A fresh look at the generalized parton distributions of light pseudoscalar mesons

Abstract

We present a symmetry-preserving scheme to derive the pion and kaon generalized parton distributions (GPDs) in Euclidean space. The key to maintaining crucial symmetries under this approach is the treatment of the scattering amplitude, such that it contains both the traditional leading-order contributions and the scalar/vector pole contribution automatically, the latter being necessary to ensure the soft-pion theorem. The GPD is extracted analytically via the uniqueness and definition of the Mellin moments and we find that it naturally matches the double distribution; consequently, the polynomiality condition and sum rules are satisfied. The present scheme thus paves the way for the extraction of the GPD in Euclidean space using the Dyson-Schwinger equation framework or similar continuum approaches.

Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

“…Note that models based on the Nambu-Jona-Lasinio (NJL) approximation are not impacted, since the amplitude is momentum-independent [119][120][121]. However, in the NJL approximation, the triangle diagram is not sufficient in off-forward kinematics as the meson resonances appear in the t-channel, contributing to the D-term [119,122,123]. Thus, omitting the resonances leads to a breaking of the soft pion theorem in the chiral limit.…”