Intrinsic transverse momentum and the Sivers effect #

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


Aram Kotzinian 2

SIDIS


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


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Unpolarized SIDIS & Cahn effect

frame CM * P


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approximation)/O( QkT

Ji et al: QCD factorization holds for QkP QCDTT


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Comparison with data

EMC, 280 GeV muon SIDIS


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Hadron transverse momentum dependence


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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


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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


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SSAXpp

Analyzing power:

Only Sivers effect Only Collins effect

Analysis by Anselmino et al, E704

STAR


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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


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Parameterization for Sivers effect

)()(),( TqTqsiv khxNkxA


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Anselmino et al for E704 SSA

Our parameterization:opposite sign & high values at small x

),( TqSiv kxA

u-quark d-quark


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Results: on P & D targets


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Results: K on D target


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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


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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


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Electron Ion Collider


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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


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End of Story?

),;,(,...;...;

,;TT

hq

TLP zxM pk

Zoology of FracFun


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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

Documents

Intrinsic transverse momentum and the Sivers effect #