Spin effects in fragmentation processes at RHIC
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Transcript of Spin effects in fragmentation processes at RHIC
2004-8-13, CCAST Qinghua Xu, Shandong University 1
Spin effects in fragmentation processes at RHIC
Qinghua Xu ( 徐庆华 )
Physics department, Shandong University
References:
Xu Q.H., Liu C.X., and Liang Z.T., Phys. Rev. D65, 114008 (2002);
Xu Qing-hua, and Liang Zuo-tang, Phys. Rev. D67, 114013 (2003);
Xu Qing-hua, and Liang Zuo-tang, hep-ph/0406119.
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Introduction
• Spin-dependent fragmentation function(spin effect in frag.):
(study the polarization and/or momentum distribution of hadrons
produced in the fragmentation of a polarized quark.)
hadronization mechanism;
to study spin structure of nucleon, as filters for exotic p.d.f, e.g., g(x) and q(x)!• Hyperon polarizations (, +) are widely used to study
polarized fragmentation function, since their polarization
can be measured through their self-analyzing decay.
cosP1 )(cos W
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Previous study of polarized fragmentation function
SU(6)
DIS
(Boros, Liang,PRD’98)
e
e0Z
0fq
0fq fr
agm
enta
tion
XHqqZee ff 000
E.g., at the Z0 pole,
<Pf>= -0.94 for f=s,d,b;
<Pf>= -0.67 for f=u,c.
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• The DIS data available:
HERMES(PRD01), E665(EPC00) ----- large error !
NOMAD(NPB00), better statistics, but energy too low !
• RHIC spin program (pp collision) is promising:
(a) high statistics (high luminosity)
(b) high energy (200-500GeV).
• Available theoretical studies in pp collisions:
D.de Florian,M.Stratmann, W.Vogelsang, Phys. Rev. Lett. 81(1998);
C. Boros, J.T.Londergan, A.W.Thomas, Phys. Rev. D62 (2000);
B.Q. Ma, I.Schmidt, J.Soffer, J.J.Yang, Nucl. Phys. A703 (2002);
Xu Q.H., Liu C.X, Liang Z.T., Phys. Rev. D65, 114008 (2002).
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PH in high pT jets at RHIC
• Hyperon production with high pT:
HXpp
),(ˆ
),(),()( 222
2
c
Hc
T
cdab
bbaabcd
acbaT
HXpp
zDddp
dxfxfdzdxdx
ddp
d
),(ˆ
),(),()(
2222
cHc
T
cdab
bbaabcd
acbaT
zDddp
dxfxfdzdxdx
ddp
d
helicity distribution function
longitudinally polarized fragmentation function
),(),( 22 zDzDD Hc
Hc
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Contribution of gluon and quark jet(s) to production
Quark jets dominate the
Hyperon production with high PT !
From gluon fragmentation
From quark fragmentation
PYTHIA
• Different subprocess: qqqq, qgqg, gggg ……, but :
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polarized fragmentation function
We divide the produced Hi’s in into four groups:
(a) directly produced and contain the qf ;
(b) decay products of polarized heavier hyperons ; (c) directly produced but don’t contain the qf ;
(d) decay products of unpolarized heavier hyperons. Those from (a) and (b) can be polarized, (c) and (d) are not! Hence :
XHq if
: spin transfer factor)(/)( )()(,, zDzDt ii
i
H
f
H
fF
fH
(z))( ,,,
,
i
i
i Hf
FfH
ba
Hf DtzD
),( 2zDHf
• : fraction of spin carried by qf in Hi (qf….) SU(6), DIS
• for (b) qf Hj +X
aFfH i
t ,,
aFfH
DHH
bFfHH ijiji
ttt ,,,
,,,
decay spin transfer factor in HjHi +X’.
can be obtained from generator (e.g.PYTHIA)
Results of hyperon polarization
SU(6), set II
SU(6), set I(GRSV00)
DIS, set I
DIS, set II(GRSV96)
SU(6), set I
DIS, set I
SU(6), set II
DIS, set II
GeV) andGeV ( 50013 spT
• The decay contribution of is very large, while origin of + is much cleaner!
(1) P is very small .
(2) Difference between results of SU(6) and DIS is small.(3) P has a strong dependence of
different sets of f (x) !
• P+ is large .
• Difference between results of SU(6) and DIS is large.
• P+ has a weak dependence
of different sets of f (x) !
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containing fragmenting u
containing fragmenting s
decay contribution
GeV) 500 and GeV 13( spT
Contribution of directly produced and contain a fragmenting u play the dominant role!
In the limiting case that there is only this contribution in :
Different models only differ in the constant ,
Hence , we can study p.d.f. from P+ in pp reactions.
F
ut
,
Xpp
Characteristic of + production in pp+X
uTL
F
uTL PtP ,,
(lim),
Polarization of fragmenting u, related to polarized p.d.f.
