Review of Lattice QCD Studies of Hadronic Vacuum Polarization Contribution to Muon $g−2$

Abstract

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-σ deviations in the muon g − 2 between the BNL experiment with 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.

New physics searches at the BESIII experiment

“…Since HVP effects are non-perturbative, they cannot be directly computed from first-principle QCD. Recent computer-based lattice QCD (LQCD) calculations have made significant progress but the uncertainties are still large [ 152 , 153 ]. The most reliable determinations to date of HVP contributions to ( g − 2) μ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\alpha (m^2_Z)$\end{document} use dispersion relations with input from experimental measurements of cross sections for e + e − annihilation into hadrons [ 136 ].…”

Self-learning Monte-Carlo for non-abelian gauge theory with dynamical fermions

“…Pol } are determined by a linear regression with prior HMC run 3 . In general cases, one can include more and more extended loops to improve the acceptance rate.…”

“…From a practical point of view, guaranteeing the convergence is inevitable because it allows for uses of the computational result in precise phenomenology. (See [2,3] and references therein, for example).…”

Gauge covariant neural network for 4 dimensional non-abelian gauge theory

“…Great achievements have done with a Markov chain Monte-Carlo algorithm called Hybrid Monte Carlo (HMC) (33) and its variant (34). We can calculate matrix elements in matrix elements for the anomalous magnetic moments in g − 2 (35), form factors and low-energy constants for analytic calculation (36), and thermodynamics of QCD (37) using lattice QCD and its numerical calculations.…”