Electroproduction of the $N^{*}\mathbf{(}1535\mathbf{)}$ Resonance at Large Momentum Transfer

We report on the first lattice calculation of light-cone distribution amplitudes of the $N^{*}(1535)$ resonance, which are used to calculate the transition form factors at large momentum transfers using light-cone sum rules. In the region $Q^2>2{\mathrm{GeV}}^2$, where the light-cone expansion is expected to converge, the results appear to be in good agreement with the experimental data.

Figure 1

Barycentric plot of the distribution amplitudes for nucleon (up) and $N^{\star }(1535)$ (down) at ${\mu }_{\overline{\mathrm{MS}}}=1\mathrm{GeV}$ using the central values of the lattice results. The lines of constant $x_1$, $x_2$, and $x_3$ are parallel to the sides of the triangle labeled by $x_2$, $x_3$, and $x_1$, respectively.

Figure 2

The LCSR calculation for the helicity amplitudes $A_{1/2}(Q^2)$ and $S_{1/2}(Q^2)$ for the electroproduction of the $N^{*}(1535)$ resonance using the lattice results from Table  for the lowest moments of the $N^{*}(1535)$ DAs. The curves are obtained using the central values of the lattice parameters, and the shaded areas show the corresponding uncertainty.