Transversity (transverse spin and transverse motion) (unravelling the spin-orbital motion of partons?) Towards transversity distributions: theory and experiments Collins mechanism Transverse Single Spin Asymmetries Sivers mechanism Spin and k┴ dependent parton distributions (TMD) Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Parton distributions and (or are fundamental leading-twist quark distributions quark distribution – well known all equally important quark helicity distribution – known transversity distribution – unknown gluon helicity distribution – poorly known related to chiral-even related to chiral-odd positivity bound Mauro Anselmino, Como, September 7, 2005 Transversity 2005

decouples from DIS (no quark helicity flip) + + – – + = – + + + + + – = in helicity basis + – decouples from DIS (no quark helicity flip) + – Mauro Anselmino, Como, September 7, 2005 Transversity 2005

– + + – + – – + – + + – – + h1 x h1 h1 x Collins function h1 must couple to another chiral-odd function. For example: D-Y, pp → l+l– X, and SIDIS, l p → l π X, processes – + h1 x h1 – + J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 + – + – + – h1 x Collins function – + + – J. Collins, 1993 Mauro Anselmino, Como, September 7, 2005 Transversity 2005

– + +1 –1 No gluon contribution to h1 simple Q2 evolution Q2 = 25 GeV2 Q02 = 0.23 GeV2 V. Barone, T. Calarco, A. Drago Mauro Anselmino, Como, September 7, 2005 Transversity 2005

h1 in Drell-Yan processes Q2 = M2 l– γ* qT p p qL Elementary LO interaction: 3 planes: plane polarization vectors, ┴ plenty of spin effects p-γ* plane, l+l– γ* plane Mauro Anselmino, Como, September 7, 2005 Transversity 2005

h1q (x, Q2) evolution much slower than h1 from at RHIC RHIC energies: small x1 and/or x2 h1q (x, Q2) evolution much slower than Δq(x, Q2) and q(x, Q2) at small x Barone, Calarco, Drago ATT at RHIC is very small smaller s would help Martin, Schäfer, Stratmann, Vogelsang talk by A. Mukherjee Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora h1 from at GSI large x1,x2 GSI energies: one measures h1 in the quark valence region: ATT is estimated to be large, between 0.2 and 0.4 PAX proposal: hep-ex/0505054 Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora Mauro Anselmino, Como, September 7, 2005 Transversity 2005

talks by M. Guzzi, A. Bianconi Energy for Drell-Yan processes "safe region": QCD corrections might be very large at smaller values of M: yes, for cross-sections, not for ATT K-factor almost spin-independent Fermilab E866 800 GeV/c H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270 V. Barone et al., in preparation talks by M. Guzzi, A. Bianconi Mauro Anselmino, Como, September 7, 2005 Transversity 2005

s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2 Mauro Anselmino, Como, September 7, 2005 Transversity 2005

s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2 Mauro Anselmino, Como, September 7, 2005 Transversity 2005

data from CERN WA39, π N processes, s = 80 GeV2 Mauro Anselmino, Como, September 7, 2005 Transversity 2005

h1 x Collins from SIDIS processes Asymmetry in the fragmentation of a transversely polarized quark φ Sq p┴ pq (Fundamental QCD property? D. Sivers) q’ q y initial q spin is transferred to final q', which fragments Sq Sq’ p┴ “Trento conventions” ΦS Φh x Amsterdam notations Mauro Anselmino, Como, September 7, 2005 Transversity 2005

neglecting intrinsic motion in partonic distributions: Collins function transversity some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1) Mauro Anselmino, Como, September 7, 2005 Transversity 2005

fit to HERMES data on Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Extraction of Collins functions from HERMES + BELLE data P1 depends on (talk by R. Seidl) M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Fits to HERMES Collins data, preliminary results Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Fits to BELLE Collins data, preliminary results Mauro Anselmino, Como, September 7, 2005 Transversity 2005

HERMES + BELLE: Collins function is not zero Theory: probably universal Collins, Metz Amrath, Bacchetta, Metz, Kundu, Mulders, … Models: few, in disagreement pion-quark vertex ? loop? assumes h1 = ∆q disfavoured Collins functions = 0 Talk by. A. Bacchetta Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Alternative accesses to transversity Inclusive Λ production and measure of Λ polarization transverse fragmentation function p X COMPASS analysis in progress Talk by A. Ferrero Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Two pion production: interference fragmentation function Talks by P. van der Nat, M. Radici Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Vector meson production: (generalized fragmentation function) Inclusive hadronic production: Talk by F. Murgia Single Spin Asymmetry in D-Y processes (Boer-Mulders distribution) Talks by D. Boer, G. Goldstein, M. Radici Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Transverse SSA S p' p – p – p' PT y p' x PT θ z p – p – p' Single Spin Asymmetry in elastic scattering. Example: 6 independent helicity amplitudes Mauro Anselmino, Como, September 7, 2005 Transversity 2005

for a generic configuration: y ΦS Φ x S p' PT θ p – p z – p' for a generic configuration: Mauro Anselmino, Como, September 7, 2005 Transversity 2005

large SSA observed at hadron level needs helicity flip + relative phase + – + + x + + + + at quark level large SSA observed at hadron level Mauro Anselmino, Como, September 7, 2005 Transversity 2005

SSA, pp → πX BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 E704 √s = 20 GeV 0.7 < pT < 2.0 STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5 E704 √s = 20 GeV 0.7 < pT < 2.0 SSA, pp → πX Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Unweighted Collins moment: Unweighted Sivers moment: Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Transverse Λ polarization in unpolarized p-Be scattering at Fermilab Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Mauro Anselmino, Como, September 7, 2005 Transversity 2005

+ – S Brodsky, Hwang, Schmidt model for Sivers function p X q q diquark diquark needs k┴ dependent quark distribution in p↑: Sivers function Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Sivers asymmetry in SIDIS Amsterdam notations Sivers asymmetry in SIDIS talk by A. Prokudin p┴ = PT – z k┴ + O(k┴2/Q2) Mauro Anselmino, Como, September 7, 2005 Transversity 2005

M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181 Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Deuteron target Mauro Anselmino, Como, September 7, 2005 Transversity 2005

First p┴ moments of extracted Sivers functions, compared with models M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin First p┴ moments of extracted Sivers functions, compared with models data from HERMES and COMPASS Mauro Anselmino, Como, September 7, 2005 Transversity 2005

SSA in p↑p → π X E704 data, E = 200 GeV fit to AN with Sivers effects alone maximized value of AN with Collins effects alone U. D’Alesio, F. Murgia M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia Mauro Anselmino, Como, September 7, 2005 Transversity 2005

HERMES + E704: Sivers function is not zero Talks by M. Burkardt D. Sivers, X. Artru Spin-k┴ partonic correlations in nucleons Theory: not quite universal J. Collins, a “QCD theorem” Models: few, in fair agreement Talk by A. Baccheta chiral models, A. Drago, P. Pobilytsa M. Burkardt Sum rules: talk by O. Teryaev Mauro Anselmino, Como, September 7, 2005 Transversity 2005

Looking forward to an interesting workshop, thanks! Mauro Anselmino, Como, September 7, 2005 Transversity 2005