Xpp
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P+ in and g(x) Xpp
XHpp
• Subprocesses involved,
)(),(ˆ
),(),(
2)(
22
min
fHfqqg
bbaf
ba
p
T
qgzDd
xqxgdzdxdxdpd
ff
T
qqg gqq
• P+ in
ddP /
: Xpp
qqg qgq
(dominant)
(negligible)
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P+ in at GeV 200s Xpp
BB02 g
GRSV00 g
AAC g
)01(
)ph/0406119-hep Liang, (Xu,
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Transverse polarization of hyperons with high pT and q(x)
)(
)(
)()(
)()(
HXpp
XHppT
XHppXHpp
XHppXHppHT d
d
dd
ddP
d
dzDxfxfdzdxdxdp
d
d dcbaTH
cTbbaabcd
aba
p
T
XHppT
T
)(222
)( ˆ),(),(),(
min
• PH in transversely polarized pp collisions:
• For , similar as the longitudinally polarized case,
)(
)()(
)()(
, zD
zDT H
c
HcTF
cH
),( 2)( zDHcT
, (z))( ,,,
,
i
i
i Hc
FcH
ba
HcT DTzD
(z) ,,
, , ,
( )i iH Hc c
a b c d
D z D
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P+ with pT>13 GeV in at GeV. 500sXpp
Numerical results for + polarization
)(xq
(J.Soffer)
(B.Q.Ma et al)
take
for a simple assumption!
FfH
FfH ii
tT ,,
Spin alignment of vector meson
• The data at LEP:
• K*0
spz /2
]cos)()[()W(cosθ 20000 131
4
3• Polarization of V:
00 : Prob. of being in h= 0 state.
Spin alignment exists in fragmentation of a longitudinally polarized quark !
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• 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 qf
0 ; (B) do not 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).
)(
)|()(
)(
),|(),()(
zn
BznB
zn
fAznfAz V
f
VV
(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., 00(B)=1/3
(ii) V(A,f) is calculated according to the assumption:
Spin of V(qf0q-bar) = Spin of qf
0 + Spin of q-bar
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• transforming it to the coupled basis and obtain:
)1)(1()(2
)1(0
)(2
)1()1()(
2
)1(
0)(2
)1()1)(1(
3
1),(
zfyxf
yxf
zfyxf
yxf
zf
zf
V
PPiPPP
iPPP
PPiPPP
iPPP
PP
PPfA
• Hence:
qPPPP zyx for ),,(
• The spin density matrix of V can be obtained from the product:
zyx
yxz
f
fqqqq
PiPP
iPPP
P
Pff
1
1
10
01
4
100
zf
zfV
PP
PPfA
3
1),(00
Calculation of V(A,f)
To get V00(A,f ) > 1/3,
signs of Pf and Pz should be opposite!
Pf is the polarization of qf0 ,
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• Fitting the data, we obtained that: 5.0 , fz PP
XKZee 0*0
PRD(2001). Liang, Liu, Xu,
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Spin alignment of V in pp-->VX
(a) spin alignment of V in
at s=500 GeV and pT>13 GeV.
VXpp
fz PP
• Is this relation universal for the fragmentation of a longitudinally polarized quark ?
• Applying it to other process
to make further tests !
DIS, pp collisions…PRD(2003). Liang, Xu,
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Fig: Spin alignment of V in pp reaction at s=500 GeV and pT>13 GeV.
(b) in helicity frame
Spin alignment in transversely polarized pp collisions
(a) in transversity frame
Light cone model
Soffer inequality
• Further extents to the transversely polarized case! .qTTq PP
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Summary
• Spin dependent fragmentation function is studied from
PH in high pT jets in polarized pp collisions. We find that,
+ is more suitable than for this purpose.
• + polarization in can provide important information on g(x). + polarization in can provide useful information on q(x). Numerical results are given.
• Spin alignment of vector meson in polarized pp collisions are studied at RHIC energy.
Xpp
Xpp
Thank you!
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20
20
20
20
||||||
||||||
sXsX
sXsXh
XqhXqh
XqhXqhP
ss
ss
s s
s s
X X ss
X X ss
hXqhXq
hXqhXqQ
20
20
20
20
0||||||
||||||
0 0( )q h q X x • Polarization of h(q0x) from
0QPh
• Fraction of spin carried by q0 in a hadron h
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zqi
qT
iqTzq
iqT
iqTh
qhq
hqq PeP
ePP
eP
eP
1
1
1
1
4
1
2
2
00 3
1)(
qT
qTh
P
PA
3100 /
.qTTq PP z-distribution of type (a) +
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dfH
cfH
bfH
afH
f j
bHHH
DHH
afHf
FfH
H
iiii
jijjiii
i nnnn
nPtnPtP
,,,,
,,,,
),(ˆ),(),( 2)(22min
c
Hc
cdabbba
abcdacbap TH zDdxfxfdzdxdxdpn
Ti
• :independent of polarization properties, and can
be obtained by hadronization model or event generator (PYTHIA …)!
• Hyperon polarization can be given by:
: decay spin transfer factor in HjHi +X’.DHH ji
t ,
aFfH
DHH
bFfHH ijiji
ttt ,,,
,,,
• For hyperons of group (b), qf Hj +X
Hi +X ’
ˆ
ˆ
),(
),(2
2
d
d
xq
xqPf
( , , , )iH
n a b c d
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P+ in Xpp
BB02
GRSV00
GeV. 8 and GeV 200 Tps
AAC00
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Fig: P+ with 0<<1.5 in at GeV. 500s Xpp