h. avakian, argonne, april 8 1 harut avakian (jlab) modification of transverse momentum...

H. Avakian, Argonne, April 81

Harut Avakian (JLab)Harut Avakian (JLab)

Modification of transverse momentum distributions in nucleiModification of transverse momentum distributions in nuclei

Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider

Argonne National Laboratory, April 7 - 9, 2010

•TMDs and spin-orbit correlations•kT-distributions•Higher twists in SIDIS

•MC-simulations•Projections for observables•Conclusions


Structure of the Nucleon

GPDs/IPDs

d2kT

d2kT

TMD PDFs f1

u(x,kT), .. h1u(x,kT)

Gauge invariant definition (Belitsky,Ji,Yuan 2003)Universality of kT-dependent PDFs (Collins,Metz 2003)Factorization for small kT. (Ji,Ma,Yuan 2005)

Wpu(k,rT) “Mother” Wigner distributions

d2 r T

PDFs f1u(x), .. h1

u(x)

quark polarization


kT and FSI

l l’

x,kT

proton

spectator system

•The difference is coming from final state interactions (different remnant)

Tang,Wang & Zhou

Phys.Rev.D77:125010,2008

lT

l l’

x,k’T l’T

spectator systemnucleus

total transverse momentum broadening squaredBHS 2002

Collins 2002Ji,Yuan 2002

soft gluon exchanges included in the distribution function (gauge link)


SIDIS: partonic cross sections

kT

PT = p┴ +z kT

p┴

Ji,Ma,Yuan Phys.Rev.D71:034005,2005

Is the info on x-kT correlations accessible in kT integrated observables?


Quark distributions at large kQuark distributions at large kTT: models: models

Effect of the orbital motion on

the q- may be most significant

JMR model

q

DqMR , R=s,a

u/u

(dipole formfactor), J.Ellis, D-S.Hwang, A.Kotzinian

Higher probability to find a quark anti-aligned with proton spin at large kT

(H.A.,S.Brodsky, A.Deur,F.Yuan 2007)


Quark distributions at large kQuark distributions at large kTT: lattice: lattice

Higher probability to find a d-quark at large kT

Higher probability to find a quark anti-aligned with proton spin at large kT

B.Musch arXiv:0907.2381

Understanding the transverse structure is crucial!


A1

A1 PT-dependence

CLAS data suggests that width of g1 is less than the width of f1

AnselminoCollins

Lattice

New CLAS data would allow multidimensional binning to study kT-dependence for fixed x

PT

PT

arXiv:1003.4549


Quark distributions at large kQuark distributions at large kTT

Higher probability to find a hadron at large PT in nuclei

kT-distributions may be wider in nuclei?

PT = p┴ +z kT

bigger effect at large z


Jet limit: Higher Twist azimuthal asymmetriesJet limit: Higher Twist azimuthal asymmetries

No leading twist, provide access to quark-gluon correlations

T-odd

H.A.,A.Efremov,P.Schweitzer,F.Yuan arXiv:1001.5467

“interaction dependent”

Twist-2

Twist-3


Modification of Cahn effect

•Large cosn moments observed at COMPASS

Bag model

arXiv:1001.3146 Gao, Liang & Wang

•Nuclear modification of Cahn may provide info on kT broadening and proton TMDs


s

x

h

PT

Fragmenting quark polarization

C

C

y

x

S h

PTS = +h

HT function related to force on the quark. M.Burkardt (2008)

Collins mechanism for SSACollins mechanism for SSAfragmentation of transversely polarized quarks into unpolarized hadrons

x

PT

h

S=y

x

PT

h

S=y


Electroproduction kinematics: JLab12→EIC

JLab 0.1<xB<0.7 JLab@12GeV

Study of high x domain requires high luminosity, low x higher energies

EIC

JLab12

Q2

EIC

collider experiments

H1, ZEUS 10-4<xB<0.02

EIC 10-4<xB<0.3gluons (and quarks)

fixed target experiments

COMPASS 0.006<xB<0.3

HERMES 0.02<xB<0.3

gluons/valence and sea quarks

valence quarks

EIC (4x60):


LEPTO/PEPSI: quark distributions

Need to model TMDs in LUND MC

•Implemented in PEPSI modification to LEPTO done by A. Kotzinian •Add different widths for q+ and q-

z>0.1

z>0.3

MC with Cahn

Event Generator with polarized electron and nucleon: PEPSI,….

