Calculation of transverse momentum dependent distributions beyond the leading power

Abstract

We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-b expansion for transverse momentum dependent (TMD) distributions at all powers of b. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor (M2b2)n and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.

The Drell-Yan process with pions and polarized nucleons

“…The theoretical and phenomenological understanding of TMDs witnessed an incredible rate of developments in the recent years including NNLO and NNNLO calculations of the evolution kernel of unpolarized TMDs [75][76][77][78][79][80][81][82][83], NLO calculations for the quark helicity distribution [84], NLO [84] and NNLO [85] calculations for transversity and pretzelosity, and NLO calculations for the Sivers function [86][87][88][89][90]. Recently also the first non-trivial expression for the small-b expansion of the pretzelosity distribution was derived [91]. However, in the context of quark model applications we face two challenges.…”

“…In this situation in previous quark model studies, TMD evolution effects were often estimated approximately [57][58][59] based on an heuristic Gaussian Ansatz for transverse parton momenta with energy dependent Gaussian widths. While providing a useful description of data on many processes including pion-induced Drell-Yan [92], it is important to improve the simple Gaussian treatment in view of the recent progress in the TMD theory [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. We will therefore use TMD evolution [2] at Next-to-Leading Logarithmic (NLL) precision to describe the transverse momentum dependence of the Drell-Yan process.…”

QCD factorization for chiral-odd parton quasi- and pseudo-distributions

“…[24,25] from the analysis of the small-q T part of the transverse spin asymmetry data. Chiral-odd distributions can therefore be addressed similarly by studying the chiral-odd TMDs, see [26][27][28] for the relevant relations. In this way, the Qiu-Sterman projection of the underlying quark-gluon correlation function that is related to e(x) gives rise to the Boer-Mulders function and, thus, could be observed in the cos(2φ)-modulation in unpolarized Drell-Yan processes [29].…”

QCD factorization for twist-three axial-vector parton quasidistributions

“…Our definition is common in the literature on the DIS structure function g 2 (x, Q 2 ), e.g., [4,18,72]. In applications to semi-inclusive reactions [36,37,[40][41][42]73] The corresponding momentum fraction distributions T and ∆T (defined as in (3.16)) are related to S ± as…”

“…More recently, the interest in twist-three effects was fueled by studies of transverse momentum dependent (TMD) parton distributions. In this case, the twist-three distributions arise in the collinear limit for many TMD distributions already at the leading power [34][35][36][37]. In particular, the single transverse spin asymmetry is sensitive to the Sivers function [38], which matches the Qiu-Sterman function [39] in the collinear limit.…”