Gravitational transverse momentum distribution of proton

TL;DR

This paper introduces the first calculation of quark gravitational transverse-momentum distributions using a light-front quark--diquark model inspired by AdS/QCD, deriving analytical expressions and exploring their physical implications.

Contribution

It provides the first analytical derivation of unpolarized gravitational TMDs and PDFs within a light-front quark--diquark model inspired by soft-wall AdS/QCD.

Findings

Derived analytical expressions for gravitational TMDs and PDFs for up and down quarks.

Verified model-independent relations between gravitational TMDs and quark TMDs.

Explored connections between gravitational TMDs, pressure, shear-force distributions, and longitudinal momentum.

Abstract

We present the first study of quark gravitational transverse-momentum distributions within the light-front quark--diquark model (LFQDM) inspired by the soft-wall AdS/QCD framework. We derive analytical expressions for the six unpolarized (T-even) gravitational transverse-momentum-dependent distributions (gravitational--TMDs) for up and down quarks within the model and compute the corresponding gravitational parton distribution functions (gravitational--PDFs). We further verify that these unpolarized gravitational--TMDs satisfy the model-independent relations with quark TMDs. In addition, we explore the connection of gravitational TMDs with the transverse isotropic pressure and shear-force distributions in momentum space, as well as with the average longitudinal momentum carried by up and down quarks within the model.