Studies of the transverse structure of the nucleon at JLab Marco Mirazita INFN – Laboratori Nazionali di Frascati INPC2013 – Firenze, 2-7 June 20131

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

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

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

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

Double spin asymmetry 6 small differences among pions fairly flat distributions R=0.6 R=1 R=0.4 Comparison with gaussian model PRELIMINARY New CLAS data under analysis 2D (x,pT) extraction

Extracting TMD from data 7 Phenomenological fits of asymmetries - gauss P T dependence Monte Carlo implementation of gauss model Distorsions due to phace space limits f1f1 D1D1 Bessel-weighting method allows the model-independent extraction of TMDs Fourier-transform of TMDs in b T space - no convolution integrals - directly comparable with lattice Double Spin Asymmetry

Di-hadron way to TMDs Single hadron production Double hadron production  struck quark fragmenting in a hadron pair 8 Unpolarized cross section  Advantages - no convolution  Disadvantages - more complicated kinematics - unknown but measurable DiFF e + e - →(  ) (  ) X

JLab at 12 GeV 9 CH L-2 Hall A - SBS Solid Hall C – HMS/SHMS Hall B – CLAS12 RICH beam pipe target  DC1 DC2 DC3 CLAS12 RICH

SIDIS measurements at JLab12 10 CLAS12  /K Hall C  /K CLAS12  /K Hall C  /K CLAS12  /K Solid  PROTON D2D2 3 He Hall A  /K Solid  proton and neutron targets, unpolarized as well as longitudinally and transversely polarized complementary detectors ID of final hadrons flavor separation of TMDs

Sivers Asymmetry in CLAS12 for  11

Transversity at JLab12 with DiHadrons 12 Measurements with polarized protonsMeasurements with polarized neutrons CLAS12 SoLID

Conclusions 13  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

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Boer-Mulders effect 15 amplitudes are positive in low-z and high p T 2 regions and show a strong kinematic dependence predicted amplitudes are very small and agree with data only in high-z and low p T 2 regions unpolarized hydrogen target z=0.11z=0.17 z=0.23z=0.30 z=0.37z=0.49 p T 2 =0.004p T 2 =0.06 p T 2 =0.12 p T 2 =0.21 p T 2 =0.50p T 2 =0.34

Cahn effect 16 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 z=0.11z=0.17 z=0.23z=0.30 z=0.37z=0.49 p T 2 =0.004 p T 2 =0.06 p T 2 =0.21 p T 2 =0.50 p T 2 =0.12 p T 2 =0.34

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

Accessing HT terms at JLab Beam spin asymmetry in pion SIDIS HT analog of Sivers HT correction to D 1 and Collins qgq correlation forces 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  18

Significantly positive K + moments K - moments consistent with zero K + amplitude >  + amplitude Unexpected from u-quark dominance SIVERS Sivers and Collins with kaons K + and  + asymmetries consistent within error bars K - and  - 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

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 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 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 22 Bessel-weighted cross section asymmetry Boer,Gamber,Musch,Prokudin - arXiv: Test of the extraction of Fourier-transformed TMDs with MonteCarlo data