High statistics analysis using anisotropic clover lattices: IV. Volume dependence of light hadron masses

Abstract

The volume dependence of the octet baryon masses and relations among them are explored with Lattice QCD. Calculations are performed with ${n}_{f}=2+1$ clover fermion discretization in four lattice volumes, with spatial extent $L\ensuremath{\sim}2.0$, 2.5, 3.0 and 3.9 fm, with an anisotropic lattice spacing of ${b}_{s}\ensuremath{\sim}0.123\text{ }\text{ }\mathrm{fm}$ in the spatial direction, and ${b}_{t}={b}_{s}/3.5$ in the time direction, and at a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}390\text{ }\text{ }\mathrm{MeV}$. The typical precision of the ground-state baryon mass determination is $\ensuremath{\lesssim}0.2%$, enabling a precise exploration of the volume dependence of the masses, the Gell-Mann--Okubo mass relation, and of other mass combinations. A comparison of the volume dependence with the predictions of heavy baryon chiral perturbation theory is performed in both the $\mathrm{SU}(2{)}_{L}\ensuremath{\bigotimes}\mathrm{SU}(2{)}_{R}$ and $\mathrm{SU}(3{)}_{L}\ensuremath{\bigotimes}\mathrm{SU}(3{)}_{R}$ expansions. Predictions of the three-flavor expansion for the hadron masses are found to describe the observed volume dependences reasonably well. Further, the $\ensuremath{\Delta}N\ensuremath{\pi}$ axial coupling constant is extracted from the volume dependence of the nucleon mass in the two-flavor expansion, with only small modifications in the three-flavor expansion from the inclusion of kaons and $\ensuremath{\eta}$'s. At a given value of ${m}_{\ensuremath{\pi}}L$, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at ${m}_{\ensuremath{\pi}}\ensuremath{\sim}140\text{ }\text{ }\mathrm{MeV}$ than at ${m}_{\ensuremath{\pi}}\ensuremath{\sim}390\text{ }\text{ }\mathrm{MeV}$ due to a coefficient that scales as $\ensuremath{\sim}{m}_{\ensuremath{\pi}}^{3}$. This is relevant for the design of future ensembles of lattice gauge-field configurations. Finally, the volume dependence of the pion and kaon masses are analyzed with two-flavor and three-flavor chiral perturbation theory.