Off-shell modifications of the pion generalized parton distributions and transverse momentum dependent parton distributions

TL;DR

This paper investigates how off-shell effects alter pion generalized parton distributions and transverse momentum dependent distributions using the Nambu-Jona-Lasinio model, revealing modifications and breakdowns of certain properties compared to on-shell cases.

Contribution

It introduces a detailed analysis of off-shell modifications in pion GPDs and TMDs, including correction functions and the impact of broken symmetry properties.

Findings

Off-shell GPDs differ significantly from on-shell ones.

New off-shell form factors arise due to broken crossing symmetry.

Off-shell TMDs show notable dependence on transverse momentum.

Abstract

The off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu-Jona-Lasinio model. In our previous papers, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. It is particularly intriguing to compare the differences between on-shell and off-shell pion GPDs, which allows us to explore the effects associated with off-shellness. Due to the absence of crossing symmetry, the moments of GPDs also incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs due to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for instance, symmetry properties and polynomiality conditions may no longer hold. Additionally, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $\bm{k}_{\perp}$.