Parton distribution functions and transverse momentum dependence of heavy mesons

TL;DR

This paper derives the light-front wave functions of heavy mesons from Bethe-Salpeter equations and calculates their transverse momentum and parton distribution functions, revealing mass-dependent narrowing and non-factorizable distributions.

Contribution

It introduces a method to obtain heavy meson wave functions from Bethe-Salpeter projections and analyzes their transverse momentum and parton distributions, highlighting unique mass-dependent features.

Findings

Distributions become narrower and shift to larger x with increasing meson mass.

Transverse momentum distributions do not factorize into separate x and k_perp^2 functions.

Fall-off of distributions with k_perp^2 is slower than in light mesons.

Abstract

The leading Fock state light-front wave functions of heavy quarkonia and $D$ and $B$ mesons are obtained from the projections of their Bethe-Salpeter wave functions on the light front. We compute therefrom their leading-twist time-reversal even transverse momentum distributions and parton distribution functions. Mirroring the behavior of parton distribution amplitudes, the support of both distributions is increasingly narrower and shifted towards larger $x$ as a function of the meson mass. The dependence of $x$ and $\k_\perp^2$ of the transverse distributions does not factorize into separate functions, and their fall-off with $\k_\perp^2$ is much slower than that of light mesons.