Magnetic moments of the spin-$\frac{3}{2}$ doubly heavy baryons

In this work, we investigate the chiral corrections to the magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons systematically up to next-to-next-to-leading order with the heavy baryon chiral perturbation theory. The numerical results are given up to next-to-leading order: ${\mu }_{{\mathrm{\Xi }}_{cc}^{\ast ++}}=1.72{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{cc}^{\ast +}}=-0.09{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{cc}^{\ast +}}=0.99{\mu }_N$. As a by-product, we have also calculated the magnetic moments of the spin-$\frac{3}{2}$ doubly bottom baryons and charmed bottom baryons: ${\mu }_{{\mathrm{\Xi }}_{bb}^{\ast 0}}=0.63{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{bb}^{\ast -}}=-0.79{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{bb}^{\ast -}}=0.12{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{bc}^{\ast +}}=1.12{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{bc}^{\ast 0}}=-0.40{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{bc}^{\ast 0}}=0.56{\mu }_N$.