Fisica dello Spin27 Settembre 2005, Otranto1 Surprises: Transverse Single Spin Asymmetries (unintegrated polarized parton distributions) Single Spin Asymmetries (SSA) in elastic processes Single Spin Asymmetries in pQCD and in data Parton intrinsic motion and spin Spin - Transverse Momentum Dependent distribution and fragmentation functions Phenomenology of SSA in inclusive processes Mysteries: spin asymmetries in pp pp processes

Fisica dello Spin27 Settembre 2005, Otranto2 S p p'p' – p PTPT θ – p ' 5 independent helicity amplitudes z y x Example: Transverse single spin asymmetries in elastic scattering

Fisica dello Spin27 Settembre 2005, Otranto3 S p p'p' – p PTPT θ – p ' z y x ΦSΦS Φ for a generic configuration :

Fisica dello Spin27 Settembre 2005, Otranto4 needs helicity flip + relative phase – x at quark level but large SSA observed at hadron level! QED and QCD interactions conserve helicity, up to corrections Single spin asymmetries at partonic level. Example:

Fisica dello Spin27 Settembre 2005, Otranto5 Helicity conservation in pQCD or QED odd numbers of gamma matrices

Fisica dello Spin27 Settembre 2005, Otranto6 BNL-AGS s = 6.6 GeV 0.6 < p T < 1.2 E704 s = 20 GeV 0.7 < p T < 2.0 experimental data on SSA observed transverse Single Spin Asymmetries

Fisica dello Spin27 Settembre 2005, Otranto7 S p– p PTPT z y x X – PT– PT A N = simple left-right asymmetry

Fisica dello Spin27 Settembre 2005, Otranto8 STAR-RHIC s = 200 GeV 1.1 < p T < 2.5 A N stays at high energies ….

Fisica dello Spin27 Settembre 2005, Otranto9 Sivers moment

Fisica dello Spin27 Settembre 2005, Otranto10 Collins moment

Fisica dello Spin27 Settembre 2005, Otranto11 Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

Fisica dello Spin27 Settembre 2005, Otranto12

Fisica dello Spin27 Settembre 2005, Otranto13 Spin is challenging 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

Fisica dello Spin27 Settembre 2005, Otranto14 needs k dependent quark distribution in p (Sivers mechanism) or p dependent fragmentation of polarized quark (Collins mechanism) z y x ΦSΦS ΦπΦπ X p S PTPT Transverse single spin asymmetries in SIDIS if partons inside p are all collinear there cannot be (at LO) any P T

Fisica dello Spin27 Settembre 2005, Otranto15 There must be a primordial intrinsic k due to quark confinement: There is intrinsic k generated by QCD evolution ±1 ± ± k k dependent parton distributions (TMD) The elementary interaction depends on Azimuthal dependence in unpolarized SIDIS cross section (Cahn effect)

Fisica dello Spin27 Settembre 2005, Otranto16 EMC data

Fisica dello Spin27 Settembre 2005, Otranto17 a b c X X BNL data, PLB 73 (1978) F. Murgia, U. DAlesio original idea from Feynman-Field non collinear configurations

Fisica dello Spin27 Settembre 2005, Otranto18 X p S + – Brodsky, Hwang, Schmidt model for Sivers function q q diquark, Q cannot be forward in order to have a SSA intrinsic k of quark

Fisica dello Spin27 Settembre 2005, Otranto19 p = P T – z k + O(k 2 /Q 2 ) Sivers mechanism in SIDIS p S k φ q

Fisica dello Spin27 Settembre 2005, Otranto20 M.A., U.DAlesio, M.Boglione, A.Kotzinian, A Prokudin from Sivers mechanism

Fisica dello Spin27 Settembre 2005, Otranto21 Deuteron target

Fisica dello Spin27 Settembre 2005, Otranto22 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 chiral models M. Burkardt

Fisica dello Spin27 Settembre 2005, Otranto23 Collins mechanism for SSA 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 (Fundamental QCD property? D. Sivers)

Fisica dello Spin27 Settembre 2005, Otranto24 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

Fisica dello Spin27 Settembre 2005, Otranto25 fit to HERMES data on

Fisica dello Spin27 Settembre 2005, Otranto26 p S k φ q pqpq φ SqSq p Amsterdam group notations spin-k correlations Sivers functionCollins function

Fisica dello Spin27 Settembre 2005, Otranto27 p SqSq k φ q pqpq φ SΛSΛ p Amsterdam group notations spin-k correlations Boer-Mulders function polarizing f.f.