Transversity transverse spin and transverse motion unravelling the

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 1

Parton distributions and (or are fundamental leading-twist quark distributions quark distribution – well known quark helicity distribution – known all equally important 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 2

+ + – + – – + + + – = = in helicity basis + + Mauro Anselmino, Como, September 7, 2005 – – decouples from DIS (no quark helicity flip) Transversity 2005 3

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 – + + + Mauro Anselmino, Como, September 7, 2005 – – + – h 1 x h 1 J. Ralston and D. Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 h 1 x Collins function – J. Collins, 1993 Transversity 2005 4

No gluon contribution to h 1 simple Q 2 evolution +1 – 1 + – Q 2 = 25 Ge. V 2 Q 02 = 0. 23 Ge. V 2 V. Barone, T. Calarco, A. Drago Mauro Anselmino, Como, September 7, 2005 Transversity 2005 5

h 1 in Drell-Yan processes l+ γ* p Q 2 = M 2 l– q. T q. L p Elementary LO interaction: 3 planes: plane ┴ polarization vectors, p-γ* plane, l+l– γ* plane Mauro Anselmino, Como, September 7, 2005 plenty of spin effects Transversity 2005 6

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

h 1 from at GSI large x 1, x 2 GSI energies: one measures h 1 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 8

Energy for Drell-Yan processes "safe region": Fermilab E 866 800 Ge. V/c QCD corrections might be very large at smaller values of M: yes, for cross-sections, not for ATT K-factor almost spin-independent 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 9

s=30 Ge. V 2 s=210 Ge. V 2 Mauro Anselmino, Como, September 7, 2005 s=45 Ge. V 2 s=900 Ge. V 2 Transversity 2005 10

s=30 Ge. V 2 s=210 Ge. V 2 Mauro Anselmino, Como, September 7, 2005 s=45 Ge. V 2 s=900 Ge. V 2 Transversity 2005 11

data from CERN WA 39, π N processes, s = 80 Ge. V 2 Mauro Anselmino, Como, September 7, 2005 Transversity 2005 12

h 1 x Collins from SIDIS processes Asymmetry in the fragmentation of a transversely polarized quark φ S q p┴ pq (Fundamental QCD property? D. Sivers) q’ q y initial q spin is transferred to final q', which fragments “Trento conventions” Sq Sq’ p┴ Φh x Amsterdam notations Mauro Anselmino, Como, September 7, 2005 ΦS Transversity 2005 13

neglecting intrinsic motion in partonic distributions: tra ns ve rsi ty Collins function some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h 1) Mauro Anselmino, Como, September 7, 2005 Transversity 2005 14

fit to HERMES data on Mauro Anselmino, Como, September 7, 2005 Transversity 2005 15

Extraction of Collins functions from HERMES + BELLE data P 1 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 16

Fits to HERMES Collins data, preliminary results Mauro Anselmino, Como, September 7, 2005 Transversity 2005 17

Fits to BELLE Collins data, preliminary results Mauro Anselmino, Como, September 7, 2005 Transversity 2005 18

HERMES + BELLE: Collins function is not zero Theory: probably universal Collins, Metz Models: few, in disagreement Amrath, Bacchetta, Metz, Kundu, Mulders, … pion-quark vertex ? loop? assumes h 1 = ∆q disfavoured Collins functions = 0 Talk by. A. Bacchetta Mauro Anselmino, Como, September 7, 2005 Transversity 2005 19

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 20

Two pion production: interference fragmentation function Talks by P. van der Nat, M. Radici Mauro Anselmino, Como, September 7, 2005 Transversity 2005 21

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 22

Transverse SSA S p p' θ PT –p y x z – p' Single Spin Asymmetry in elastic scattering. Example: 6 independent helicity amplitudes Mauro Anselmino, Como, September 7, 2005 Transversity 2005 23

y ΦS S p Φ x p' θ PT –p z – p' for a generic configuration: Mauro Anselmino, Como, September 7, 2005 Transversity 2005 24

needs helicity flip + relative phase + – + + x + + at quark level large SSA observed at hadron level Mauro Anselmino, Como, September 7, 2005 Transversity 2005 25

BNL-AGS √s = 6. 6 Ge. V 0. 6 < p. T < 1. 2 E 704 √s = 20 Ge. V 0. 7 < p. T < 2. 0 STAR-RHIC √s = 200 Ge. V 1. 1 < p. T < 2. 5 E 704 √s = 20 Ge. V 0. 7 < p. T < 2. 0 SSA, pp → πX Mauro Anselmino, Como, September 7, 2005 Transversity 2005 26

Unweighted Collins moment: Mauro Anselmino, Como, September 7, 2005 Unweighted Sivers moment: Transversity 2005 27

Transverse Λ polarization in unpolarized p-Be scattering at Fermilab Mauro Anselmino, Como, September 7, 2005 Transversity 2005 28

Mauro Anselmino, Como, September 7, 2005 Transversity 2005 29

Brodsky, Hwang, Schmidt model for Sivers function S p X q + diquark q – diquark needs k┴ dependent quark distribution in p↑: Sivers function Mauro Anselmino, Como, September 7, 2005 Transversity 2005 30

Amsterdam notations Sivers asymmetry in SIDIS talk by A. Prokudin p┴ = PT – z k┴ + O(k┴ 2/Q 2) Mauro Anselmino, Como, September 7, 2005 Transversity 2005 31

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 32

Deuteron target Mauro Anselmino, Como, September 7, 2005 Transversity 2005 33

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 34

SSA in p↑p → π X E 704 data, E = 200 Ge. V 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 35

HERMES + E 704: Sivers function is not zero Spin-k┴ partonic correlations in nucleons Talks by M. Burkardt D. Sivers, X. Artru 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 36

Looking forward to an interesting workshop, thanks! Mauro Anselmino, Como, September 7, 2005 Transversity 2005 37