The transverse spin structure of the nucleon Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007

The longitudinal structure of nucleons is “simple” It has been studied for almost 40 years xP P Q2

essentially x and Q2 degrees of freedom ….

Very good or good knowledge of q(x,Q2), g(x,Q2) and Δq(x,Q2) Poor knowledge of Δg(x,Q2) (Research Plan for Spin Physics at RHIC) Talk by L. De Nardo

The transverse structure is much more interesting and less studied spin-k┴ correlations? orbiting quarks? ? Transverse Momentum Dependent distribution functions Space dependent distribution functions

The mother of all functions M. Diehl, Trento workshop, June 07 Wigner function (Belitsky, Ji, Yuan) GPD’s TMD’s

SSA in SIDIS: Sivers functions TMDs in SIDIS SSA in SIDIS: Sivers functions Collins function from e+e- unpolarized processes (Belle) and first extraction of transversity SSA in hadronic processes Future measurements and transversity (Trento workshop on “Transverse momentum, spin, and position distributions of partons in hadrons”, June 07)

Main source of information on transverse nucleon structure SIDIS kinematics according to Trento conventions (2004)

Polarized SIDIS cross section, up to subleading order in 1/Q Kotzinian, NP B441 (1995) 234 Mulders and Tangermann, NP B461 (1996) 197 Boer and Mulders, PR D57 (1998) 5780 Bacchetta et al., PL B595 (2004) 309 Bacchetta et al., JHEP 0702 (2007) 093 SIDISLAND

SIDIS in parton model with intrinsic k┴ factorization holds at large Q2, and Ji, Ma, Yuan

Azimuthal dependence induced by quark intrinsic motion EMC data, µp and µd, E between 100 and 280 GeV M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin

Boer-Mulders function Sivers function Boer-Mulders function

8 leading-twist spin-k┴ dependent distribution functions Courtesy of Aram Kotzinian

Polarizing fragmentation function Collins function Polarizing fragmentation function

Large K+ asymmetry!

Talk by G. Schnell

COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons small values due to deuteron target: cancellation between u and d contributions talk by T. Iwata

(Kretzer fragmentation functions) M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin A fit of HERMES + COMPASS pion data, information on u and d Sivers funtions no sea contribution sea contribution? (Kretzer fragmentation functions)

Fragmentation functions DSS = de Florian, Sassot, Stratmann KRE = Kretzer HKNS = Hirai, Kumano, Nagai, Sudoh

M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin fit of HERMES + COMPASS pion and kaon data, with new set of fragmentation functions (de Florian, Sassot, Stratmann)

Predictions for JLab

Present knowledge of Sivers function (u,d) M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan The first and 1/2-transverse moments of the Sivers quark distribution functions. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions of the various parameterizations.

What do we learn from the Sivers distribution? number density of partons with longitudinal momentum fraction x and transverse momentum k┴, inside a proton with spin S M. Burkardt, PR D69, 091501 (2004)

Total amount of intrinsic momentum carried by partons of flavour a for a proton moving along the +z-axis and polarization vector S

Numerical estimates from SIDIS data U. D’Alesio Sivers functions extracted from AN data in give also opposite results, with

Sivers function and orbital angular momentum D. Sivers Sivers mechanism originates from then it is related to the quark orbital angular momentum For a proton moving along z and polarized along y

Sivers function and proton anomalous magnetic moment M. Burkardt, S. Brodsky, Z. Lu, I. Schmidt Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities in qualitative agreement with large z data: related result (M. Burkardt)

Collins function from e+e– processes (spin effects without polarization, D. Boer) j1 j2-p e- thrust-axis e+e- CMS frame: BELLE @ KEK

Fit of BELLE data

Extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin C. Türk

h1u and h1d have opposite signs What do we learn (if anything yet) from the transversity distributions and the Collins functions ? h1u and h1d have opposite signs They are both smaller than Soffer bound Still large uncertainties Tensor charges appear to be smaller than results from lattice QCD calculations M. Wakamatsu, hep-ph/0705.2917 Collins functions well below the positivity bound. Favoured and unfavoured ones have opposite signs, comparable magnitudes Only the very beginning …

TMDs and SSAs in hadronic collisions (abandoning safe grounds ….) (collinear configurations) factorization theorem (?) a b c X PDF FF pQCD elementary interactions

RHIC data excellent agreement with data for unpolarized cross section, but no SSA

experimental data on SSA BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 E704 √s = 20 GeV 0.7 < pT < 2.0 observed transverse Single Spin Asymmetries E704 √s = 20 GeV 0.7 < pT < 2.0 experimental data on SSA

talk by L. Bland STAR-RHIC √s = 200 GeV 1.2 < pT < 2.8 and AN stays at high energies …. talk by L. Bland

SSA in hadronic processes: intrinsic k┴, factorization? Two main different (?) approaches Generalization of collinear scheme (M. A., M. Boglione, U. D’Alesio, E. Leader, F. Murgia, S. Melis) a b c X

main remaining contribution to SSA from Sivers effect It generalizes to polarized case plenty of phases main remaining contribution to SSA from Sivers effect

U. D’Alesio, F. Murgia E704 data STAR data fit prediction

Higher-twist partonic correlations (Efremov, Teryaev; Qiu, Sterman; Kouvaris, Vogelsang, Yuan) contribution to SSA twist-3 functions hard interactions “collinear expansion” at order ki┴

fits of E704 and STAR data Kouvaris, Qiu, Vogelsang, Yuan

Gluonic pole cross sections and SSA in Bacchetta, Bomhof, Mulders, Pijlman; Vogelsang, Yuan factorization ? (Collins) Sivers contribution to SSA gluonic pole cross sections take into account gauge links Diagram dependent Gauge link Colour factors (breaking of factorization?)

Gluonic pole cross sections and SSA in to be compared with the usual cross section

Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory ! Simple QED example: DIS: attractive Drell-Yan: repulsive Same in QCD: As a result:

factorization holds, two scales, M2, and TMDs and SSAs in Drell-Yan processes (returning to safer grounds and looking at future ….) p Q2 = M2 qT qL l+ l– γ* factorization holds, two scales, M2, and

Unpolarized cross section already very interesting Collins-Soper frame

! ! ! (Polarized) Drell-Yan cross sections allow to access many TMDs (Boer-Mulders, …) D-YLAND verify whether and offer the golden channel to measure the transversity distribution ! ! ! Talks by R. Kaiser, M. Contalbrigo

Conclusions Increasing knowledge about quark transverse motion, and spin-k┴ correlations (Sivers function) First experimental information on h1 Work in progress on GPDs and quark space distribution (Lq) Towards resolving the orbital motion of quarks in a proton … More data from HERMES, COMPASS, JLab and RHIC Thanks