Resummation for polarized semi-inclusive deep-inelastic scattering at small transverse momentum

Abstract

We study the transverse-momentum distribution of hadrons produced in semi-inclusive deep-inelastic scattering (SIDIS). We consider cross sections for various combinations of polarizations of the initial lepton and nucleon or the produced hadron, for which we perform the resummation of large double-logarithmic perturbative corrections arising at small transverse momentum. We present phenomenological results for the processes lp → lπX with longitudinally polarized leptons and protons. We discuss the impact of the perturbative resummation and of estimated non-perturbative contributions on the corresponding cross sections and their spin asymmetry. Our results should be relevant for ongoing studies in the COMPASS experiment at CERN, and for future experiments at the proposed eRHIC collider at BNL.

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions

“…For the polarized case of interest here, studies are presented in Refs. [29]. We will clarify in which sense our results correspond to the ones presented in the resummation literature.…”

“…(37,38,41,42,43) of Ref. [29]. Differences occur only for the terms with δ(1 − x) and can be ascribed to the contribution from the hard scattering.…”

“…The sum goes over all quark and antiquark flavors and include also gluon, j = q,q, g. Appropriate coefficient functions should be used in each case from Eqs. (28,29,30), ⊗ denotes the convolution in longitudinal momentum fractions of Eq. (22).…”

“…Polarized DIS has been discussed in Ref. [29]. For instance, we can compare the results for the unpolarized structure function of Eq.…”

SIDIS cross sections: perturbative and non-perturbative aspects

“…The CSS resummation scheme was originally developed for DY processes, but can be applied to SemiInclusive Deep Inelastic Scattering (SIDIS) reactions as well. For unpolarized SIDIS processes, N → hX, the following CSS expression [7,8] holds…”