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

TL;DR

This paper computes the masses and sigma terms of doubly charmed baryons up to order p^4 in covariant baryon chiral perturbation theory, providing results consistent with lattice QCD and experimental data, and predicting key physical quantities.

Contribution

It extends previous calculations to higher order in chiral perturbation theory, offering detailed mass and sigma term predictions for doubly charmed baryons with finite volume corrections.

Findings

Mass of $\Xi_{cc}$ consistent with LHCb measurement

Predicted sigma terms and mass splittings for doubly charmed baryons

Chiral extrapolation method validated against lattice QCD data

Abstract

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 $\Xi_{cc}$ 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 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 $\Xi_{cc}$ and $\Omega_{cc}$ 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.