Studies of the transverse structure of the nucleon

Studies of the transverse structure of the nucleon at JLab Marco Mirazita INFN – Laboratori Nazionali di Frascati INPC 2013 – Firenze, 2 -7 June 2013 1

From PDFs to TMDs Parton Distributions Functions (PDFs) - parton model in collinear approximation x. P P Transverse Momentum Dependent distributions (TMDs) - parton model with gluons and sea quarks - partons have transverse momentum angular momentum - full decomposition of the nucleon spin x. P+k. T P 2

TMDs in SIDIS FF DF Many terms already at leading order • higher order suppressed by M/Q • Structure Function Fragmentation Function q h • Azimuthal modulation • Beam and/or target polarizations • Cross section difference • Spin Asymmetries 3

TMD measurements at JLab • Very high luminosity • Transversely polarized He target Hall B • High luminosity • large acceptance • Very high luminosity • precision measurements 4

Transverse target SSA on neutron Hall A Collins effect Sivers effect • Small Collins • Larger Sivers for p+ than for p- Different results from the proton • non-zero Collins signal for p+ • opposite behaviour for Sivers HERMES proton data 5

Double spin asymmetry R=1 R=0. 6 R=0. 4 Comparison with gaussian model • small differences among pions • fairly flat distributions New CLAS data under analysis 2 D (x, p. T) extraction N I M I P L E R Y R A 6

Extracting TMD from data Phenomenological fits of asymmetries - gauss PT dependence Monte Carlo implementation of gauss model Bessel-weighting method allows the model-independent extraction of TMDs f 1 Double Spin Asymmetry Distorsions due to phace space limits D 1 Fourier-transform of TMDs in b. T space - no convolution integrals - directly comparable with lattice 7

Di-hadron way to TMDs Single hadron production Double hadron production Ø struck quark fragmenting in a hadron pair Unpolarized cross section ØAdvantages - no convolution ØDisadvantages - more complicated kinematics - unknown but measurable Di. FF e+e-→(pp) X 8

JLab at 12 Ge. V CH L-2 Hall A - SBS Solid Hall C – HMS/SHMS CLAS 12 RICH target q DC 3 DC 1 DC 2 RIC H beam pipe Hall B – CLAS 12 9

SIDIS measurements at JLab 12 PROTON CLAS 12 Hall C p/K CLAS 12 Solid p/K p D 2 CLAS 12 Hall C p/K CLAS 12 p/K 3 He • proton and neutron targets, unpolarized as well as longitudinally and transversely polarized • complementary detectors • ID of final hadrons flavor separation of TMDs Solid p Hall A Solid p/K p 10

Sivers Asymmetry in CLAS 12 for p 11

Transversity at JLab 12 with Di. Hadrons Measurements with polarized protons CLAS 12 Measurements with polarized neutrons So. LID 12

Conclusions q. Correlation of spin and transverse momentum of partons is crucial to understand the nucleon structure in terms of quark and gluon degrees of freedom q. Measurements of azimuthal dependencies of single and double spin asymmetries indicate that these correlations may be significant q. JLab with the 6 Ge. V electron beam has played a major role in these studies q. Studies of the spin-structure of the nucleon is one of the main driving forces behind the upgrade of Jefferson Lab 13

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Boer-Mulders effect unpolarized hydrogen target z=0. 11 z=0. 17 z=0. 23 z=0. 30 z=0. 37 z=0. 49 p. T 2=0. 004 p. T 2=0. 06 p. T 2=0. 12 p. T 2=0. 21 p. T 2=0. 34 p. T 2=0. 50 amplitudes are positive in low-z and high p. T 2 regions and show a strong kinematic dependence 2 predicted amplitudes are very small and agree with data only in high-z and low p 15 T regions

Cahn effect z=0. 11 z=0. 17 p. T 2=0. 06 p. T 2=0. 004 z=0. 23 z=0. 30 p. T 2=0. 12 z=0. 37 z=0. 49 p. T 2=0. 34 p. T 2=0. 21 p. T 2=0. 50 amplitudes are significantly non-zero and show a sign change (positive to negative) towards high p. T 2 predicted amplitudes have similar trends but are systematically larger 16

PT dependence of the cross section Unpolarized SIDIS pion production transverse momentum dependence of f 1 Hall C u p+ d p. Sivers asimmetry Simplified analysis assuming only valence quarks and two FF u and d quarks have different transverse momentum widths 17

Accessing HT terms at JLab Beam spin asymmetry in pion SIDIS Higher Twist TMD table - suppressed ~M/Q • polarized quarks in unpolarized nucleon HT correction to qgq correlation HT analog D 1 and Collins forces acting on of Sivers the quarks • same asymmetry for charged and neutral pions null Collins contribution? • non-zero contribution from g 18

Sivers and Collins with kaons SIVERS • Significantly positive K+moments • K- moments consistent with zero • K+ amplitude > + amplitude Unexpected from u-quark dominance COLLINS • K+ and + asymmetries consistent within error bars • K- and - asymmetries may have opposite sign

Transversity PDF model-independent extraction in collinear approximation proton Di. FF from BELLE data SIDIS Di. Hadron data - red: Hermes - blue: COMPASS deuteron Curves from Torino parametrization (gauss) A. Courtoy, DIS 2012 20

The Multi-Hall SIDIS program at JLab M. 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 spinorbit correlations in the fragmentation in particular. Higher-twist effects will be present in both TMDs and fragmentation processes due to the still relatively low Q 2 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. 21

Bessel analysis of BSA Boer, Gamber, Musch, Prokudin - ar. Xiv: 1107. 5294 Bessel-weighted cross section asymmetry Test of the extraction of Fourier-transformed TMDs with Monte. Carlo data 22