Abstract
We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, [see formula in PDF],in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a−1 = 2.33 GeV. We compare two integrals of [see formula in PDF], momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of [see formula in PDF] with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in [see formula in PDF].
Highlights
The muon anomalous magnetic moment (g-2) is an essential observable for a rigorous test of the standard model (SM)
In this proceedings we focus on the lattice QCD computation of ahμvp using connected hadronic vacuum polarization (HVP) diagram on two volumes, L = 5.4 and 8.1 fm, at physical pion, namely there are two variations of mπL = 3.8 and 5.8, in order for a solid study of finite volume effect in lattice QCD without effective models
In this paper we use two different ways to evaluate Eq (1) on the lattice; one is the direct Q2 integral of Eq 1 using the continuous function of vacuum polarization function (VPF) obtained by fitting lattice data, and another one is an time-slice summation of vector-vector current correlator on the lattice using the conversion of Eq(1)
Summary
The muon anomalous magnetic moment (g-2) is an essential observable for a rigorous test of the standard model (SM). The upcoming experiment in FermiLab [5] and J-PARC [6] is aiming for a factor 4 improvement from aEμ821 up to the decade, and so that the same order of precision should be achieved even from the theoretical side In this proceedings we focus on the lattice QCD computation of ahμvp using connected HVP diagram on two volumes, L = 5.4 and 8.1 fm, at physical pion (mπ 0.14 GeV), namely there are two variations of mπL = 3.8 and 5.8, in order for a solid study of finite volume effect in lattice QCD without effective models. Our study provides an essential instruction for the future lattice QCD computation to reach sub-percent level of ahμvp
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