Transversity transverse spin and transverse motion Transversity distributions
Transversity (transverse spin and transverse motion) Transversity distributions – (some) theory Transversity distributions - experiments Transverse Single Spin Asymmetries (how to test a Quantum Field Theory) Spin and k┴ dependent parton distributions (TMD) Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
+ + – + – – + + + – = = in helicity basis + + Mauro Anselmino, Prague, August 1, 2005 – – decouples from DIS Hadron Structure and Hadron Spectroscopy
Helicity conservation in p. QCD or QED Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 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 Hadron Structure and Hadron Spectroscopy
Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
D. De Florian, G. A. Navarro and R. Sassot, hep-ph/0506326 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
h 1 in Drell-Yan processes l+ γ* p Q 2 = M 2 l– q. T p q. L Elementary LO interaction: 3 planes: plane ┴ polarization vectors, p-γ* plane, l+l– γ* plane Mauro Anselmino, Prague, August 1, 2005 plenty of spin effects Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Barone, Calarco, Drago Martin, Schäfer, Stratmann, Vogelsang Hadron Structure and Hadron Spectroscopy
h 1 from GSI energies: at GSI large x 1, x 2 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 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
s=30 Ge. V 2 s=210 Ge. V 2 Mauro Anselmino, Prague, August 1, 2005 s=45 Ge. V 2 s=900 Ge. V 2 Hadron Structure and Hadron Spectroscopy
s=30 Ge. V 2 s=210 Ge. V 2 Mauro Anselmino, Prague, August 1, 2005 s=45 Ge. V 2 s=900 Ge. V 2 Hadron Structure and Hadron Spectroscopy
data from CERN WA 39, π N processes, s = 80 Ge. V 2 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
h 1 x Collins from SIDIS processes φ S q Spin effect comes from fragmentation of a transversely polarized quark q’ q p┴ pq initial q spin is transfered to final q', which fragments y Sq Sq’ p┴ Φh ΦS x Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
fit to HERMES data on Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Extraction of Collins functions from HERMES + BELLE data P 1 depends on (talk by Matthias) M. A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Fits to HERMES Collins data, preliminary results Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Fits to BELLE Collins data, preliminary results Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Alternative accesses to transversity Inclusive Λ production and measure of Λ polarization (transverse fragmentation function) Two pion production: l p↑ → π π X (interference fragmentation function) Vector meson production: l p↑ → ρ X (generalized fragmentation function) Inclusive hadronic production: p p↑ → π X Single Spin Asymmetry in D-Y processes (higher-twist transversity distribution) Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
S Transverse SSA p p' θ PT –p y x z – p' Single Spin Asymmetry in elastic scattering. Example: 6 independent helicity amplitudes Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
y ΦS S p Φ x p' θ PT –p z – p' for a generic configuration: Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
needs helicity flip + relative phase + – + + x + + at quark level large SSA observed at hadron level Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Unweighted Collins moment: Mauro Anselmino, Prague, August 1, 2005 Unweighted Sivers moment: Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Sivers asymmetry in SIDIS p┴ = PT – z k┴ + O(k┴ 2/Q 2) Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Deuteron target Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
First p┴ moments of extracted Sivers functions, compared with models Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Predictions for COMPASS, hydrogen target Q 2 > 1 (Ge. V/c)2 PT > 0. 1 Ge. V/c 0. 2 < zh < 0. 9 W 2 > 25 Ge. V 2 Eh > 4 Ge. V 0. 1 < y < 0. 9 0. 4 ≤ zh ≤ 1 0. 2 ≤ PT ≤ 1 Ge. V/c 0. 02 ≤ x. B ≤ 1 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
Predictions for K production at HERMES Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
The spin story goes on. . . . Polarization data has often been the graveyard of fashionable theories. If theorists had their way, they might just ban such measurements altogether out of self-protection. J. D. Bjorken St. Croix, 1987 Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy
- Slides: 36