polarized semi-inclusive dis in current and target fragmentation

JLab, May 27, 2005 Aram Kotzinian 1

Polarized Semi-Inclusive DIS in Current and Target Fragmentation

Introduction The flavor separation of the quark helicity distributionsThe spin and azimuthal asymmetries in the current and target fragmentation regions Polarization of Λs produced in SIDIS of polarized leptons on unpolarized targetConclusions

Aram Kotzinian

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


Lepton-Nucleon EM Interactions

Study of Confinement in QCDStructure of nucleon & hadronization dynamics

Elastic – Form-factors

Exclusive – GPDs

DIS – DFs

SIDIS:CFR: DFs & Fragmentation Functions

TFR: Fracture Functions

More general: Hadronization Functions

Spin phenomena play crucial role in all channels


DIS

2 2 2( , ) (1 (1 ) ) ( )

, , , , ,

qq

x Q y e q x

q u u d d s s


Nucleon Spin from polarized DIS

Gluon Spin

Nucleonspin zLG

2

1

2

1Quark Spin

Orbital Angular Momentum

2 2 2( , ) (1 (1 ) ) ( )

( ) ( ) ( )

qq

x Q y e q x

q x q x q x

Spin Sum Rule

COMPASS 2005

LSS 2005


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 CFR &TFR)

The typical hadronic correlation length in rapidity is

Illustrations from P. Mulders:


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

Parton DF, hard X-section & Hadronization are factorized

Implemented in LEPTO + JETSET (hadronization)


Flavor separation using SIDIS

0.028 0.033 0.009s

Leader & Stamenov, 2003:

Non-negative strange quark

polarization is almost

impossible

HERMES analysis


Purity method for flavor separation

Purities are calculated using LEPTO

( )q Nf x N

( )hqD z

qq

h


LO SIDIS in LEPTO- Before

- After

-Example: valence struck quark

quarkTarget remnant

Natural question: does Lund hadronization exactly correspond to independent quark fragmentation in the CFR with z>0.2? (A.K.2004)

The important property of FFs is universality:

1. Independence of Bjorken variable x2. Target type independence3. Process type independence ),,(

),,(),(

2/

2,/2

QzxN

QzxNQzD

DISNq

SIDIShNqh

q


Bjorken variable dependence of “FFs” in LEPTO

2 2

0.1

1.5

x

Q GeV

2 2

0.1

3.4

x

Q GeV

2

2

F

Cuts:

Q 1

W 10

y<0.85;

0.023<x<0.6

E >3.5

0.2

x >0.1

GeV

GeV

GeV

z

The dependence of “FFs” on x

cannot be attributed to Q2 evolution


Target type dependence of “FFs” in LEPTO

Example oftarget remnant: removed valence u-quark:

( )p u ud ( )n u dd

There is dependence of “FFs” on the

target type at 10% level


The primary hadrons produced in string fragmentationcome from the string as a whole, rather than from

an individual parton.

LUND string fragmentation


Even for meson production in the CFR the hadronization in LEPTO is more complicated than SIDIS description with independent FFs

Hadronization Functions (HF)

More general framework -- Fracture Functions (Teryaev, T-odd, SSA…)

We are dealing with LUND Hadronization Functions:

),,(),(),,( 2/

22/ QxxHQxqQxxM F

hNqF

hNq

),,( 2/ QxxM F

hNq

LEPTO is a model for Fracture Functions:

The dependence on target flavor is due to dependence on target remnant flavor quantum numbers. What about spin quantum numbers?

Violation of naïve x-z factorization and isotopic invariance of FF


Dependence on target remnant spin state (unpolarized LEPTO)

Example: valence u-quark is removed from proton. Default LEPTO: the remnant (ud) diquark is in 75% (25%) of cases scalar (vector)

Even in unpolarized LEPTO there is a dependence on targetremnant spin state

0{( ) }, 1.ud u w

1{( ) }, 1.ud u w

(ud)0: first rank Λ is possible(ud)1: first rank Λ is impossible


Target remnant in Polarized SIDIS

JETSET is based on SU(6) quark-diquark model

Probabilities of different string spin configurations depend on quark and target polarizations, target type and process type

90% scalar

100% vector


Polarized SIDIS & HF-- spin dependent cross section and HFs

These Eqs. coincide with those proposed by Gluk&Reya (polarized FFs). In contrast with FFs, HFs in addition to z depend on x and target type

hN Nl

hNq Nq

H /and

0hq NH double spin effect, as in DFs.


For validity of purity method most important is the second relation

),,(),(

),,(),(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

The standard expression for SIDIS asymmetry is obtained when


Toy model (A.K.2003)u

( ud)

In JETSET there is a pointer indicating whether produced

hadron is coming from quark or diquark end of the string.

