Finite-volume correction on the hadronic vacuum polarization contribution to the 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 hvp µ ) in lattice QCD at (near) physical pion mass using two different volumes: (5.4 fm) 4 and (8.1 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) × 10 −10 difference for light quark a hvp µ between (5.4 fm) 4 and (8.1 fm) 4 lattice in 146 MeV pion.

Hadronic vacuum polarization contribution to the muon g−2 with ( 2+1 )-flavor lattice QCD on a larger than Shintani1, Kuramashi2 2019Phys. Rev. DSelf Cite835660View full textAdd to dashboardCite

“…We have studied the systematic uncertainties in the LQCD calculation of a hvp µ on the PACS10 gauge configurations which have a greater than (10 fm) 4 box size at the physical point with two different lattice cutoffs. This study and previous work [22] are the direct LQCD calculations without use of any ansatz or reliance on any effective models. The optimized LQCD calculation of HVP on sufficiently large lattice size at the physical point allows us to access the deep IR regime where the contributions of multihadron states become manifest.…”

“…Our result in Eq. (22) indicates that the actual FV effect tends to be larger than the ChPT prediction, which may provide useful information on other recent LQCD results using ChPT or another analysis to correct the FV effect for a hvp µ on (4 to 5 fm) 3 box [14, 16-18] 4 . The similar analysis is made for the strange quark sector [a hvp µ ] s .…”

“…[22,47], the combination of AMA with the deflated Schwartz alternative procedure (SAP) preconditioning [48] achieves the remarkable performance on the large lattice, and it then allows us a precise calculation of a hvp µ , especially, in a long distance region. In fact the condition number in the AMA method with the deflated SAP preconditioning does not have large volume dependence [22] since the low mode is effectively eliminated by the projection with a deflation filed so that the computational cost to solve the light quark propagator does not increase even if the lattice size is enlarged. Although the computational cost of generation of deflation fields is increased in large lattice size, it takes only a few percent of the total computational cost [22] in deflated SAP preconditioning.…”

Analysis of systematic error in hadronic vacuum polarization contribution to muon g-2

“…As we will explain below, the lattice we used in this study is symmetric and its spatial/temporal extension is large enough to control the finite volume effect and the backward state propagation (BSP) effect investigated in [7]. We can perform the integral of Eq.…”

“…Recent LQCD calculations are carried out combined with an estimate of effective models, for instance, chiral perturbation theory (ChPT) [5] or Gounaris-Sakurai (GS) parametrization [6,4], used to correct the FV effect on (∼ 6 fm) 3 boxes at a long distance. As pointed out in our previous study [7] it is essentially important to assess the FV effect in the LQCD computation of HVP (g − 2) µ employing the direct comparison between different volumes at the physical pion mass without any reliance on the effective models. In this proceedings, we perform more precise comparison with ChPT using an enlarged lattice more than (10 fm) 4 at the physical pion mass, which are the subset of PACS10 configurations [8] generated by the PACS Collaboration.…”