Two-Loop Renormalization-Group Evolution for the Nucleon Distribution Amplitude

TL;DR

This paper calculates the two-loop renormalization-group evolution for the nucleon distribution amplitude, enabling more precise predictions of nucleon form factors in quantum chromodynamics.

Contribution

It provides the first derivation of the two-loop RG equation for the nucleon distribution amplitude, completing the next-to-leading-logarithmic corrections in the framework.

Findings

Two-loop RG evolution significantly affects nucleon form factor predictions.

Analytic solutions for scale dependence of distribution amplitude coefficients.

Impacts observed on models of nucleon distribution amplitudes.

Abstract

We determine for the first time the two-loop renormalization-group (RG) equation for the nucleon light-cone distribution amplitude, which constitutes the last missing ingredient for the complete next-to-leading-logarithmic corrections to the nucleon form factors in the hard-collinear factorization framework. Applying the conformal expansion for this fundamental nucleon distribution amplitude then enables us to construct an analytic solution that captures the desired scale dependence of phenomenologically interesting series coefficients. Importantly, the two-loop RG evolutions of these central hadronic quantities can bring about noticeable impacts on the corresponding leading-logarithmic results for three sample models of the nucleon distribution amplitude.