  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.
