Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory

We study finite-volume effects on the masses of the ground-state octet baryons using covariant baryon chiral perturbation theory (ChPT) up to next-to-leading order by analyzing the latest $n_f=2+1$ lattice quantum chromodynamics (LQCD) results from the NPLQCD Collaboration. Contributions of virtual decuplet baryons are taken into account using the consistent coupling scheme. We compare our results with those obtained from heavy baryon ChPT and show that, although both approaches can describe well the lattice data, the underlying physics is different: In heavy baryon ChPT, virtual decuplet baryons play a more important role than they do in covariant ChPT. This is because the virtual octet-baryon contributions to finite-volume corrections are larger in covariant ChPT than in heavy baryon ChPT, while the contributions of intermediate decuplet baryons are smaller, because of relativistic effects. We observe that for the octet-baryon masses, at fixed $m_{\pi }L$ ($\gg 1$) finite-volume corrections decrease as $m_{\pi }$ approaches its physical value, provided that the strange quark mass is at or close to its physical value, as in most lattice quantum chromodynamics setups.

Figure 1

Feynman diagrams contributing to finite-volume effects on the masses of the ground-state octet baryons up to next-to-leading order. Solid lines denote octet baryons, solid double lines decuplet baryons, and dashed lines represent pseudoscalar mesons.

Figure 2

Finite-volume corrections, $\delta G_N$ (left) and $\delta G_D$ (right), as functions of lattice size $L$ for $m_{\pi }=0.2$ and 0.4 GeV. In the evaluation of $\delta G_{D/N}$ in covariant ChPT $M_0=0.8\mathrm{GeV}$. The decuplet-octet mass gap is set to be $\Delta =0.231\mathrm{GeV}$.

Figure 3

Finite-volume effects, $\delta G_N/G_N$ (left) and $\delta G_D/G_D$ (right), as functions of $e^{-m_{\pi }L}/(m_{\pi }L)$ for $m_{\pi }=0.2$ and 0.4 GeV. In the left figure, the black and red dashed lines coincide. In the evaluation of $\delta G_{D/N}$ ($G_{D/N}$) in EOMS ChPT $M_0=0.8\mathrm{GeV}$. The decuplet-octet mass gap is set to be $\Delta =0.231\mathrm{GeV}$.

Figure 4

The NPLQCD octet-mass data [17] fitted with NLO EOMS ChPT and HBChPT. The bands are the full results at the 68% confidence level and the solid (dashed) lines are the best fits with $C=0$.

Figure 5

Predicted finite-volume corrections for the ground-state octet baryons using the best fitted LECs determined from the NPLQCD data [17], where $m_s$ is assumed to have its physical value, and $m_K$ ($m_{\eta }$) are related to $m_{\pi }$ through leading-order ChPT: $m_K^2=\frac{1}{2}(2B_0{m}_s+m_{\pi }^2)$, $m_{\eta }^2=\frac{1}{3}(4m_K^2-m_{\pi }^2)$, and $2B_0{m}_s=(2m_K^2-m_{\pi }^2){|}_{\mathrm{phys}}$.