the following processes contribute

Consistent with the data from CERN R608, P=-0.620.04.


Tests of (v): spins of qs and qs-bar are anti-aligned

(2) P in e-pe-K+ with polarized electron beam

svv sdu 0,0)( Ksu sv

)( yDPP eu

K

2

2

)1(1)1(1)(

yy

yD

)( yDPP e

Consistent with the recent results by CLAS!

Liang and Xu, PRD (2002).Only the following processes contribute


Tests of (V): spins of qs and qs-bar are anti-aligned(3) Predictions for PH e-pe-HK with polarized electron beam

ss qq ssa

//:)(

ss qq ssb //:)(

2/1:)( //// sqsqsqsq ssss PPc

0Kepe

Three cases:


nepe

Kepe 0

Polarizations of different baryons in

BMepe


Tests of (iv): spin transfer in qh+X(1) PH in e+e-Z0 q0q0-bar H+X

Max of |P|

SU(6)

DIS

SU(6) agrees with the data not worse than DIS!

Boros,Liang, PRD(98)


Tests of (iv): spin transfer in qh+X(2) PH in XHlNl '

Predictions have been made. Data are available, but statistics is too low,

energy is two low. Further measurements at COMAPSS?

Liu, Xu and Liang, PRD(2001);

Liang and Liu, PRD(2002).


Tests of (iv): spin transfer in qh+X(3) Prediction for PH in p+p H+X at high pT and high energies.

Sigma polarization in more suitable to test different models for spin transfer in qh+X, since:The polarization is much higher; Decay contribution is smaller;Influence from the difference in parametrization of p.d.f. is smaller.

Waiting for the Results from RHIC!

Xu, Liu and Liang, PRD(2002)


Tests of (iv): spin transfer in qh+X(4) Spin alignment of V in high energy reactions

5.0

).()( ),(PRD(2001). Liang, Liu, Xu,

00

ff qPqPqqV

00: probability for V to be in the helicity 0 state.spz /2

.*000 XKqqZee ff Data from OPAL

unpolarized: 00 =1/3.



Measurements from COMPASS!?

Xu and Liang, PRD(2002).XVlpl



Measurements at RHIC!?

Xu and Liang, PRD(2003).XVpp


Summary and outlookA physical picture is proposed to relate hyperon

polarization in unpolarized hh/hA collisions to the left-right asymmetry in singly polarized hh collisions.

Reasonable agreements with the available data have been obtained.

Tests of different ingredients of the picture have been proposed, compared with the available data. They can be further tested by future experiments.

Thanks !

hyperon polarization in hh/ha collisions and related problems

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