SIR05, JLab, May 20, 2005 Aram Kotzinian 1

SSA in the target fragmentation region of SIDIS

Cahn and Sivers effects

Phenomenology & Data in the CFR

Intrinsic transverse momentum of partons in LEPTO

Results for TFR of SIDIS

Discussion & Conclusions

Aram Kotzinian

Torino University & INFNOn leave in absence from YerPhI, Armenia and JINR, Russia

M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin: PRD 71,

074006 (2005)

A.K.: arXiv:hep-ph/0504081

SIR05, JLab, May 20, 2005 Aram Kotzinian 2

Unpolarized SIDIS & Cahn effect

)/O( QkT

Ji et al: QCD factorization holds for QkP QCDTT

Quadratic in

Linear in and proportional to 2k

hz

hz

approximation

SIR05, JLab, May 20, 2005 Aram Kotzinian 3

Comparison with data

Non Gaussian tail; x, z and flavor dependence of intrinsic and fragmentation transv. momentum

SIR05, JLab, May 20, 2005 Aram Kotzinian 4

Brodsky, Hwang & Schmidt, 2002: FSI

+

2

( , ) 0NTq P

f x k

Collins, 2002; Belitski, Ji &Yuan, 2003: Wilson gauge link

Boer, Mulders & Teryaev, 1997: twist three gluonic pole

In standard approach the effective treatment of the Sivers effect isadopted as correlation in quark distribution in transversely polarized nucleon

ˆT TS (p×k )

Interpretation of Sivers effect

SIR05, JLab, May 20, 2005 Aram Kotzinian 5

Parameterization for Sivers effect

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Data

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New HERMES data

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( )q Nf x N

( )hqD z

qq

h

CFR: TMD dependent description

( , , ) ( , ; )lN lhX lq lq hq q N q q

q

d f x d D z T Tk s ;S p s

Well clasified correlations in distribution and fragmentation functions

ˆ T TS (p×k ) Sivers effect

ˆ T Ts (p×k ) Boer-Mulders distribution

L LS ×s Helicity distribution

ˆ hT Ts (q×p ) Collins effect in quark fragmentation

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TFR & Fracture Functions

( , )qh NM x z N

q

h

( ) ( ) ( , ))lN lhX lq lq h qq q h N

q

d d f x D z M x z

( , , , ; )q hh N q NM x zT Tk s ; p S

1994: Trentadue & Veneziano; Graudenz; … Fracture functions: probability of finding a parton q with momentum fraction x and a hadron h with the CMS energy fraction Eh/EN

More correlations for TMD dependent FracFuncs

; s

( ) ...

h h

h

L T T L T T

T T T T

S (p ×k ) (p ×k )

S p (s ×k )

SIR05, JLab, May 20, 2005 Aram Kotzinian 10

Azimuths in SIDISIn one-photon approximation the general structure of azimuthal angles dependences in polarized SIDIS can be found from very general principles (A.K. 1995). Valid both for CFR and TFR.

SIR05, JLab, May 20, 2005 Aram Kotzinian 11

u

( ud)

R

R

R

u

u

d

d

d

s

d

s

+ρ

0π

-π

+K

Soft

Str

ong

Inte

ract

ion

Hadronization

( , , ) ( , , , ; )lN lhX lq lq q hq q N h N q F N

q

d f x d H x x T T Tk s ;S k s ; p S

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Quark intrinsic transverse momentum in LEPTO

- Generate virtual photon – quark scattering in collinear configuration:

- Before

- After hard scattering

- Rotate in l-l’ plane

- Generate intrinsic transverse momentum of quark (Gaussian kT)

- Generate uniform azimuthal distribution of quark (flat by default)

- Rotate around virtual photon

Tk z

q

zplane ll

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Implementing Cahn and Sivers effects in LEPTO

The common feature of Cahn and Sivers effects Unpolarized initial and final quarks

Fragmenting quark-target remnant system is similar to that in default LEPTO but the direction of is now modulated

Cahn:

Sivers:

Generate the final quark azimuth according to above distributions

z

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Results: Cahn

Imbalance of measured in TFR and CFR: neutrals?

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Results: Sivers

Predictions for JLab 12 GeVxF-dependence

Red triangles with error bars – projected statistical accuracy for 1000h data taking (H.Avagyan).

z and xBj-dependences

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Results: Sivers JLab 12 GeV

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SSA in PP-interactions

E704. Curves: by Anselmino et al, STAR (hep-ex/0505024)

xF<0 in PP corresponds to xF>0 in SIDIS. In both cases backward with respect to polarized proton flight direction in CMS. Both the active quark and the proton remnant are flying in forward direction. Which particles provide transverse momentum balance?

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Discussion & ConclusionsBoth Cahn and Sivers effects are implemented in LEPTO. Possible effects of polarized hadronization were neglected.

Existing data in CFR are well described by modified LEPTOThe measured Cahn effect in the TFR is not well described

Is there an universal mechanism describing SSA in SIDIS and PP interactions?

It will be interesting to implement Cahn and Sivers effects in PHYTIA

It is important to perform new measurements of both effects in the TFR (JLab, HERMES, Electron Ion Colliders)

This will help better understand hadronization mechanism Do the neutral hadrons compensate Cahn effect in CFR?Is there a similarity with PP-reaction?Multihadron final states distributions can enhance effects

Fracture Function“Global” analysisClassification of spin and TMD dependent correlations in Fracture Functions