Chirality distributions inside baryons in ${\rm QCD_2}$

Abstract

The connection between the spin distribution and the topological structure of the baryon is an open and important problem. Here we address it using QCD in $(1+1)$ spacetime dimensions, which is exactly solvable at large number of colors $N$. It is found that the distribution of chirality inside a baryon is drastically different from a chirality distribution inside states with zero baryon number, ``mesons". This difference is shown to arise from the topological structure of the baryon -- at large $N$, all of the baryon's chirality is concentrated near $x=0$, whereas in a meson state it vanishes in the small $x$ limit. Our results illustrate how the constituent features of the baryon reemerge and are tied to the topological features of the bosonized solitonic solution. Possible implications for QCD in $(3+1)$ dimensions and for deep inelastic scattering experiments are discussed.