Symmetric LUND fragmentation: each string breaking

starting with equal probabilities from q or qq end.


PEPSI MCModel A: default PEPSI

Model B: neglect contribution of events to asymmetries

with hadrons originated from diquark


Beam Energy Dependence

Situation is different for higher energies:

dependencies of “FFs” extracted from MC

on x, target type and target remnant quantum numbers

are weaker


LUND MC is proved to be capable to describe data in a wide range of kinematics.The new concept of (polarized) hadronization is introduced and studied using LEPTO event generator

The hadronization in LEPTO is more general than simple LO x-z factorized picture with independent fragmentation, for example, it describes well TFR.

It necessary to modify PEPSI MC event generator by including polarization in hadronization.

The purity method have to be modified to include polarized HFs. Within this new approach one can include all hadrons (CFR+TFR) for flavor separation analysis.

More studies on the accuracy of different methods of the polarized quark DF extraction using SIDIS asymmetries are needed.Alternative measurements are highly desirable

SIDIS at different beam energies: COMPASS, JLab, EICW production in polarized p+p collisions (Anti)neutrino DIS on polarized targets (Neutrino Factory)

Conclusions 1


Melnitchouk & Thomas: Meson Cloud Model

100 % anticorrelated with target polarization contradiction with neutrino data for unpolarized target

Longitudinal polarization of Λ in the TFR

Λ-polarization in TFR


Karliner, Kharzeev , Sapozhnikov, Alberg, Ellis & A.K. Nucleon wave function contains an admixture with

component:

π,K masses are small at the typical hadronic mass scale: a strong attraction in the − channel.

pairs from vacuum in state

Intrinsic Strangeness Model

ss

qq 0

3P

Polarized proton:Spin crisis: 1.0s

0PJ


J.Ellis, A.K. & D.Naumov (2002)


qq q

Rank from diquark

Rank from quark

NOMAD (43.8 GeV) COMPASS (160 GeV)

No clean separation of the quark and diquark fragmentation

Λ parent


Λ polarization in quark & diquark fragmentation

Λ polarization from the diquark fragmentation

Λ polarization from the quark fragmentation


Spin Transfer

We use Lund string fragmentation model incorporated in LEPTO6.5.1 and JETSET7.4.

We consider two extreme cases when polarization transfer is nonzero:

model A: the hyperon contains the stuck quark: Rq = 1

the hyperon contains the remnant diquark: Rqq = 1

model B: the hyperon originates from the stuck quark: Rq ≥ 1

the hyperon originates from the remnant diquark: Rqq ≥ 1


Fixing free parameters

We vary two correlation coefficients ( and ) in order to fit our models A and B to the NOMAD Λ polarization data.

We fit to the following 4 NOMAD points to find our free parameters:


Results

Predictions for JLab 5.75 GeV


Predictions for CLAS

Predictions for xF-dependence at JLab 12 GeVRed squares with error bars – projected statistical accuracy for

1000h data taking (H.Avagyan).


Predictions for EIC

5 GeV/c electron + 50 GeV/c proton, 9.04.0 GeV/c, .1 ,1 2

Beam yQP

Good separation of the quark and diquark fragmentation allows to distinguish betweendifferent spin transfer mechanisms from quark and diquark


Conclusions 2

Predictions for Λ polarization are very sensitive to production mechanism

A phenomenological polarized intrinsic strangeness + SU(6) model is able to describe all available data on longitudinal polarization of Λ in full kinematic range

New measurements at different energies will serve as a test for proposed models


Unpolarized SIDIS & Cahn effect

frame CM * P

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

No exact factorization !Bj hx z

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

)/O( QkT

Ji et al: QCD factorization holds for QkP QCDTT

Quadratic in

Linear in and proportional to 2k

hz

hz

approximation


Comparison with data

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


Parameterization for Sivers effect


Data


New HERMES data


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

Cahn:

Sivers:

Generate the final quark azimuth according to above distributions

z


Results: Cahn

Imbalance of measured in TFR and CFR: neutrals?


Results: Sivers

Predictions for xF-dependence at JLab 12 GeV

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)

Both the active quark and the polarized proton remnant are flying in forward direction.

Which final hadrons provide transverse momentum balance?

h

P

( )hqD z

P( )q Nf x

( , )q N

f x Tk

( )hqD z

ST


Conclusions 3Both 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 Function“Global” analysisClassification of spin and TMD dependent correlations in Fracture Functions


Conclusions

Spin phenomena in SIDIS can play very important role for modeling and understanding the QCD dynamics

Access to TFR opens a new field both for theoretical and experimental investigations

JLab@12 GeV is ideally placed to make important breakthroughs over a wide spectrum of discovery in nucleon structure and hadronization dynamics

Thanks for hospitality

@ JLab


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HERMES check

polarized semi-inclusive dis in current and target fragmentation

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