Electromagnetic and gravitational form factors of $\Delta$ resonance in a covariant quark-diquark approach

TL;DR

This paper calculates electromagnetic and gravitational form factors of the $$ resonance using a covariant quark-diquark model, aligning well with lattice data and providing insights into its internal structure.

Contribution

It introduces a covariant quark-diquark approach to simultaneously compute electromagnetic and gravitational form factors of the $$ resonance, including new insights into the D-term.

Findings

Reproduces electromagnetic form factors consistent with lattice results.

Provides gravitational form factors revealing mass and spin distributions.

Offers interpretation of the D-term sign and physical meaning.

Abstract

In this work, the electromagnetic and gravitational form factors of a spin-$3/2$ particle, $\Delta$ 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 well reproduce the electromagnetic monopole, dipole, quadrupole, and octupole form factors comparing 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 displayed for the $\Delta$ isobar. In addition, some discussions of the sign and the interpretation of the D-term are particularly given.