Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Abstract: We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be $a_\mu^{\rm HVP~LO}=715.4(16.3)(9.2) \times 10^{-10}$, where the first error is statistical and the second is systematic. By supplementing lattice data for very short and long distances with experimental R-ratio data using the compilation of Ref. [1], we significantly improve the precision of our calculation and find $a_\mu^{\rm HVP~LO} = 692.5(1.4)(0.5)(0.7)(2.1) \times 10^{-10}$ with lattice statistical, lattice systematic, R-ratio statistical, and R-ratio systematic errors given separately. This is the currently most precise determination of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. In addition, we present the first lattice calculation of the light-quark QED correction at physical pion mass.

• The paper presents the most precise HVP computation for muon g-2 using lattice QCD+QED combined with experimental R-ratio data.
• It utilizes advanced techniques like low-mode averaging and truncated deflated solver to address QED and strong isospin-breaking effects.
• The refined results reduce the discrepancy between theory and experiment, guiding future muon g-2 studies at Fermilab and J-PARC.

Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment

The study presented in the paper "Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment" focuses on evaluating the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$. Utilizing a first-principles approach in lattice quantum chromodynamics and quantum electrodynamics (QCD+QED), the authors perform computations using physical pion masses. This assessment is critical as $a_\mu$ is a precision quantity sensitive to contributions from both the standard model and potential new physics. Discrepancies between theoretical predictions and experimental observations of $a_\mu$ at the level of $3-4\sigma$ suggest the possible presence of physics beyond the standard model, underscoring the necessity to refine theoretical estimates of HVP contributions.

Methodology and Results

The authors employ lattice QCD combined with experimental data from the R-ratio method to compute the HVP contribution. Their lattice setup incorporates up, down, strange, and charm quarks with non-degenerate masses, addressing both QED and strong isospin-breaking effects. They obtain an HVP contribution of $$a_\mu^{\text{HVP LO}} = 715.4(16.3)(9.2) \times 10^{-10}$$ from lattice computations alone, where the uncertainties are statistical and systematic, respectively. More refined results stem from using lattice data alongside experimental data at specific kinematic regions, yielding $$a_\mu^{\text{HVP LO}} = 692.5(1.4)(0.5)(0.7)(2.1) \times 10^{-10}$$ with individual uncertainties labeled as lattice statistical, lattice systematic, R-ratio statistical, and R-ratio systematic errors.

Figures within the paper, such as the comparison of lattice and experimental evaluations of $w_tC(t)$, highlight how each data set excels at different scales: R-ratio data at short and long distances and lattice data at intermediate distances. The lattice calculations involve sophisticated techniques like low-mode averaging and the truncated deflated solver (AMA), ensuring robust statistical estimations with an optimal use of computational resources.

Implications and Future Work

The calculations presented achieve the most precise determination to date of the leading-order HVP contribution to $a_\mu$, reducing tensions between theoretical predictions and experimental results. The work enhances the reliability of lattice QCD in similar high-precision tests, hinting at the capability of lattice methods to validate and complement experimental findings. Consequently, this ongoing research informs both theoretical pursuits and experimental endeavors, particularly those aiming to probe the muon's magnetic moment more accurately, such as at Fermilab's E989 and J-PARC's E34 experiments.

Future research directions involve extending the precision of lattice computations through simulations at smaller lattice spacings, larger volumes, and leveraging newer experimental input. The blend of theoretical computations and empirical data will further help to decode the muon $g-2$ puzzle, presenting an avenue for potential discoveries in particle physics. These efforts will ensure unprecedented accuracy, confirming or challenging the boundaries of the standard model.

In summary, this paper makes a significant contribution to the understanding of the muon anomalous magnetic moment $a_\mu$ through a detailed computational approach, setting a benchmark for precision in testing the standard model's predictions and exploring new physics.