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

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

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

Mauro Anselmino, Como, September 7, 2005 Transversity h 1 must couple to another chiral-odd function. For example: D-Y, pp l + l – X, and SIDIS, l p l π X, processes + + – + + – + – – – + – + – h 1 x h 1 h 1 x Collins function J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 J. Collins, 1993

Mauro Anselmino, Como, September 7, 2005 Transversity – + +1 –1 No gluon contribution to h 1 simple Q 2 evolution Q 2 = 25 GeV 2 Q 0 2 = 0.23 GeV 2 V. Barone, T. Calarco, A. Drago

Mauro Anselmino, Como, September 7, 2005 Transversity Elementary LO interaction: 3 planes: plane polarization vectors, p-γ* plane, l + l – γ* plane plenty of spin effects p p Q 2 = M 2 qTqT qLqL l+l+ l–l– γ*γ* h 1 in Drell-Yan processes

Mauro Anselmino, Como, September 7, 2005 Transversity h 1 from RHIC energies: small x 1 and/or x 2 h 1q (x, Q 2 ) evolution much slower than Δq(x, Q 2 ) and q(x, Q 2 ) at small x A TT at RHIC is very small smaller s would help Martin, Schäfer, Stratmann, Vogelsang Barone, Calarco, Drago at RHIC talk by A. Mukherjee

Mauro Anselmino, Como, September 7, 2005 Transversity h 1 from GSI energies: large x 1,x 2 one measures h 1 in the quark valence region: A TT is estimated to be large, between 0.2 and 0.4 at GSI PAX proposal: hep-ex/ Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora

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

Mauro Anselmino, Como, September 7, 2005 Transversity s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

Mauro Anselmino, Como, September 7, 2005 Transversity s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

Mauro Anselmino, Como, September 7, 2005 Transversity data from CERN WA39, π N processes, s = 80 GeV 2

Mauro Anselmino, Como, September 7, 2005 Transversity h 1 x Collins from SIDIS processes Asymmetry in the fragmentation of a transversely polarized quark pqpq φ SqSq p initial q spin is transferred to final q', which fragments SqSq SqSq p x y ΦSΦS ΦhΦh q q Trento conventions (Fundamental QCD property? D. Sivers) Amsterdam notations

Mauro Anselmino, Como, September 7, 2005 Transversity neglecting intrinsic motion in partonic distributions: Collins function some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h 1 ) transversity

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

Mauro Anselmino, Como, September 7, 2005 Transversity Extraction of Collins functions from HERMES + BELLE data P 1 depends on (talk by R. Seidl) M.A, M. Boglione, U. DAlesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation

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

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

Mauro Anselmino, Como, September 7, 2005 Transversity HERMES + BELLE: Collins function is not zero Theory: probably universal Collins, Metz Models: few, in disagreement Amrath, Bacchetta, Metz, Kundu, Mulders, … assumes h 1 = q disfavoured Collins functions = 0 pion-quark vertex ? loop? Talk by. A. Bacchetta

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

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

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

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

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

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

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

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

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

Mauro Anselmino, Como, September 7, 2005 Transversity

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

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

Mauro Anselmino, Como, September 7, 2005 Transversity M.A, M. Boglione, U. DAlesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/ (PRD 71, ) and hep-ph/

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

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

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

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

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