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

We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order [i.e., $\mathcal{O}(p^4)$] in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite-volume corrections. Up to $\mathcal{O}(p^3)$, all relevant low-energy constants can be well determined. As a consequence, we obtain the physical values for the masses of ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Omega }}_{cc}$ baryons by extrapolating to the physical limit. Our determination of the ${\mathrm{\Xi }}_{cc}$ mass is consistent with the recent experimental value by LHCb Collaboration, however, larger than the one by SELEX Collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the ${\mathrm{\Xi }}_{cc}$ and ${\mathrm{\Omega }}_{cc}$ states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of $\mathcal{O}(p^4)$ order, where more unknown constants are involved, when more data are available for unphysical pion masses.

Figure 1

One-particle-irreducible diagrams. Dashed and solid lines represent pions and nucleons, respectively. Numbers in the squares mark the chiral orders of the vertices.

Figure 2

Finite-volume corrections to loop integrals as functions of the lattice size $L$.

Figure 3

Masses of doubly charmed baryons as functions of $m_c$ for different pion masses and lattice sizes.

Figure 4

Physical masses of the doubly charmed baryons.

Figure 5

Quark mass dependences of the sigma terms for the doubly charmed baryons.

Figure 6

Quark mass dependence of the mass splitting.