Abstract
In the factorized picture of semi-inclusive hadronic processes the naive time-reversal odd parton distributions exist by virtue of the gauge link which renders it color gauge invariant. The link characterizes the dynamical effect of initial/final-state interactions of the active parton due soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, studies of final-state interaction have been approximated by perturbative one-gluon approximation in Abelian models. We include higher-order gluonic contributions from the gauge link by applying non-perturbative eikonal methods incorporating color degrees of freedom in a calculation of the Boer–Mulders function of the pion. Using this framework we explore under what conditions the Boer–Mulders function can be described in terms of factorization of final state interactions and a spatial distribution in impact parameter space.
Highlights
Over the past two decades the transverse partonic structure of hadrons has been the subject of a great deal of theoretical and experimental investigation. Central to these studies are the early observations of large transverse single spin asymmetries (TSSAs) in inclusive hadron production from proton–proton scattering over a wide range of beam energies [1,2,3,4]
TSSAs have been observed in lepton–hadron semi-inclusive deep inelastic scattering (SIDIS) at the COMPASS [5] and HERMES [6,7] experiments and at Jefferson Lab [8,9], as well as in inclusive production of pseudo-scalar mesons in proton–proton collins at RHIC [10,11,12,13]
In this Letter we examined the FSIs of an active quark in a pion which are essential to generate a non-vanishing chirally-odd and time-reversal odd (T-odd) parton distribution i.e. the Boer–Mulders function
Summary
Over the past two decades the transverse partonic structure of hadrons has been the subject of a great deal of theoretical and experimental investigation. T-odd PDFs emerge from the gauge link structure of the multi-parton quark and/or gluon correlation functions [26,32,33,34] which describe initial/final-state interactions (ISI/FSI) of the active parton via soft gluon exchanges with the target remnant. The field-theoretical definition of transverse-momentum dependent (TMD) parton distributions in terms of hadronic matrix elements of quark operators serves as the starting point of our analysis. Boer–Mulders function (2) and the first derivative of the impact parameter GPD H1π , Eq (4), reveals that they differ by the operator Ii which represents the FSIs. In various model calculations [45,46, 62,68] the FSIs are treated such that the two effects of a distortion of the transverse space parton distribution and the FSIs factorize resulting in the relation.
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