Acceptance checkDesign parameters

Smearing/resolution routinesUse GEANT as input

Physics analysis using the “reconstructed” event sample


(p) = 0.05 + 0.06*p [GeV] %

EIC 4x60 (Lumi 1033,cm-2sec-1 , ~1 hour)

K*s can be studied with EIC

<x>=0.1, <Q2>=4


Nonperturbative TMD Perturbative region

sinLU~FLU~ 1/Q (Twist-3)

In the perturbative limit 1/PT behavior expected

Study for SSA transition from non-perturbative to perturbative regime.

EIC will significantly increase the PT range.

PT-dependence of beam SSA

4x60 100 days, L=1033cm-2s-1


Boer-Mulders Asymmetry with CLAS12 & EIC

CLAS12 and EIC studies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations and test unified theory (Ji et al)

Nonperturbative TMDPerturbative region

Transversely polarized quarks in the unpolarized nucleon-

CLAS12

EIC

e p5-GeV 50 GeV

sin(C) =cos(2h)

Perturbative limit calculations available for :

J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238


Summary

Studies of spin and azimuthal asymmetries in semi-inclusive processes at EIC :

•Measure nuclear modification of transverse momentum distributions and spin-orbit correlations of partons at small x, in a wide range of Q•Study quark-gluon correlations (HT) in nucleon and nucleus•Provide information on correlations of longitudinal and transverse degrees of freedom

EIC: Studies of nuclear modifications of spin orbit and quark-gluon correlations combined with JLab12 data will help construct a more complete picture about the structure of the nucleon and nuclei.


Support slides….


High energy quarks at small angles

Struck quark kinematics (EIC 4x60)

q


SIDIS (*p->X) x-section at leading twist

•Measure Boer-Mulders distribution functions and probe the polarized fragmentation function•Measurements from different experiments consistent

TMD PDFs


kT and FSI

l l’

x,kT

proton

spectator system

•The difference is coming from final state interactions (different remnant)

Tang,Wang & Zhou

Phys.Rev.D77:125010,2008

lT

l l’

x,k’T l’T

spectator systemnucleus

total transverse momentum broadening squaredBHS 2002

Collins 2002Ji,Yuan 2002


Transverse force on the polarized quarks

Interpreting HT (quark-gluon-quark correlations) as force on the quarks (Burkardt hep-ph:0810.3589)

Quark polarized in the x-direction with kT in the y-direction

Force on the active quark right after scattering (t=0)


EIC: Kinematics Coverage

Major part of current particles at large angles in Lab frame (PID at large angles crucial).

e p5 GeV 50 GeV

e’+X all

xF>0

z>0.3

EIC-MC

xF>0 (CFR)

xF<0 ( TFR)

EIC-MC


sinLU(UL) ~FLU(UL)~ 1/Q (Twist-3)

1/Q behavior expected (fixed x bin)

Study for Q2 dependence of beam SSA allows to check the higher twist nature and access quark-gluon correlations.

Q2-dependence of beam SSA


EIC medium energy

• Electron energy: 3-11 GeV

• Proton energy: 20-60 GeV

– More symmetric kinematics provides better resolution and particle id

• Luminosity: ~ 1034 cm-2 s-1

– in range around s ~ 1000 GeV2

• Polarized electrons and light ions

– longitudinal and transverse

• Limited R&D needs

• 3 interaction regions (detectors)

• Potential upgrade with high-energy ring

Main FeaturesMain Features• Electron energy: 4-20 GeV

• Proton energy: 50-250 GeV

– More symmetric kinematics provides better resolution and particle id

• Luminosity: ~ 1033 cm-2 s-1

– in range around s ~ 1000-10000 GeV2

• Polarized electrons and light ions

– longitudinal and transverse

• Limited R&D needs

• ? interaction regions (detectors)

• 90% of hardware can be reused

EIC@JLabEIC@RHIC

Slides are for a “generic” US version of an EIC (5x50 or 4x60):• polarized beams (longitudinal and transverse, > 70%)• luminosities of at least 1033


