Magnetic dipole moment of the $\mathrm{\Delta }(1232)$ in chiral perturbation theory

The magnetic dipole moment of the $\mathrm{\Delta }(1232)$ is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the $\mathrm{\Delta }(1232)$, at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.