Contact interaction analysis of pion GTMDs

TL;DR

This paper uses a contact interaction model to calculate pion GTMDs and related distributions, revealing insights into hadronic mass scale, distribution form factors, and internal quark dynamics, with implications for understanding pion structure.

Contribution

It introduces a contact interaction approach to compute pion GTMDs and explores their physical implications, including mass distribution and internal pressure characteristics.

Findings

GTMD size and shape are largely determined by the hadronic mass scale.

The pion's mass distribution form factor is harder than its electromagnetic form factor.

The pressure distribution near the pion's core is comparable to that in neutron stars.

Abstract

A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction's simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions (GPDs), it is found that the pion's mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion's core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions (TMDs), their magnitude and domain of support decrease with increasing twist. The simplest Wigner distribution associated with the pion's twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.