Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD (1902.04223v2)

Abstract: 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 muon's 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 $1.3\sigma$ 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.

Evaluation of the Hadronic-Vacuum-Polarization Contribution to the Muon's Anomalous Magnetic Moment from Lattice QCD

This paper addresses the important issue of calculating the hadronic vacuum polarization (HVP) contribution to the muon's anomalous magnetic moment, denoted as $a_\mu$. The work employs four-flavor lattice Quantum Chromodynamics (QCD) to evaluate this contribution from connected diagrams involving up (u) and down (d) quarks, while omitting electromagnetic effects. This investigation is crucial for high-precision tests of the Standard Model (SM) as it relates to potentially revealing new physics through discrepancies between theoretical calculations and experimental measurements of $a_\mu$.

Background and Significance

The muon's anomalous magnetic moment has long been of interest due to its sensitivity to virtual processes involving heavy particles and unobserved forces. Theoretical predictions within the SM need to match experimental observations with high precision. A current 3.5-4$\sigma$ discrepancy exists between theoretical predictions and measurements of $a_\mu$ which could suggest new physics.

Lattice QCD provides an ab-initio method for calculating the contributions to $a_\mu$, especially significant given the complexity of non-perturbative QCD effects involved in forming the leading-order HVP. Past phenomenological approaches have leveraged experimental data from $e^+e^-$-scattering to determine the HVP, but lattice QCD directly calculates the requisite hadronic contributions.

Methodology

The authors utilized QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks, maintaining the physical pion mass across various lattice spacings for their simulations. These configurations permitted the first-principles calculation of the contributions to $a_\mu$ by the connected quark diagrams under these lattice conditions.

The key result of the paper is the determination of the connected contribution to the muon's anomalous magnetic moment from this lattice QCD framework. The authors processed data from multiple ensembles of lattice configurations, allowing for extrapolation to the continuum limit and the capture of finite-volume corrections.

This calculation obtained $$a_{\mu}^{ll}({\rm conn.}) = 637.8(8.8) \times 10^{-10}$$, delineating the contributions from the $u/d$ quarks in an isospin-symmetric regime. These results are cross-validated against other lattice-QCD and phenomenological determinations, agreeing within present uncertainties of approximately 1.3$\sigma$ below the "no new physics" benchmark defined by the current experimental results.

Implications and Future Directions

The result presented suggests that lattice QCD can potentially resolve current discrepancies between theoretical and experimental determinations of $a_\mu$. This paper places emphasis on reducing systematic errors through significant computational and methodological strides, including considering quark mass tuning and electromagnetic effects.

For practical implications, further refined calculations of QED corrections, strong-isospin breaking, and quark-line disconnected contributions will enhance the comparison with experimental results. As lattice QCD techniques and computational power evolve, the disclosed approach holds promise for reducing theoretical uncertainties to the 0.2\% level, sufficient to substantiate or contest emergent gaps hinting at physics beyond the SM.

In summary, this paper presents a detailed and rigorous lattice QCD calculation of a key Standard Model parameter, laying the groundwork for future efforts to tighten the SM constraints or discover new physics through detailed examination of the muon's anomalous magnetic moment.