Strangeness and Spin in Fundamental Physics Mauro Anselmino: The transverse spin structure of the nucleon Delia Hasch: The transverse spin structure of the nucleon – exp. Elliot Leader: The longitudinal spin structure of the nucleon Werner Vogelsang: QCD spin physics in hadronic interactions Naohito Saito: Spin Physics at RHIC - experiment Raimondo Bertini : Spin physics with strangeness Spin lectures Spin seminars Robert Jaffe: Gluon spin basics Harut Avakian: Spin Physics at JLab Mariaelena Boglione: The first way to transversity Varenna, June 19-29, 2007

– Parton transverse motion, spin-k ┴ correlation, orbiting?

Transverse single spin asymmetries in SIDIS, experimentally observed (D. Hasch) z y x ΦSΦS ΦπΦπ X p S PTPT in collinear configurations there cannot be (at LO) any P T

Mauro Anselmino: The transverse spin structure of the nucleon - II About partonic intrinsic motion and SSA Estimate of transverse motion of quarks TMDs: spin-intrinsic motion correlations in distribution and fragmentation functions Sivers and Collins functions; SSA in SIDIS Coupling Collins function and Transversity What do we learn from Sivers functions? The full structure of TMDs in SIDIS

p p Q 2 = M 2 qTqT qLqL l+l+ l–l– Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and of hadrons within fragmentation jets uncertainty principle gluon radiation ±1 ± ± k┴k┴ Partonic intrinsic motion q T distribution of lepton pairs in D-Y processes

Hadron distribution in jets in e + e – processes p T distribution of hadrons in SIDIS

Parton Model with intrinsic motion Assume: struck parton carries 4-momentum k k P k’

factorization holds at large Q 2, and Ji, Ma, Yuan observables at SIDIS in parton model with intrinsic k ┴

Elementary Mandelstam variables: The on shell condition for the final quark implies

neglecting terms one has “Cahn effect”

assuming: one finds: with clear dependence on(assumed to be constant) and Find best values by fitting data on Φ h and P T dependences

EMC data, µp and µd, E between 100 and 280 GeV M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin, C. Türk

Large P T data explained by NLO QCD corrections EMC data

How does intrinsic motion help with SSA? One can introduce spin-k ┴ correlation in the Parton Distribution Functions (PDFs) and in the parton Fragmentation Functions (FFs) X Only possible (scalar) correlation is

TMDs: Sivers function Boer-Mulders function

Collins function Polarizing fragmentation function

Sivers effect in SIDIS

Brodsky, Hwang, Schmidt model for Sivers function X p S + – q q diquark needs k ┴ dependent quark distribution in p ↑ : Sivers function

M.A., M. Boglione, U.D’Alesio, A.Kotzinian, F. Murgia, A Prokudin Fit of HERMES data on

Deuteron target

First p ┴ moments of extracted Sivers functions, compared with models M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin data from HERMES and COMPASS hep-ph/

The first and 1/2-transverse moments of the Sivers quark distribution functions, defined in Eqs. (3, 9), as extracted in Refs. [20, 21, 23]. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions of the various parameterizations. M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan

Spin effect comes from fragmentation of a transversely polarized quark initial q spin is transfered to final q', which fragments q q’ Collins effect in SIDIS

Collins effect in SIDIS couples to transversity, seminar of E. Boglione for combined extraction

fit to HERMES data on W. Vogelsang and F. Yuan Soffer-saturated h 1

A. V. Efremov, K. Goeke and P. Schweitzer (h 1 from quark-soliton model)

COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons small values due to deuteron target: cancellation between u and d contributions

S number density of partons with longitudinal momentum fraction x and transverse momentum k ┴, inside a proton with spin S M. Burkardt, PR D69, (2004 ) What do we learn from the Sivers distribution?

Total amount of intrinsic momentum carried by partons of flavour a for a proton moving along the +z-axis and polarization vector S

Sivers functions extracted from A N data in give also opposite results, with Numerical estimates from SIDIS data U. D’Alesio

Sivers function and proton anomalous magnetic moment M. Burkardt, S. Brodsky, Z. Lu, I. Schmidt Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities in qualitative agreement with large z data:

The leading-twist correlator, with intrinsic k ┴, contains several other functions.....

8 leading-twist spin-k ┴ dependent distribution functions Courtesy of Aram Kotzinian

Polarized SIDIS cross section, up to subleading order in 1/Q Kotzinian, NP B441 (1995) 234 Mulders and Tangermann, NP B461 (1996) 197 Boer and Mulders, PR D57 (1998) 5780 Bacchetta et al., PL B595 (2004) 309 Bacchetta et al., JHEP 0702 (2007) 093 SIDISLAND