Form factors of $\Delta$(1232) and the electromagnetic $N-\Delta$ transition

In this work, the electromagnetic and gravitational form factors of $\Delta$ isobars, as well as the electromagnetic $N-\Delta$ transition form factors are studied systematically and continuously using a covariant quark-diquark approach with the pion cloud effect. In our model, the baryon is treated as the two-body system to simplify calculations, and the quarks are assumed to be surrounded by the pion cloud. The related physical properties, such as the charge radius and magnetic moment of $\Delta$ and the helicity amplitudes of the $N-\Delta$ transition are obtained and discussed. Our results for the form factors of both $\Delta$(1232) and the electromagnetic $N-\Delta$ transition are in reasonable agreement with the experimental or lattice results. Moreover, we found that the pion cloud plays an important role in the results through enlarging the magnetic transition form factor $G_M(t)$ and shifting the sign of the D-term of $\Delta$ to negative.