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: $\mu_{\Xi^{++}_{cc}}=-0.25\mu_{N}$, $\mu_{\Xi^{+}_{cc}}=0.85\mu_{N}$, $\mu_{\Omega^{+}_{cc}}=0.78\mu_{N}$. 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 $[bc]q$): $\mu_{\Xi^{0}_{bb}}=-0.84\mu_{N}$, $\mu_{\Xi^{-}_{bb}}=0.26\mu_{N}$, $\mu_{\Omega^{-}_{bb}}=0.19\mu_{N}$, $\mu_{\Xi^{+}_{\{bc\}q}}=-0.54\mu_{N}$, $\mu_{\Xi^{0}_{\{bc\}q}}=0.56\mu_{N}$, $\mu_{\Omega^{0}_{\{bc\}q}}=0.49\mu_{N}$, $\mu_{\Xi^{+}_{[bc]q}}=0.69\mu_{N}$, $\mu_{\Xi^{0}_{[bc]q}}=-0.59\mu_{N}$, $\mu_{\Omega^{0}_{[bc]q}}=0.24\mu_{N}$.