1 SSH05, BNL, June 2, 2005 Aram Kotzinian SSA in the target fragmentation region of SIDIS Cahn and Sivers effects Phenomenology & Data in the CFR Intrinsic

SSH05, BNL, June 2, 2005 Aram Kotzinian 1

SSA in the target fragmentation region of SIDIS

Cahn and Sivers effectsPhenomenology & Data in the CFRIntrinsic transverse momentum of partons in LEPTOResults for TFRDiscussion & 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


Unpolarized SIDIS & Cahn effect

frame CM * P

x & z are light cone variables defined with respect z & axesz

No exact factorization !Bj hx z


approximation)/O( QkT

Ji et al: QCD factorization holds for QkP QCDTT

Quadratic in

Linear in and proportional to 2k

hz

hz


Comparison with data: 1

EMC, 280 GeV muon SIDIS







Non Gaussian tail; x, z and flavor dependence of intrinsic and fragmentation transverse momentum?


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 )

Sivers effect


Parameterization for Sivers effect


Asymmetry


Data


New HERMES data


SIDIS in LO QCD: CFR

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

q

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

Well classified correlations in TMD distr. and fragm. functions

1ˆ Tf T TS (p×k ) Sivers distribution

1ˆ h T Ts (p×k ) Boer distribution

1Lg L LS s Helicity distribution

1ˆ H h

T Ts (q×p ) Collins effect in quark fragmentation

( )q Nf x N

( )hqD z

qq

h

p

1( ) Lh T T Lk s S Mulders distribution


SIDIS in LO QCD: TFR

( , )qh NM x z N

q

h

( , )lN lhX lq lq qh N

q

d d M x z

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

1994: Trentadue & Veneziano; Graudenz; … Fracture functions: conditional probability of finding a parton q with momentum

fraction x and a hadron h with the CMS energy fraction z

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 )


Ed. Berger criterion: separation of quark and target remnant fragmentations)

The typical hadronic correlation length in rapidity is

Illustrations from P. Mulders:

EIC: good separation of two mechanisms


LUND String Fragmentation

( , , ) ( , , , ; )q hh N q F

lN lhX lq lqq q N

qNd xd H xf x TT Tk s ; k pS s ; S

u

( ud)

R

R

R

u

u

d

d

d

s

d

s

+ρ

0π

-π

+K

Soft

Str

ong

Inte

ract

ion

qq

q

Ran

k f

rom

diq

uark

Ran

k f

rom

qu

ark

h

LEPTO: Parton DF, hard X-section & Hadronization are factorized

hq NH L LS s Double spin effect – polarized hadronization


),,(),(

),,(),(1),,(),(

),,(

),,(

),(),(

),,(),(

),,(

2/

2

2/

22

/22

2/

2/

2

22

/22

21

QzxHQxq

QzxHQxqQzxHQxqe

QzxH

QzxH

QxqQxq

QzxHQxqe

QzxA

hNq

hNq

q

hNqq

hNq

hNq

q

hNqq

h

Asymmetry in longitudinally polarized SIDIS

The standard expression for SIDIS asymmetry is obtained when

0hq NH at HERMES energies in LEPTO ~10-15%

A.K.: arXiv:hep-ph/0410093; EPJC (2005)


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


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

z

Cahn:

Sivers:

Generate the final quark azimuth according to above distributions


Results: Cahn

Imbalance of measured in TFR and CFR: neutrals?


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


Results: Sivers JLab 12 GeV


SSA in PP-interactionsE704. Curves: by Anselmino et al,

STAR hep-ex/0505024

More complicated string (color) configurations in the final state.Both the active quark and the polarized proton remnant are flying in forward direction. Which picture gives dominant contribution?

h

P

( )hqD z

P( )q Nf x

( , )q N

f x Tk

( )hqD z

ST

hP

P( )q Nf x

( )hqD z

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

Which final hadrons providetransverse momentum balance?Look at forward baryons


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?Multihadron final states distributions can enhance effects Is there a similarity with PP-reaction?

Fracture FunctionClassification of spin and TMD dependent correlations in Fracture Functions“Global” analysis


Thanks to SSA05

organizers

for hospitality @ BNL

Documents

1 SSH05, BNL, June 2, 2005 Aram Kotzinian SSA in the target fragmentation region of SIDIS Cahn and Sivers effects Phenomenology & Data in the CFR Intrinsic