Abstract
We study the finite-volume correction on the hadronic vacuum polarization contribution to the muon g-2 ($a_\mu^{\rm hvp}$) in lattice QCD at (near) physical pion mass using two different volumes: $(5.4~{\rm fm})^4$ and $(8.1~{\rm fm})^4$. 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 $10(26)\times10^{-10}$ difference for light quark $a_\mu^{\rm hvp}$ between $(5.4~{\rm fm})^4$ and $(8.1~{\rm fm})^4$ lattice in 146 MeV pion.
Highlights
The muon anomalous magnetic moment (g − 2) is an essential observable for a rigorous test of the standard model (SM) of particle physics
This paper presents the study of the FV correction for the connected diagram of the hadronic vacuum polarization contribution to muon g − 2 from the direct comparison with two volumes, L 1⁄4 5.4 and 8.1 fm, in purely lattice QCD, which is an independent way from the other lattice studies [29,31,33]
Using the high-statistics lattice data boosted by the AMA method, we obtain that the light-quark contribution to 1⁄2ahμvplat estimated in the time-slice summation on L 1⁄4 5.4 fm is the ð10 Æ 26Þ × 10−10 shift from L 1⁄4 8.1 fm as the FV correction at 146 MeV pion, correspondingly, the 1% Æ 4% effect to the dispersive estimate of ahμvp ≈ 700 × 10−10 and 1⁄2ahμvplat taken as the upper and lower bound in Eq (17) is obtained in Eqs. (14) and (16)
Summary
The muon anomalous magnetic moment (g − 2) is an essential observable for a rigorous test of the standard model (SM) of particle physics. The theory uncertainty is currently dominated by the leading-order QCD contribution, i.e., the hadronic vacuum polarization (HVP) contribution. Lattice QCD, which is a rigorous computation from the first principle of QCD, is able to provide the pure QCD contribution to ahμvp for the whole energy region, and its calculation is completely independent from the dispersive approach. To study FV correction to ahμvp in purely lattice QCD, we compare the connected HVP diagram between two volumes, L 1⁄4 5.4 and 8.1 fm, at nearly physical pion (mπ ≃ 0.14 GeV), which are corresponding to two variations of mπL 1⁄4 3.8 and 5.8. Our study provides a test of the usage of an effective-field theory for the FV correction as used in [29,31,33] and a crosscheck from pure lattice calculation.
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