Abstract
Starting from a definition of transverse momentum-dependent parton distributions (TMDs) in terms of hadronic matrix elements of a quark bilocal operator containing a staple-shaped gauge link, selected TMD observables can be evaluated within Lattice QCD. A TMD ratio describing the Boer-Mulders effect in the pion is investigated, with a particular emphasis on its evolution as a function of a Collins-Soper-type parameter which quantifies the proximity of the staple-shaped gauge links to the light cone.
Highlights
Transverse momentum-dependent parton distribution functions1 (TMDs) encode information about the distribution of transverse momentum among partons in a hadron, as extracted from physical processes such as semiinclusive deep inelastic scattering (SIDIS) or the Drell-Yan (DY) process
A schematic illustration of the principal elements involved in a description of SIDIS is given by Fig. 1; they include the hard, perturbative vertex, a TMD encoding the structure of the nucleon, and a fragmentation function describing the hadronization of the struck quark
Including these final-state interactions modifies the momentum distributions encoded in the TMDs; the manner in which they formally enter the theoretical definition of TMDs will be elucidated further below
Summary
Transverse momentum-dependent parton distribution functions (TMDs) encode information about the distribution of transverse (as well as longitudinal) momentum among partons in a hadron, as extracted from physical processes such as semiinclusive deep inelastic scattering (SIDIS) or the Drell-Yan (DY) process. As indicated, final-state gluon exchanges between the struck quark and the hadron remnant decisively influence the description of SIDIS (in the DY process, initial-state interactions play an analogous role) Including these final-state interactions modifies the momentum distributions encoded in the TMDs; the manner in which they formally enter the theoretical definition of TMDs will be elucidated further below. These final state effects are important in that they break time-reversal invariance and generate nontrivial T-odd TMDs, leading to corresponding angular asymmetries in experimental cross sections. Exploratory results for the T-odd Boer-Mulders transverse momentum shift in the pion are given, expanding on the initial study of nucleon TMDs reported in Ref. [8]
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