Searching for intrinsic motion effects in SIDIS Strategy (within LO parton model): Based on work in collaboration with E. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin Phys. Rev. D71 (2005) 074006, hep-ph/0501196 See also talk by E. Leader Mauro Anselmino Partonic structure of hadrons (Concepts and Phenomenology), Trento ECT*, May 9-14, 2005

qT distribution of lepton pairs in D-Y processes Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and of hadrons within fragmentation jets Uncertainty principle Gluon radiation qT distribution of lepton pairs in D-Y processes pT distribution of hadrons in SIDIS, Hadron distribution in jets in e+e– processes Large pT particle production in ···· Transverse motion is usually integrated, but there might be important spin-k┴ correlations

Spin-k┴ correlations in distribution and fragmentation functions π Pq k┴ Collins effect = fragmentation of polarized quark depends on Pq· (pq x k┴) pq q P k┴ Sivers effect = number of partons in polarized proton depends on P · (p x k┴) p Pq q k┴ Boer-Mulders effect = polarization of partons in unpolarized proton depends on Pq · (p x k┴) p PΛ Λ k┴ Polarizing fragmentation function = polarization of final hadron (Λ) depends on PΛ· (pq x k┴) pq Pq· (pq x k┴), P · (p x k┴) ~ Collins, Sivers angles

SIDIS kinematics according to Trento conventions (2004)

Unpolarized SIDIS (LO) M. Arneodo et al (EMC): Z. Phys. C 34 (1987) 277

assuming collinear fragmentation, φ = Φh Cahn: the observed azimuthal dependence is related to the intrinsic k┴ of quarks (at least for small PT values) assuming collinear fragmentation, φ = Φh These modulations of the cross section with azimuthal angle are denoted as “Cahn effect”.

The situation is more complicated as the produced hadron has also intrinsic transverse momentum with respect to the fragmenting parton. neglecting terms

Find best values by fitting data on Φh and PT dependences assuming: one finds with clear dependence on (assumed to be constant) Find best values by fitting data on Φh and PT dependences

EMC data, µp and µd, E between 100 and 280 GeV EMC data, µp and µd, E between 100 and 280 GeV. Dashed line = exact kinematics, red solid line = only terms up to O(k┴/Q)

The closed area shows effects of varying by 20% Data from E665, ELab= 490 GeV. σ is integrated from PTcut to PTmax. At low PTcut the non perturbative k┴ contributions dominate. At large PTcut NLO pQCD contributions take over

EMC data

Fitting the unpolarized data leads to the best values EMC data Fitting the unpolarized data leads to the best values

Polarized SIDIS and Sivers asymmetry possibility of SSA Sivers effect: can be isolated by proper weighting

hydrogen target Ee = 27.57 GeV

our best fits + predictions for PT dependence PDF: MRST LO 2001 FF: Kretzer our best fits + predictions for PT dependence ------ = exact kinematics = only terms up to O(k ┴/Q) closed area corresponds to one-sigma deviation at 90% CL

comparisons of our previous fits (+ predictions) with new data

COMPASS data for charged hadron production Al parameters fixed from HERMES data

HERMES data on In this case both Sivers and Collins effect can contribute; results show a clear need for Collins or H-T contributions

Our predictions for K production at HERMES FF: Kretzer

Conclusions A complete QCD description of the proton structure and hard processes requires the explicit inclusion of transverse motion, which is essential for spin effects Attempted consistent phenomenological approach in SIDIS and in hadro-production Many progresses and many (more) open problems: x, z and Q2 dependence of <k┴2> and <p┴2> QCD evolution of spin-k┴ dependent distribution and fragmentation functions More and more precise experimental data ………………………..