Strangeness and Spin in Fundamental Physics Varenna, June 19-29, 2007 Spin lectures 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 seminars Robert Jaffe: Gluon spin basics Harut Avakian: Spin Physics at JLab Mariaelena Boglione: The first way to transversity

Why spin ? ….

Single Spin Asymmetries Mauro Anselmino: The transverse spin structure of the nucleon - I Central object of investigation: the proton transverse internal structure, that is the quark transverse spin and transverse motion (with respect to the direction of motion) Why transverse? How? Single Spin Asymmetries Transverse Momentum Dependent distribution and fragmentation functions (TMDs) Combining all together and learning…

How and what do we know about the longitudinal proton structure. (E How and what do we know about the longitudinal proton structure? (E. Leader) xP P Naive parton model:

= imaginary part of forward scattering amplitude Total cross section for process = imaginary part of forward scattering amplitude handbag diagram

Longitudinally polarized DIS gives information on the helicity distributions of quarks (and, indirectly, of gluons)

QCD interactions induce a well known Q2 dependence factorization: universality: same q(x,Q2) measured in DIS can be used in other processes

essentially x and Q2 degrees of freedom ….

The transverse structure is much more interesting and less studied spin-k┴ correlations? orbiting quarks? ? Transverse Momentum Dependent distribution functions Space dependent distribution functions

Transversity distribution are all fundamental, and different, leading-twist quark distributions, equally important – –

The correlator at leading twist, in collinear configuration:

Does transversally polarized DIS give information on the transversity distributions of quarks? No! in helicity basis:

odd numbers of gamma matrices QED and QCD interations (and SM weak interactions) conserve helicity: h1 decouples from DIS no h1 in DIS odd numbers of gamma matrices

Possible access transversity: Drell-Yan processes

SIDIS,

– + What do we know about transversity? (E. Boglione seminar) Q2 = 25 GeV2 Q02 = 0.23 GeV2 V. Barone, T. Calarco, A. Drago What do we know about transversity? (E. Boglione seminar) No gluon contribution to h1, simple Q2 evolution – + +1 –1 Soffer bound tensor charge from lattice

(The problem of) Single Spin Asymmetries What are SSA? SSA in QED and QCD, helicity conservation SSA at hadronic level, experiments Transverse SSA related to intrinsic partonic motion, new spin effects in distribution and fragmentation functions ….

5 independent helicity amplitudes Transverse single spin asymmetries in elastic scattering S p p' – p PT θ – p' z y x Example: 5 independent helicity amplitudes

for a generic configuration: S p p' – p PT θ – p' z y x ΦS Φ for a generic configuration: AN is zero for longitudinal spin

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

SSA in inclusive processes: PT z y x X – PT AN = simple left-right asymmetry

based on factorization theorem (in collinear configuration) Cross section for in pQCD (W. Vogelsang) based on factorization theorem (in collinear configuration) a b c X PDF FF pQCD elementary interactions

Latest PHENIX data on unpolarized cross section RHIC, Latest PHENIX data on unpolarized cross section

was considered almost a theorem SSA? a b c X FF pQCD elementary SSA transversity was considered almost a theorem

experimental data on SSA BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 E704 √s = 20 GeV 0.7 < pT < 2.0 observed transverse Single Spin Asymmetries E704 √s = 20 GeV 0.7 < pT < 2.0 experimental data on SSA

and AN stays at high energies …. STAR-RHIC √s = 200 GeV 1.2 < pT < 2.8 and AN stays at high energies ….

in collinear configurations there cannot be (at LO) any PT Transverse single spin asymmetries in SIDIS, experimentally observed (D. Hasch) z y x ΦS Φπ X p S PT in collinear configurations there cannot be (at LO) any PT

Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

And now ....... ? 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