Masses of doubly charmed baryons in the extended on-mass-shell renormalization scheme

In this work, we investigate the mass corrections of the doubly charmed baryons up to $N^2LO$ in the extended-on-mass-shell (EOMS) renormalization scheme, comparing with the results of heavy baryon chiral perturbation theory. We find that the terms from the heavy baryon approach are a subset of those obtained in the EOMS scheme. By fitting the lattice data, we can determine the parameters $\tilde{m}$, $\alpha$, $c_1$ and $c_7$ from the Lagrangian, while in the heavy baryon approach no information on $c_1$ can be obtained from the baryons mass. Correspondingly, the masses of $m_{\Xi_{cc}}$ and $m_{\Omega_{cc}}$ are predicted, in the EOMS scheme, extrapolating the results from different values of the charm quark and the pion masses of the lattice QCD calculations.