The Nucleon Distribution Amplitudes and their application to nucleon form factors and the $N \to \Delta$ transition at intermediate values of $Q^2$

TL;DR

This paper compares lattice and other models of nucleon distribution amplitudes, investigates their contributions to nucleon and N to Delta transition form factors at intermediate Q^2, and finds good agreement with experimental data.

Contribution

It provides a detailed analysis of nucleon distribution amplitudes up to twist 6 and their application to form factors, including conformal d-wave contributions, with comparisons to experimental results.

Findings

Good agreement with experimental form factors for nucleon and N to Delta transitions.

Inclusion of twist 6 and conformal d-wave contributions improves modeling accuracy.

LO QCD calculations show promising results despite potential NLO corrections.

Abstract

We compare a recent lattice determination of the nucleon distribution amplitudes with other approaches and models. We study the nucleon distribution amplitudes up to twist 6 in next-to leading conformal spin and we also investigate conformal d-wave contributions to the leading twist distribution amplitude. With the help of light-cone sum rules one can relate the distribution amplitudes to the form factors of the nucleon or the $ N \to \Delta$ transition at intermediate values of the momentum transfer. We compare our results with experimental data in the range 1 GeV$^2 \leq Q^2 \leq 10$ GeV$^2$. Keeping in mind that we are working only in LO QCD and NLO-QCD corrections might be sizeable we already obtain a surprisingly good agreement for the nucleon form factors $G_M^n$, $G_M^p$, $G_A^p$ and $G_T^p$ and for the $N \to \Delta$ transition form factor ratios $R_{EM}$ and $R_{SM}$.