Finite size effect on pseudoscalar meson sector in 2+1 flavor QCD at the physical point

Abstract

We investigate the finite size effect on pseudoscalar meson masses and decay constants using a subset of the "PACS10" configurations which are generated keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We have tried two kinds of analyses, fixing $κ$ values or measured axial Ward identity quark masses. Comparing the results on (5.4 fm$)^4$ and (10.8 fm$)^4$ lattices, we have found a sizable finite size effect on the pseudoscalar meson sector in the former analysis: a 2.1(8)%, 4.8(1.6)%, and 0.36(31)% finite size effect on $m_π$, $m_{\rm ud}$, and $f_π$, respectively, on the (5.4 fm$)^4$ lattice. For the latter analysis, the finite size effect on the pseudoscalar meson decay constants is 0.66(33)% for $f_π$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_π$. These values with two-sigma error bars are consistent with the predictions from the full one-loop SU(3) chiral perturbation theory, which are 0.20% for $f_π$, 0.08% for $f_K$, and 0.13% for $f_K/f_π$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision.

7 pages, 10 figures, published version