spin structure of nucleon and spin transfer in high energy fragmentation processes
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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).
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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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?
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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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
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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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
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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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).
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 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.
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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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
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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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
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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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
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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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
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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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)
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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Transverse Lambda polarization in
A rough estimation by taking:
Xepe )(
)allongitudin()transverse( ).1( ,,F
fF
f tt
)allongitudin,()transverse,( ).2( xqxq
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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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
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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Polarization of other H’s in
(1) Longitudinal polarization:
HXepe
Significantly higher than |P|.
Decay influence is neglegible.
Xepe
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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Polarization of + in
(2) Transversal polarization:
Xepe )(
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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Hyperon polarization in
(1) 100% polarization of the struck quark. (2) Flavor separation
HXp
are more suitable to study spin transfer!Xp
Xp
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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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?
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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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)
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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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.
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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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
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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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.
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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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 !
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