Spin effects in MC generators

Dubna, September, 2005 Aram Kotzinian 1

Spin effects in MC generators

The spin and azimuthal asymmetries in the current and target fragmentation regions

The flavor separation of the quark helicity distributions

Conclusions

Aram Kotzinian

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

Dubna, SPIN-05


Sivers effect in pp l+l- + X

One class of nonperturbative input:

only distribution functions, no hadronization effects are present

Modify PYTHIA to include Sivers effect: azimuthal correlations of the parton

transverse momentum and transverse spin on nucleon in distribution functions

1 2

11 21 1 2 2( , ) ( , ) qq l lh

h h l l Xq h q h

q

d f x f dx T T; kSk

( , )q N

f x Tk

ST

( , )q Nf x Tk*

p

p

q

q

Siv

z TS

Tk

SivTS

N

qk


Sivers effect in pp l+l- + X

at =14.4 GeV

p p X

s

q p

q p

*

at =200 GeV

p p X

s

Similar values as in Anselmino et al: hep-ph/0507181


SIDIS in LO QCD: CFR

( , ;( , ) ), hq q

lN lhXq q N

q

lq lqd f dx D z T Tp sk s ;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

1ˆ( )( ) Lh T T Lk s p S Mulders distribution


SIDIS Event Generators and LUND String Fragmentation

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

lqlN lhN N

qXq q

q

ld x xd Hf x T TTk s ; pS k s ; S

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 PHYTIA and LEPTO + JETSET (hadronization)

R

R

u

u

d

d

s

d

s

R

Sof

t S

tron

g In

tera

ctio

n

u

(ud)Λ

d

ρ0

π-

K+

π+

quarkTarget remnant


Quark transverse momentum in MC generators

- 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

A.K. hep-ph/0504081


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, xBj and PT dependences


Results: Sivers JLab 12 GeV


Purity method for flavor separation

Purities are calculated using LEPTO

( )q Nf x N

( )hqD z

qq

h


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

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 type:

removed valence u-quark:

( )p u ud ( )n u dd

There is dependence of “FFs” on the

target type at 10% level


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


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

Spin dependence of hadronization: A.K. (hep-ph/0410093, EPJ C, 2005)

The standard expression for SIDIS asymmetry is obtained when2 2( , , ) ( , )h

q NH x z Q D z Q 2( , , ) 0hq NH x z Q and


Toy model using PEPSI MCModel A: default PEPSI

Model B: neglect contribution of events to asymmetries

with hadrons origin pointing to diquark

(A.K. PLB 552, 2003)


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


Remarks on TMD hadronization

For TMD dependent HFs the new spin-azimuth correlations depending

on both transverse momentum of quark in nucleon and final hadron are

possible:

s

( )

h

h

h

L T T

L T T

T T T T

S (p ×k )

(p ×k )

S p (s ×k )

Unpolarized lepton, long. polarized target

Unpolarized target, long. polarized lepton

Unpolarized lepton, trans. polarized target

( , , , ; )q hh N q F NH x xT Tk s ; p S


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.

One can try to modify PEPSI MC event generator by including polarization in hadronization.

The purity method have to be modified to take into account the 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 parton 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 (flavor separation)


Conclusions (azimuthal asymmetries)

Both Cahn and Sivers effects are implemented in LEPTO. Possible effects of polarized hadronization were neglected.

Existing data in CFR are well described by modified LEPTO

The measured Cahn effect in the TFR is not well described

It is important to perform new measurements of both Cahn and Sivers 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 Sivers effect in TFR compensating asymmetry in CFR?

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


additional slides


Ed. Berger criterion (separation of CFR &TFR)

The typical hadronic correlation length in rapidity is

Illustrations from P. Mulders:


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 provides 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.



HERMES check

xF ? xF > 0.1


LO x-z factorization

1 2 1 2

1 1 2 2

1 2 1 1 2 2 1

Measure:

Cal

ˆ ( , ) 4 ( ) ( ) ( ) ( )

( ) ( ) ( )

ˆ ( , ) 4 ( ) ( ) ( )

ˆ ˆ( , ; ) ( , ) ( , )

4 ( ) ( ) ( ) 4 ( ) (

culate:

) ( )

r(z; , ) 4 ( ) ( , ; ) ( ) (

p u d

d u

p

p p

x z u x D z d x D z

r z D z D z

x z u x r z d x

R x x z x z x z

u x r z d x u x r z d x

x x u x R x x z u x R x

1

2 1

1

2

2

2

Have to be independent of ,

Check for differ

c

en

hoic

t choices of

, ; ) ( ) ( )

,

e

x z d x d x

x

x x

x

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Spin effects in MC generators

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