Nucleon distribution amplitudes and their application to nucleon form factors and theN→Δtransition at intermediate values ofQ2

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 $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition at intermediate values of the momentum transfer. We compare our results with experimental data in the range $1\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\le}{Q}^{2}\ensuremath{\le}10\text{ }\text{ }{\mathrm{GeV}}^{2}$. Keeping in mind that we are working only in leading order QCD and next-to-leading order 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 $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ transition form factor ratios ${R}_{\mathrm{EM}}$ and ${R}_{\mathrm{SM}}$.