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We calculate the masses and sigma terms of the doubly charmed baryons up tonext-to-next-to-next-to-leading order (i.e., $\mathcal{O}(p^4)$) in a covariantbaryon chiral perturbation theory by using the extended-on-mass-shellrenormalization scheme. Their expressions both in infinite and finite volumesare provided for chiral extrapolation in lattice QCD. As a first application,our chiral results of the masses are confronted with the existing lattice QCDdata in the presence of finite volume corrections. Up to $\mathcal{O}(p^3)$ allrelevant low energy constants can be well determined. As a consequence, weobtain the physical values for the masses of $\Xi_{cc}$ and $\Omega_{cc}$baryons by extrapolating to the physical limit. Our determination of the$\Xi_{cc}$ mass is consistent with the recent experimental value by LHCbcollaboration, however, larger than the one by SELEX collaboration. Inaddition, we predict the pion-baryon and strangeness-baryon sigma terms, aswell as the mass splitting between the $\Xi_{cc}$ and $\Omega_{cc}$ states.Their quark mass dependences are also discussed. The numerical procedure can beapplied to the chiral results of $\mathcal{O}(p^4)$ order, where more unknownconstants are involved, when more data are available for unphysical pionmasses.

Masses and sigma terms of doubly charmed baryons up to $\mathcal{O}(p^4)$ in manifestly Lorentz-invariant baryon chiral perturbation theory