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Intrinsic transverse momentum and the Sivers effect #. Intrinsic transverse momentum of quarks Why it is actual Cahn effect Single target spin asymmetries Sivers effect Collins effect. Aram Kotzinian Torino University & INFN On leave in absence from YerPhI, Armenia and JINR, Russia. - PowerPoint PPT Presentation
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Transversity workshopTrento, June 16, 2004
Aram Kotzinian 1
Intrinsic transverse momentum and the Sivers effect
Intrinsic transverse momentum of quarks Why it is actualCahn effect
Single target spin asymmetriesSivers effectCollins effect
Aram Kotzinian
Torino University & INFNOn leave in absence from YerPhI, Armenia and JINR, Russia
In collaboration with M. Anselmino, M. Boglione, U. D'Alesio, F. Murgia & A. Prokudin
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 2
SIDIS
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 3
Intrinsic transverse momentum roleGluon polarization measurement
LP
QCDCompton
PGF
QCDCQCDC
LLLPLP
LLPGFPGF
LLlhhXlN RaRa
q
qRa
G
ΔGA
R strongly depends on the intrinsic and fragmentationTk Tp
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 4
Unpolarized SIDIS & Cahn effect
frame CM * P
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 5
approximation)/O( QkT
Ji et al: QCD factorization holds for QkP QCDTT
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 6
Comparison with data
EMC, 280 GeV muon SIDIS
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 7
Hadron transverse momentum dependence
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 8
Collins Effect
ColT
h
qTq
TT
h
q
h
qpzH
mp
spzDzD sin),(),(),( 22
Tp
q
TS
h
Tp
x
y
Col
Front view
Colq
TS
q
h h
Tp
Side view
azimuthal modulation of transversely polarized quark FF
0),( 1
22
1 ppzDpdp T
h
q
h
02
),(2
222
2 mp
pzHpdp T
h
q
h
Up-Down asymmetry = 0
Nonzero Left-Right asymmetry
0),(2
)(1
0
2
221
0
2 h
h
qh
hzH
mp
pddzzpdz Tp
Schaefer-Teryaev SR:hadrons transverse momentaare compensated in the quark fragmentation
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 9
Sivers Effect
Azimuthal modulation of quark transverse momentum for a transversely polarized nucleon
Quark transverse momentum is compensated by that of target remnant
SivNS
N
qTk
),(),( 11 TT kxfxf k
)sin(),(1),(),( 1 SivTqSivTTT kxASkxfxf k
Unpolarized DF:
Polarized DF:
),(
),(),(
1
1
T
TTT
qSiv xf
xfxA
k
kk
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 10
SSAXpp
Analyzing power:
Only Sivers effect Only Collins effect
Analysis by Anselmino et al, E704
STAR
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 11
One can describe the data using only Collins effect
HERMES SSA ULA
Efremov, Goeke & Schweitzer: one can neglect the Sivers effect
Schweitzer & Bacchetta: there is a room for Sivers effect
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 12
Parameterization for Sivers effect
)()(),( TqTqsiv khxNkxA
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 13
Anselmino et al for E704 SSA
Our parameterization:opposite sign & high values at small x
),( TqSiv kxA
u-quark d-quark
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 14
Results: on P & D targets
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 15
Results: K on D target
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 16
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 17
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 18
Quark intrinsic transverse momentum in LEPTO
- Generate virtual photon – quark scattering in collinear configuration:
- Before
- After
- Rotate
- Generate intrinsic transverse momentum of quark (Gaussian)Tk
- Generate uniform azimuthal distribution of quark
- Rotate
q
z
zplane ll
- Generate quark azimuthal angle according to Sivers distribution
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 19
Modified LEPTO MC predictions for JLAB SSA
Opposite signs of asymmetry in the target and current fragmentationIn principle, one can check origin of by measuring it in the TFR
SivULA
ULA
85.0
(GeV/c) 1
withevents 1022
7
y
Q
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 20
Electron Ion Collider
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 21
Modified LEPTO MC predictions for EIC SSA
Opposite signs of asymmetry in the target and current fragmentationIn principle, one can check origin of by measuring it in the TFR
SivULA
ULA
85.0
(GeV/c) 1
withevents 1022
7
y
Q
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 22
End of Story?
),;,(,...;...;
,;TT
hq
TLP zxM pk
Zoology of FracFun
Transversity workshopTrento, June 16, 2004
Aram Kotzinian 23
Conclusions
Intrinsic transverse momentum in simple parton model approach allows to describe
Hadron transverse momentum dependence in SIDIS
Cahn effect
HERMES SSA data on longitudinally polarized target
It is important to investigate the SSA in the TFRSivers effect?
Collins effect from target remnant hadronization?
We need more precise data on transversely polarized targets