Baryon Distribution Amplitudes in QCD

TL;DR

This paper introduces a new theoretical approach to describe leading twist light-cone baryon distribution amplitudes in QCD, revealing a hidden quantum number and providing exact solutions for certain components.

Contribution

It develops an integrability-based framework for baryon distribution amplitudes, identifying a hidden quantum number and solving evolution equations analytically for key components.

Findings

Exact solutions for the lowest anomalous dimension component for all moments.

Identification of a finite mass gap in the spectrum of $mbda=1/2$ operators.

Asymptotic expansion for higher levels at large moments.

Abstract

We develop a new theoretical framework for the description of leading twist light-cone baryon distribution amplitudes which is based on integrability of the helicity $\lambda=3/2$ evolution equation to leading logarithmic accuracy. A physical interpretation is that one can identify a new `hidden' quantum number which distinguishes components in the $\lambda=3/2$ distribution amplitudes with different scale dependence. The solution of the corresponding evolution equation is reduced to a simple three-term recurrence relation. The exact analytic solution is found for the component with the lowest anomalous dimension for all moments $N$, and the WKB-type expansion is constructed for other levels, which becomes asymptotically exact at large $N$. Evolution equations for the $\lambda=1/2$ distribution amplitudes (e.g. for the nucleon) are studied as well. We find that the two lowest anomalous dimensions for the $\lambda=1/2$ operators (one for each parity) are separated from the rest of the spectrum by a finite `mass gap'. These special states can be interpreted as scalar diquarks.