# 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 similar to 2.0, 2.5, 3.0 and 3.9 fm, with an anisotropic lattice spacing of b(s) similar to 0.123 fm in the spatial direction, and b(t) = b(s)/3.5 in the time direction, and at a pion mass of m(pi) similar to 390 MeV. The typical precision of the ground-state baryon mass determination is less than or similar to 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 SU(2)(L) circle times SU(2)(R) and SU(3)(L) circle times 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 Delta N 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 eta's. At a given value of m(pi)L, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at m(pi) similar to 140 MeV than at m(pi) similar to 390 MeV due to a coefficient that scales as similar to m(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.

*This paper has been withdrawn.*