Twist-2 light-quark distribution functions in a singly heavy baryon in the large $N_c$ limit

TL;DR

This paper investigates the twist-2 light-quark distribution functions in singly heavy baryons using a large $N_c$ pion mean field framework, revealing how heavy quark mass influences quark momentum distribution.

Contribution

It introduces a novel analysis of light-quark distributions in heavy baryons within the large $N_c$ limit, incorporating both unpolarized and polarized functions and quasi-distributions.

Findings

Light quarks in heavy baryons carry less momentum than in nucleons.

The momentum deficit increases with the heavy quark mass.

The study discusses sum rules and inequalities for these distributions.

Abstract

A singly heavy baryon can be considered as a state consisting of the $N_c-1$ light valence quarks that create the pion mean field in the large $N_c$ limit. In the limit of the infinitely heavy quark mass, a heavy quark inside a singly heavy baryon is regarded as a mere static color source. It is required only to make the singly heavy baryon a color singlet. Thus, the $N_c-1$ valence quarks govern quark dynamics inside the singly heavy baryon. Within this pion mean field framework, we investigate the twist-2 unpolarized and longitudinally polarized light-quark distribution functions inside charmed and bottom baryons at a low renormalization point. We observe that the light quarks inside a heavy baryon carry less momentum than those inside a nucleon. This feature is more prominent as the heavy quark mass increases. We discuss the baryon sum rule, momentum sum rule, and the Bjorken spin sum rule for singly heavy baryons. We also discuss the inequality conditions for the quark distribution functions. In addition, we present the results for the light-quark quasi-distribution functions.