Transversity Generalized Parton Distributions of $\mathrm{\Delta }$ with the Diquark Spectator Model

We show quark transversity generalized parton pistributions (GPDs) of ${\mathrm{\Delta }}^{+}$ isobar by using the diquark spectator model for the first time. First, this model is tested by electric charge, magnetic-dipole and axial charge form factors, and it is used for calculating the transversity GPDs $H_{1,3,5,7}^{qT}$ of ${\mathrm{\Delta }}^{+}$. The quark transversity distribution $h_1$ is then obtained from the transversity GPDs in the forward limit. Then, helicity-flip amplitudes are shown numerically by using relations between the helicity amplitudes and the GPDs. Finally, by taking first moments of the GPDs, tensor form factors are obtained and we predict the tensor charge. Experimentally, $N$-$\mathrm{\Delta }$ transition GPDs are investigated in deeply virtual Compton scattering and virtual meson-production processes, and generalized distribution amplitudes, which correspond to the $s$-channel GPDs, could be investigated by the two-photon processes ${\gamma }^{\ast }\gamma \to \mathrm{\Delta }\bar{\mathrm{\Delta }}$ at the electron-positron colliders. Therefore, the spin-3/2 $\mathrm{\Delta }$ GPDs could become interesting quantities experimentally in future.