Off-shell generalized parton distributions and form factors of the pion

TL;DR

This paper investigates off-shell effects in pion GPDs, deriving new relations for off-shell form factors and emphasizing their importance in modeling physical processes involving the pion.

Contribution

It introduces exact relations between off-shell gravitational form factors of the pion and highlights the significance of off-shell effects in GPD modeling.

Findings

Derived relations between four off-shell gravitational form factors.

Off-shell effects can be significant in physical process modeling.

Constraints on off-shell GPDs of the pion.

Abstract

Off-shell effects in generalized parton distributions (GPDs) of the pion, appearing, e.g., in the Sullivan process, are considered. Due to the lack of crossing symmetry, the moments of GPDs involve also odd powers of the skewness (longitudinal momentum transfer) parameter, which results in emergence of new off-shell form factors. With current-algebra techniques, we derive exact relations between the four off-shell gravitational form factors of the pion, in analogy to the electromagnetic case. Our results place stringent constraints on the off-shell GPDs of the pion. We provide an explicit realization in terms of a chiral quark model, where we show that the off-shell effects in GPDs are potentially significant in modeling physical processes and should not be neglected.