Magnetic moments of the doubly charmed and bottomed baryons

The chiral corrections to the magnetic moments of the spin-$\frac{1}{2}$ doubly charmed baryons are systematically investigated up to next-to-next-to-leading order with heavy baryon chiral perturbation theory (HBChPT). The numerical results are calculated up to next-to-leading order: ${\mu }_{{\mathrm{\Xi }}_{cc}^{++}}=-0.25{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{cc}^{+}}=0.85{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{cc}^{+}}=0.78{\mu }_N$. We also calculate the magnetic moments of the other doubly heavy baryons, including the doubly bottomed baryons (bbq) and the doubly heavy baryons containing a light quark, a charm quark and a bottom quark ($\{bc\}q$ and $[bc]q$): ${\mu }_{{\mathrm{\Xi }}_{bb}^0}=-0.84{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{bb}^{-}}=0.26{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{bb}^{-}}=0.19{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{\{bc\}q}^{+}}=-0.54{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{\{bc\}q}^0}=0.56{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{\{bc\}q}^0}=0.49{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{[bc]q}^{+}}=0.69{\mu }_N$, ${\mu }_{{\mathrm{\Xi }}_{[bc]q}^0}=-0.59{\mu }_N$, ${\mu }_{{\mathrm{\Omega }}_{[bc]q}^0}=0.24{\mu }_N$.