spin structure of nucleon and spin transfer in high energy fragmentation processes

2004年8月29日-9月3日： MENU2004, Beijing 梁作堂(Liang Zuo-tang)，山东大学(Shandong University)

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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

ReferencesBoros & 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).


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IntroductionTwo different pictures for the quark spin composition of nucleon:

The SU(6) quark model

1 :i.e.

,

Ni

q ssi

3.0~2.0 :i.e.

30%),~(20

Ni

q ssi

The DIS picture

Question: Extending to other baryons?


3

Extracting from Inclusive DIS data

Quark Parton Model:

,)(3

22

6

1)(

8301

1

0

1pppp QQQxgdx

),(2

13 DUQ ).2(

6

38 SDUQ ,

3

2

12

1)(

3

2

12

10 SDUQ

,||2 pApQSM apap qqA

aa

25

Operator expression:

SUf(3) Symmetry in Hyperon Decay

Wigner-Eckart Theorem: )(2|| DdFifMSA abcabcca

b

:)8,...2,1}({ aa The 8-dimensional representation of the SUf(3) group.

),(2

1| 54 ip E.g.: ),(

2

12||2 3

3 DFSMpApQSM pp

p

),3(32

12||2 8

8 DFSMpApQSM pp

p

... ...3

2

12

10 Q

)],()([2

1)(

1

21 xqxqexg p

jpj

N

jj

pf

Integrated over x:

)()()( xqxqxq pj

pj

pj


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!

.15.0 ;45.0 ;80.0 ppp SDU

0 -

SU(6) DIS SU(6) DIS SU(6) DIS

U (-D)/3 0 -0.17 (-2D)/3 -1/3 -0.44 (+D)/3-F 0 -0.10

D (-D)/3 0 -0.17 (+D)/3-F 0 -0.10 (-2D)/3 -1/3 -0.44

S (+2D)/3 1 0.62 (+D)/3+F 4/3 0.82 (+D)/3+F 4/3 0.82

0 + -

SU(6) DIS SU(6) DIS SU(6) DIS

U (+D)/3 2/3 0.36 (+D)/3+F 4/3 0.82 (+D)/3-F 0 -0.10

D (+D)/3 2/3 0.36 (+D)/3-F 0 -0.10 (+D)/3-F 4/3 0.82

S (-2D)/3 -1/3 -0.44 (-2D)/3 -1/4 -0.44 (-2D)/3 -1/4 -0.44


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Question: Which should be used for fragmentation?

Before 1998, no discussion was made. One simply uses:SU(6) picture in 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).


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Spin transfer can be studiedTo study the spin transfer, we need to:

E.g., at the Z0 pole, <Pf

(q)>=-0.94 for qf=s,d,b;

<Pf(q)>=-0.67 for qf=u,c.

e

e

0Z

0fq

0fq fr

agm

enta

tion

current fragmentation region

'll

N

XHlpl '

TpXHpp high veryat

p

p

XHqqZee ff 000/*

produce a polarized quark beam, measure the polarization of h.

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.


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t FH,f =Qf /nf : fragmentation polarization transfer factor,

different in SU(6) or DIS.

HfF

DHH

HjbHfF

FfH

f

aHfF

FfH

qf

H D

tDtDtP

Pjj

,

,),(

,,)(

,,)( ][

Calculation method of PH in q0f H+X

We divide the produced H into the following 4 groups:

Pf(q): polarization of q0

f , calculable (electro-weak interaction; pQCD).

(a) Directly produced and contain (a) Directly produced and contain qq00ff . . (polarized)(polarized)

(b) Decay products of heavier (b) Decay products of heavier HHjj which contain which contain qq00ff . . (polarized)(polarized)

(c) Directly produced but do not contain (c) Directly produced but do not contain qq00ff . . (unpolarized)(unpolarized)

(d) Decay products of heavier (d) Decay products of heavier HHjj which do not contain which do not contain qq00ff . . (unpolarized)(unpolarized)

t DH,Hj : decay polarization transfer factor.

(Data and/or simple model estimations).

Independent of spin, calculable using fragmentation models (e.g. JETSET).

Boros, Liang, PRD(98).

