Electromagnetic and gravitational form factors of Δ resonance in a covariant quark-diquark approach

Abstract

In this work, the electromagnetic and gravitational form factors of a spin-$3/2$ particle, $\mathrm{\ensuremath{\Delta}}$ resonance, are simultaneously calculated with the help of a relativistic covariant quark-diquark approach. The two kinds of form factors are separately extracted from the matrix elements of the electromagnetic current and of the energy-momentum tensor of the system. Our numerical results show that the approach can reproduce the electromagnetic monopole, dipole, quadrupole, and octupole form factors well compared to the lattice calculations. Our obtained electromagnetic moments are also comparable with some other approaches. Moreover, the obtained gravitational form factors, which give the mechanical properties of the system (like the mass and spin distributions) are also given for the $\mathrm{\ensuremath{\Delta}}$ isobar. In addition, some discussions of the sign and the interpretation of the $D$ term are given.