Lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory

We present an analysis of the baryon-octet and -decuplet masses using covariant SU(3)-flavor chiral perturbation theory up to next-to-leading order. Besides the description of the physical masses we address the problem of the lattice QCD extrapolation. Using the PACS-CS Collaboration data we show that a good description of the lattice points can be achieved at next-to-leading order with the covariant loop amplitudes and phenomenologically determined values for the meson-baryon couplings. Moreover, the extrapolation to the physical point up to this order is found to be better than the linear one given at leading-order by the Gell-Mann-Okubo approach. The importance that a reliable combination of lattice QCD and chiral perturbation theory may have for hadron phenomenology is emphasized with the prediction of the pion-baryon and strange-baryon sigma terms.

Figure 1

Extrapolation of the PACS-CS results [3] on the lowest-lying baryon masses within the covariant formulation of SU(3)-$\mathrm{B}\chi \mathrm{PT}$ up to NLO. The lQCD points used in the fit are represented with the corresponding error bars which do not include the correlated uncertainties. The lattice points in $m_{\pi }^2\simeq 0.15{\mathrm{GeV}}^2$ involve a lighter strange quark mass. The diamonds denote our results after the fit and they are connected by a dotted line added to guide the eye. The boxes are lattice points not included in the fit (heavier kaon mass) and the filled diamonds are the extrapolated values which are to be compared with experimental data (crosses). The latter are slightly shifted for a better comparison with the extrapolation results.

Figure 2

Feynman diagrams contributing to the octet- and decuplet-baryons ($B$ and $T$ respectively) up to $\mathcal{O}(p^3)$ in $\chi \mathrm{PT}$. The solid lines correspond to octet-baryons, double lines to decuplet-baryons and dashed lines to mesons. The black dots indicate first-order couplings while boxes, second-order couplings.