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

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 $1{\mathrm{GeV}}^2\le Q^2\le 10{\mathrm{GeV}}^2$. 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 $N\to \Delta$ transition form factor ratios $R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$.