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تسجيل مستخدم جديدThe hadronic vacuum polarization of the muon from four-flavor lattice QCD
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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.
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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 $u$, $d$, $s$, an
d $c$ 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 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 pol
arization 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 introduce a new method for calculating the ${rm O}(alpha^3)$ hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ${ab-initio}$ lattice QCD. We first derive expressions suitable for computing the higher-order contri
butions either from the renormalized vacuum polarization function $hatPi(q^2)$, or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously-published results for the Taylor coefficients of $hatPi(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain $10^{10} a_mu^{rm HVP,HO} = -9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^+e^- to {rm hadrons}$ data plus dispersion relations.
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 f
ield 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$sigma$.
Lattice QCD (LQCD) studies for the hadron vacuum polarization (HVP) and its contribution to the muon anomalous magnetic moment (muon g-2) are reviewed. There currently exists more than 3-sigma deviations in the muon g-2 between the BNL experiment wit
h 0.5 ppm precision and the Standard Model (SM) predictions, where the latter relies on the QCD dispersion relation for the HVP. The LQCD provides an independent crosscheck of the dispersive approaches and important indications for assessing the SM prediction with measurements at ongoing/forthcoming experiments at Fermilab/J-PARC (0.14/0.1 ppm precision). The LQCD has made significant progress, in particular, in the long distance and finite volume control, continuum extrapolations, and QED and strong isospin breaking (SIB) corrections. In the recently published papers, two LQCD estimates for the HVP muon g-2 are consistent with No New Physics while the other three are not. The tension solely originates to the light-quark connected contributions and indicates some under-estimated systematics in the large distance control. The strange and charm connected contributions as well as the disconnected contributions are consistent among all LQCD groups and determined precisely. The total error is at a few percent level. It is still premature by the LQCD to confirm or infirm the deviation between the experiments and the SM predictions. If the LQCD is combined with the dispersive method, the HVP muon g-2 is predicted with 0.4% uncertainty, which is close upon the target precision required by the Fermilab/J-PARC experiments. Continuous and considerable improvements are work in progress, and there are good prospects that the target precision will get achieved within the next few years.
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