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

TL;DR

This study quantifies finite size effects on pseudoscalar meson masses and decay constants in 2+1 flavor QCD at the physical point, finding significant effects on masses but minimal impact on decay constants, consistent with chiral perturbation theory.

Contribution

It provides detailed measurements of finite size effects in pseudoscalar meson sector using large-volume lattice QCD configurations at the physical point, validating chiral perturbation theory predictions.

Findings

Finite size effect on $m_ ext{pi}$ is about 2.1% on smaller lattice.

Finite size effect on $f_ ext{pi}$ is approximately 0.66%.

Results agree with one-loop SU(3) chiral perturbation theory predictions.

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 $\kappa$ 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 $m_\pi$, $m_{\rm ud}$, and $f_\pi$, 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 $f_\pi$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_\pi$. 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 $f_\pi$, 0.08% for $f_K$, and 0.13% for $f_K/f_\pi$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision.