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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

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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

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

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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

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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

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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

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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

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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

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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

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

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

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

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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

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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

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

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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

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

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

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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

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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

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

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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

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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

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

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

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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

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

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

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Mauro Anselmino, Como, September 7, 2005 Transversity

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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

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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

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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/

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

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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

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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

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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

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

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