cahn and sivers effects in the target fragmentation region of sidis

Como, September 7, 2005 Aram Kotzinian 1

Cahn and Sivers effects in the target fragmentation region of SIDIS

Introduction Hadronization in SIDISCahn and Sivers asymmetries in the current fragmentation regions

Cahn and Sivers asymmetries in LEPTODiscussion & Conclusions

Aram Kotzinian

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

hep-ph/0504081


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


Cahn effect in CFR

Quadratic in hz

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

074006 (2005);

Linear in and proportional to 2khz

Azimuthal modulation of lepton-quark hard scattering cross section in unpolarized SIDIS


Sivers Effect in CFRAzimuthal modulation of quark transverse momentum in a transversely polarized nucleon

SivTS

N

qk

M.Anselmino, M.Boglione,

U.D’Alesio,

A.K., F.Murgia and

A.Prokudin:

PRD 71, 074006 (2005);

hep-ph/0507181

Parameters were extracted

from combined analysis of

HERMES and COMPASS

data (details in the talk of

A. Prokudin)

Siv SΦ = -Φ


Ed. Berger criterion (separation of CFR &TFR)

The typical hadronic correlation length in rapidity is

Illustrations from P. Mulders:


SIDIS in LO QCD: TFR

( , )qh NM x z N

q

h

( , )lN lhX lq l

q

qh N

q Md d 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 )


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

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 PHYTIA and LEPTO + JETSET (hadronization)


Quark kT in MC generators PYTHIA and 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


Sivers effect in pp l+l- + X

Siv

z TS

Tk

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

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

( , )q N

f x Tk

ST

( , )q Nf x Tk*

p

p

q

q


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


Implementing Cahn and Sivers effects in LEPTO

The common feature of Cahn and Sivers effects Unpolarized initial and final quarksFragmenting quark-target remnant system is similar to that in default LEPTO but the direction of is now modulatedz

Cahn:

Sivers:

Generate the final quark azimuth according to above distributions


Results: Cahn

Imbalance of measured in TFR and CFR: neutrals?

Charged hadrons azimuth

EMC Collaboration (280GeV)


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


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


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

In contrast with FFs, HFs in addition to z depend on x and target type and on struck quark and target polarization:

are the spin dependent cross section and HFs

hN Nl

hNq Nq

H /and

0hq NH double spin effect (struck quark & target), as in DFs.

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

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

lqlN lhN N

qXq q

q

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


),,(),(

),,(),(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

Asymmetries

The standard LO expression for helicity asymmetry of SIDIS is obtained when

and

s

( )

h

h

h

L T T

L T T

T T T T

S (p ×k )

(p ×k )

S p (s ×k )

For TMD dependent HFs the new spin-azimuth correlations depending on both

transverse momentum of quark in nucleon and final hadron are possible:

Unpolarized lepton, long. polarized target

Unpolarized target, long. polarized lepton

Unpolarized lepton, trans. polarized target


ConclusionsHadronization functions provide a general description of SIDIS in the whole kinematics of hadronsBoth Cahn and Sivers effects are implemented in LEPTO. Possible polarization effects in hadronization were neglected.

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

It is important to perform new measurements of Cahn, Sivers and other azimuthal asymmetries in the TFR (JLab, HERMES, Electron Ion Colliders)

This will help better understand spin dynamics in hadronization: Do neutral hadrons compensate the Cahn effect in CFR?Are there asymmetries present in TFR that compensate the Sivers effect in CFR?Do there exist any other spin-dependent azimuthal asymmetries in TFR?

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


additional slides


MC tuningMonte Carlo:

Lepto in combination with JETSET;

PDF: CTEQ-6L

Fragmentation parameters tuned to HERMES multiplicities in the acceptance

Data:

Q2>1GeV2, W2>10GeV2, z>0.2, 2GeV <p< 15GeV (, K, and P)

Excellent Agreement even at the cross section level

DATA/MC <10%!

++ --

++ --

PP++ PP--


HERMES check

xF ? xF > 0.1

cahn and sivers effects in the target fragmentation region of sidis

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