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

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