JETSET:Single particle production in hard scattering

Lund-MC should be modified to allow checks of sensitivity of measurements to different effects related to the transverse structure

- Before- After quarkTarget remnant

LUND Fragmentation Functions


Cross section is a function of scale variables x,y,z

z

SIDIS kinematical plane and observablesSIDIS kinematical plane and observables

U unpolarized

L long.polarized

T trans.polarizedBeam polarizationTarget polarization

sin2moment of the cross section for unpolarized beam and long. polarized target


Identification using the missing mass may be possible

detected

CLAS12

EIC4x60

FAST-MC

Kaon production in SIDIS

(p) = 0.05 + 0.06*p [GeV] %


JLab, Nov 2530

Azimuthal moments with unpolarized target

quark polarization


JLab, Nov 2531

Azimuthal moments with unpolarized target

quark polarization


JLab, Nov 2532

SSA with unpolarized target

quark polarization


JLab, Nov 2533


quark polarization


SSA with long. polarized target

quark polarization



quark polarization


Single hadron production in hard scattering

Measurements in different kinematical regions provide complementary information on the complex nucleon structure.

xF - momentum

in the CM frame

xF>0 (current fragmentation)

xF<0 (target fragmentation)

h

h

Target fragmentation Current fragmentation

Fracture Functions

xF

M

0-1 1

h

h

PDF GPD

kT-dependent PDFs Generalized PDFs

PDF

hFF

DA DA

exclusivesemi-inclusive semi-exclusive


production in the target fragmentation

xF - momentum

in the CM frame

Wide kinematical coverage of EIC would allow studies of hadronization in the target fragmentation region (fracture functions)

polarization in TFR provides information on contribution of strange sea to proton spin

Study polarized diquark fracture functions sensitive to the correlations between struck quark transverse momentum and the diquark spin.

x F(

)EIC CLAS12

(ud)-diquark is a spin and isospin singlet s-quark carries whole spin of uds


Collins effect

Simple string fragmentation for pions (Artru model)

leading pion out of page

production may produce an opposite

sign AUT

Leading opposite to leading (into page)

hep-ph/9606390 Fraction of in eX

% left from eX asm

20%

40%

~75%

~50%

Fraction of direct kaons may be significantly higher than the fraction of direct pions.

LUND-MC

L

z

L

z


K/K* and separations

Detection of K+ crucial for separation of different final states (,K*)


Sivers effect in the target fragmentation

A.Kotzinian

High statistics of CLAS12 will allow studies of kinematic dependences of the Sivers effect in target fragmentation region


27 G

eV

com

pass

herm

es JLab (upgraded)

JLab@6GeV

Q2

EIC

HERA

ENCENC

Hard Scattering Processes: Kinematics Coverage


collider experiments H1, ZEUS (EIC)10-4<xB<0.02 (0.3): gluons (and quarks) in the proton

fixed target experiments COMPASS, HERMES 0.006/0.02<xB<0.3 : gluons/valence and sea quarks JLab/JLab@12GeV 0.1<xB<0.7 : valence quarks

JLab

12

EIC(4

x60)

ENC(3x1

5)

Q2


Hard Scattering Processes: Kinematics Coverage


collider experiments H1, ZEUS (EIC)10-4<xB<0.02 (0.3): gluons (and quarks) in the proton

fixed target experiments COMPASS, HERMES 0.006/0.02<xB<0.3 : gluons/valence and sea quarks JLab/JLab@12GeV 0.1<xB<0.7 : valence quarks

27 G

eV

com

pass

herm

es JLab (upgraded)

JLab@6GeV

Q2

EIC

HERA

ENCENC

JLab12

EIC

ENC

Q2


hep:arXiv-09092238


TMDs: QCD based predictions

Large-Nc limit (Pobilitsa)

Brodsky & Yuan (2006) Burkardt (2007)

Large-x limit

Do not change sign (isoscalar)

All others change sign u→d (isovector)

h. avakian, argonne, april 8 1 harut avakian (jlab) modification of transverse momentum...

Documents

nuclei ktdistributions

universality of kt

small kt

quark distributionsneed

quark antialigned

study ktdependence

kt integrated observables

q twist