Studies of the transversestructure of the nucleon at

JLabMarco Mirazita

INFN – Laboratori Nazionali di Frascati

INPC2013 – Firenze, 2-7 June 2013 1

From PDFs to TMDsParton Distributions Functions (PDFs)- parton model in collinear approximation

xP

P

2

P

xP+kT

Transverse Momentum Dependent distributions (TMDs)- parton model with gluons and sea quarks- partons have transverse momentum angular

momentum- full decomposition of the nucleon spin

Tkxf

,1

3

TMDs in SIDISMany terms already at leading order• higher order suppressed by M/QDF

FF

• Structure Function

FFDFF Fragmentation

Functionqh

• Azimuthal modulation

• Beam and/or target polarizations

UNPOL

POL

NNNN

• Spin Asymmetries

• Cross section difference

POLNN

4

TMD measurements at JLab

• Very high luminosity• Transversely polarized He target

• Very high luminosity• precision measurements

Hall B

• High luminosity• large acceptance

• Small Collins • Larger Sivers for p+ than for p-

Hall AXeHee p' 3 Collins effect

11sin HhF shUT

Sivers effect

11sin DfF TUT

sh

Different results from the proton• non-zero Collins signal for p+• opposite behaviour for Sivers

HERMES proton data

Transverse target SSA on neutron

5

Double spin asymmetry

6

•small differences among pions•fairly flat distributions

11

111 1DfDg

NNNN

fPA

B

R=0.6

R=1

R=0.4

Comparison with gaussian model

1

1

fwidthpgwidthpA

T

T

fT

T

k

k

T exfkxf2

2

11 ,

gT

T

k

k

T exgkxg2

2

11 ,

PRELIMINARY

New CLAS data under analysis2D (x,pT) extraction

Xepe p

Extracting TMD from data

7

Phenomenological fits of asymmetries- gauss PT dependence

Monte Carlo implementation of gauss model

Distorsions due to phace space limits

f1

D1

Bessel-weighting method allows the model-independent extraction of TMDs

,...

,...

,

,

h

hw

PxW

PxWA

2

12

1

21

21

1 ,~,~,~,~

TT

TTBessel

bzDbxfbzDbxgA

Fourier-transform of TMDs in bT space- no convolution integrals- directly comparable with lattice

Double Spin Asymmetry

Di-hadron way to TMDsSingle hadron production

22 ,, TT kzDpxf

Double hadron production struck quark fragmenting in a hadron pair

8

Unpolarized cross section

Advantages- no convolutionDisadvantages- more complicated kinematics- unknown but measurable DiFF

e+e-→(pp) (pp) X

JLab at 12 GeV

9

CHL-2

Hall A - SBS

SolidHall C – HMS/SHMS

Hall B – CLAS12

RICH

beampipe

target

q DC1 DC2

DC3

CLAS12 RICH

SIDIS measurements at JLab12

10

CLAS12 p/KHall C p/K

CLAS12 p/K

CLAS12 p/KHall C p/K

CLAS12 p/K

CLAS12 p/KSolid p

PROTON

D2

3He

Hall A p/KSolid p

Solid p

• proton and neutron targets, unpolarized as well as longitudinally and transversely polarized

• complementary detectors• ID of final hadrons

flavor separation of TMDs

11

Sivers Asymmetry in CLAS12 for p

12

Transversity at JLab12 with DiHadronsMeasurements with polarized protons Measurements with polarized neutrons

CLAS12SoLID XeNe pp

13

Conclusions

Correlation of spin and transverse momentum of partons is crucial to understand the nucleon structure in terms of quark and gluon degrees of freedom

Measurements of azimuthal dependencies of single and double spin asymmetries indicate that these correlations may be significant

JLab with the 6 GeV electron beam has played a major role in these studies

Studies of the spin-structure of the nucleon is one of the main driving forces behind the upgrade of Jefferson Lab

14

Boer-Mulders effect

15

amplitudes are positive in low-z and high pT2 regions and show a strong kinematic

dependencepredicted amplitudes are very small and agree with data only in high-z and low pT

2 regions

unpolarized hydrogen target

z=0.11 z=0.17

z=0.23 z=0.30

z=0.37 z=0.49

pT2=0.004 pT

2=0.06

pT2=0.12 pT

2=0.21

pT2=0.50pT

2=0.34

21

21

2cos ,, TT kzHpxhA

Cahn effect

16

amplitudes are significantly non-zero and show a sign change (positive to negative) towards high pT

2 predicted amplitudes have similar trends but are systematically larger

z=0.11 z=0.17

z=0.23 z=0.30

z=0.37 z=0.49

pT2=0.004

pT2=0.06

pT2=0.21

pT2=0.50

pT2=0.12

pT2=0.34

1111cos DfHhA

17

PT dependence of the cross section

Hall C

transverse momentum dependence of f1

up+

dp-

Simplified analysis assuming only valence quarks and two FF

u and d quarks have different transverse momentum widths

Sivers asimmetry

....11 Df

Xeep pUnpolarized SIDIS pion production

18

Accessing HT terms at JLabBeam spin asymmetry in pion SIDIS

11 11

~~ DgeHGfEhALU

Xepe p

HT analog of Sivers

HT correction to D1 and Collins

qgq correlationforces acting on the quarks

Higher Twist TMD table- suppressed ~M/Q

• polarized quarks in unpolarized nucleon

• same asymmetry for charged and neutral pions null Collins contribution?• non-zero contribution from g

•Significantly positive K+moments•K- moments consistent with zero•K+ amplitude > p+ amplitude Unexpected from u-quark dominance

SIVERS

Sivers and Collins with kaons

),( suK ),( dup

• K+ and p+ asymmetries consistent within error bars

• K- and p- asymmetries may have opposite sign

COLLINS

proton

deuteron

Transversity PDF

20

DiFF from BELLE data

SIDIS DiHadron data- red: Hermes- blue: COMPASS

Curves from Torino parametrization (gauss)

A. Courtoy, DIS2012

model-independent extraction in collinear approximation

21

The Multi-Hall SIDIS program at JLabM. Aghasyan, K. Allada, H. Avakian, F. Benmokhtar, E. Cisbani, J-P. Chen, M. Contalbrigo, D. Dutta, R. Ent, D. Gaskell, H. Gao, K. Griffioen, K. Hafidi, J. Huang, X. Jiang, K. Joo, N. Kalantarians, Z-E. Meziani, M. Mirazita, H. Mkrtchyan, L.L. Pappalardo, A. Prokudin, A. Puckett, P. Rossi, X. Qian, Y. Qiang, B. Wojtsekhowski for the Jlab SIDIS working group

The complete mapping of the multi-dimensional SIDIS phase space will allow a comprehensive study of the TMDs and the transition to the perturbative regime.

Flavor separation will be possible by the use of different target nucleons and the detection of final state hadrons.

Measurements with pions and kaons in the final state will also provide important information on the hadronization mechanism in general and on the role of spin-orbit correlations in the fragmentation in particular.

Higher-twist effects will be present in both TMDs and fragmentation processes due to the still relatively low Q2 range accessible at JLab, and can apart from contributing to leading-twist observables also lead to observable asymmetries vanishing at leading twist. These are worth studying in themselves and provide important information on quark-gluon correlations.

22

Bessel analysis of BSAXepe p

Bessel-weighted cross section asymmetry

Boer,Gamber,Musch,Prokudin - arXiv:1107.5294

Test of the extraction of Fourier-transformed TMDs with MonteCarlo data