Finite-volume correction on the hadronic vacuum polarization contribution to muon g-2 in lattice QCD

Abstract

We study the finite-volume correction on the hadronic vacuum polarization contribution to the muon g-2 ($a_{\mu }^{\mathrm{hvp}}$) in lattice QCD at (near) physical pion mass using two different volumes: $(5.4\mathrm{fm}{)}^4$ and $(8.1\mathrm{fm}{)}^4$. We use an optimized AMA technique for noise reduction on $N_f=2+1$ PACS gauge configurations with stout-smeared clover-Wilson fermion action and Iwasaki gauge action at a single lattice cut-off $a^{-1}=2.33$ GeV. The calculation is performed for the quark-connected light-quark contribution in the isospin symmetric limit. We take into account the effects of backward state propagation by extending a temporal boundary condition. In addition we study a quark-mass correction to tune to the exactly same physical pion mass on different volume and compare those correction with chiral perturbation. We find $10(26)\times 10^{-10}$ difference for light quark $a_{\mu }^{\mathrm{hvp}}$ between $(5.4\mathrm{fm}{)}^4$ and $(8.1\mathrm{fm}{)}^4$ lattice in 146 MeV pion.