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

)(,

)(,

)(,, zDzDzDzDzD dH

fFcHfF

bHfF

aHfF

HfF

flavor


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P in

XqqZ/ee ff* 000

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

Max of |P|

SU(6)

DIS

Boros,Liang, PRD(98)

A systematic study of hyperon polarization in:

XHee

XHlpl '

TpXHpp highat


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is the leading in one direction, K + is the leading in the opposite.

Further predictions on hyperon polarization in e+e- annihilations

(a) Energy dependence: P at LEP II energy.

(b) Flavor separation: E.g. P in events

where: (c) Other hyperons: ),,,( 0


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Hyperon polarization inStarting point: At sufficiently high Q2 and W, hadrons in the current fragmentation regions are pure results of struck quark fragmentation.

HXpHXepe or ,

Longitudinal : ,)x(qP)y(DP)x(q

)x(qP)x(q)y(DP)x(P

f)N(

LL)l(

Lf

f)N(

LfL)l(

L)q(fL

,

)y(

)y()y(DL 2

2

11

11

Transverse: ),(/)()()( )()( xqxqPyDxP ffN

TTq

fT ,)1(1

)1(2)(

2y

yyDT

For qf from qf -qf : Pf(q) = -1.

Pf(q) for the outgoing qf in e-qf e-qf .

Advantages: Longitudinal and transverse. Automatic flavor separation.

x Bjorken


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Longitudinal Lambda polarization in

4 different combinations of beam and target polarizations PL(l) and PL

(N).

Xepe

x Bjorken

Liu, Xu,Liang, PRD(02)


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Transverse Lambda polarization in

A rough estimation by taking:

Xepe )(

)allongitudin()transverse( ).1( ,,F

fF

f tt

)allongitudin,()transverse,( ).2( xqxq


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Brief summary for polarization in

(1) Longitudinal:

Xepe

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.

(2) Transverse:

Only if the target is transversely polarized. Very small.Influence of heavier hyperon decay is high.

directly produced

in u-quark jet

decay

* decay

Frac

tion

of

even

ts


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Polarization of other H’s in

(1) Longitudinal polarization:

HXepe

Significantly higher than |P|.

Decay influence is neglegible.

Xepe


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Polarization of + in

(2) Transversal polarization:

Xepe )(


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Hyperon polarization in

(1) 100% polarization of the struck quark. (2) Flavor separation

HXp

are more suitable to study spin transfer!Xp

Xp


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polarization in

NOMAD experiments:

Xp

A characteristic feature: Data: The magnitude of the polarization increases with decreasing xF, also when xF across zero!

at NOMAD energies

Xp at E=40~ 60 GeV

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?


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polarization in

Observation: C.M. energy of the hadronic system at NOMAD:

Xp at NOMAD energies

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!

GeVW 101~

Results from LEPTO:

Num

ber o

f Lam

bda’

s

Containing the struck quark

Containing at least one valence quark from the remnant of the target

Liang, Liu, PRD(0

2)


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polarization in

Results of a rough estimation by taking the remnant contribution into account

Xp at NOMAD energies

Liang, Liu, PRD(02)

With remnant contribution

Without remnant contribution

Conclusion: the remnant contribution has to be taken into account at such energies!

Similarly at HERMES etc.


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Hyperon polarization in high p jets in polarized pp collisions

Contributions from different hard processes: etc. , , , ggggqgqgqqqq

Question: Is it possible to separate different contributions by choosing events in different kinematical regions ?

Much more complicated than that in lepton-induced reactions Gluon fragmentation (even less known than quark).

From quark Jets

From gluon Jets

qqqq qgqg

qqgg

gggg

ggqq From PYTHIA

Num

ber o

f jet

s

Num

ber o

f Lam

bda’

s


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Hyperon polarization in high p jets in polarized pp collisions

Results for Hyperon polarization

P

|P| is smallDiference is smallDecay contribution is large

polarization is better to differentiate SU(6) or DIS.


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Summary and Outlook

Spin transfer in fragmentation processes can be studied by measuring hyperon polarization in

,'

,

XHlpl

XHee

TpXHpp highat

SU(6) seems to agree better with the data forDecay 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.

,Xee

Thank you for your attention !

spin structure of nucleon and spin transfer in high energy fragmentation processes

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