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Register a new userConsistency of hadronic vacuum polarization between lattice QCD and the R-ratio
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There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, and charm sea quark gauge ensembles generated in the staggered formalism by the MILC collaboration. We study the continuum limit using inverse lattice spacings from $a^{-1}approx 1.6$ GeV to $3.5$ GeV, identical to recent studies by FNAL/HPQCD/MILC and Aubin et al. and similar to the recent study of BMW. Our calculation exhibits a tension for the particularly interesting window result of $a_mu^{rm ud, conn.,isospin, W}$ from $0.4$ fm to $1.0$ fm with previous results obtained with a different discretization of the vector current on the same gauge configurations. Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention. In this work we also provide results for $a_mu^{rm ud,conn.,isospin}$, $a_mu^{rm s,conn.,isospin}$, $a_mu^{rm SIB,conn.}$ for the total contribution and a large set of windows. For the total contribution, we find $a_mu^{rm HVP~LO}=714(27)(13) 10^{-10}$, $a_mu^{rm ud,conn.,isospin}=657(26)(12) 10^{-10}$, $a_mu^{rm s,conn.,isospin}=52.83(22)(65) 10^{-10}$, and $a_mu^{rm SIB,conn.}=9.0(0.8)(1.2) 10^{-10}$, where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.
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We determine the contribution to the anomalous magnetic moment of the muon from the $alpha^2_{mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{mu}^{mathrm{HVP,LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{mu}$ and the Standard Model of 3$sigma$.
We present a calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_mu^{mathrm hvp}$, in lattice QCD employing dynamical up and down quarks. We focus on controlling the infrared regime of the vacuum polarization function. To this end we employ several complementary approaches, including Pade fits, time moments and the time-momentum representation. We correct our results for finite-volume effects by combining the Gounaris-Sakurai parameterization of the timelike pion form factor with the Luscher formalism. On a subset of our ensembles we have derived an upper bound on the magnitude of quark-disconnected diagrams and found that they decrease the estimate for $a_mu^{mathrm hvp}$ by at most 2%. Our final result is $a_mu^{mathrm hvp}=(654pm32,{}^{+21}_{-23})cdot 10^{-10}$, where the first error is statistical, and the second denotes the combined systematic uncertainty. Based on our findings we discuss the prospects for determining $a_mu^{mathrm hvp}$ with sub-percent precision.
We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. We obtain, in this world where all pions have the mass of the $pi^0$, $10^{10} a_mu^{ll}({rm conn.}) = 637.8,(8.8)$, in agreement with independent lattice-QCD calculations. We then combine this value with published lattice-QCD results for the connected contributions from strange, charm, and bottom quarks, and an estimate of the uncertainty due to the fact that our calculation does not include strong-isospin breaking, electromagnetism, or contributions from quark-disconnected diagrams. Our final result for the total $mathcal{O}(alpha^2)$ hadronic vacuum polarization to the muons anomalous magnetic moment is~$10^{10}a_mu^{rm HVP,LO} = 699(15)_{u,d}(1)_{s,c,b}$, where the errors are from the light-quark and heavy-quark contributions, respectively. Our result agrees with both {it ab-initio} lattice-QCD calculations and phenomenological determinations from experimental $e^+e^-$-scattering data. It is $1.3sigma$ below the no new physics value of the hadronic-vacuum-polarization contribution inferred from combining the BNL E821 measurement of $a_mu$ with theoretical calculations of the other contributions.
We present an update on the ongoing calculations by the Fermilab Lattice, HPQCD, and MILC Collaboration of the leading-order (in electromagnetism) hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. Our project employs ensembles with four flavors of highly improved staggered fermions, physical light-quark masses, and four lattice spacings ranging from $a approx 0.06$ to 0.15 fm for most of the results thus far.
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.
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