Leading hadronic contribution to the muon magnetic moment from lattice QCD (2002.12347v3)

Abstract: We compute the leading order hadronic vacuum polarization (LO-HVP) contribution to the anomalous magnetic moment of the muon, $(g_\mu-2)$, using lattice QCD. Calculations are performed with four flavors of 4-stout-improved staggered quarks, at physical quark masses and at six values of the lattice spacing down to 0.064~fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. The infinite-volume limit is taken thanks to simulations performed in volumes of sizes up to 11~fm. Our result for the LO-HVP contribution to $(g_\mu-2)$ has a total uncertainty of 0.8\%. Compared to the result of the dispersive approach for this contribution, ours significantly reduces the tension between the standard model prediction for $(g_\mu-2)$ and its measurement.

• The paper presents a refined lattice QCD calculation of the muon’s hadronic vacuum polarization, achieving a 0.8% relative uncertainty.
• It leverages advanced simulation techniques like all-mode averaging and low-mode substitution to significantly reduce statistical and systematic errors.
• The study carefully addresses finite-size effects and isospin-breaking corrections to reconcile discrepancies between theoretical and experimental muon g-2 results.

Analysis of the Leading Hadronic Contribution to the Muon Magnetic Moment from Lattice QCD

This paper presents a detailed investigation into the leading-order hadronic vacuum polarization (LO-HVP) contribution to the anomalous magnetic moment of the muon, $a_\mu$, using lattice Quantum Chromodynamics (QCD). The authors provide an updated lattice QCD calculation of $a_\mu^\mathrm{LO-HVP}$, crucial for understanding the discrepancy between theoretical predictions and experimental measurements in the muon's magnetic moment. The paper notably involves collaborations across several high-performance computing centers and leverages sophisticated techniques to mitigate systematic errors inherent in lattice simulations.

Key Findings and Methodologies

1. Lattice Configuration and Simulation Details: The research utilizes 2+1+1 flavor lattice QCD configurations—comprising two light, one strange, and one charm quark—adopting the 4stout and 4HEX lattice actions. The 4HEX action notably reduces taste violations on coarser lattices.
2. Error Reduction Techniques: A central challenge in lattice QCD computations is the suppression of statistical and systematic errors. The paper implements all-mode averaging and low-mode substitution techniques, resulting in approximately an order-of-magnitude reduction in the statistical uncertainty of $a_\mu^\mathrm{light}$.
3. Finite Size and Continuum Extrapolation: Finite-size effects significantly affect lattice QCD results, especially for quantities like $a_\mu$. The authors explore these effects by conducting simulations in both typical and extended volumes, employing a combination of chiral perturbation theory and phenomenological models for corrections. The models include the Meyer-Lellouch-Lüscher-Gounaris-Sakurai (MLLGS) model and the RHO model.
4. Isospin-breaking Corrections: The paper accounts for electromagnetic and strong isospin-breaking effects up to leading-order corrections, necessitating derivative computations of observables concerning quark mass differences and electric charges.
5. Taste Improvement and Systematic Analysis: To address significant taste-breaking artifacts inherent in staggered fermions, the authors apply a physically motivated taste-improvement framework. This involves comparisons with NLO and NNLO staggered chiral perturbation theory and phenomenological SRHO models.

Results

The final result obtained is $a_\mu = 707.5[5.5] \times 10^{-10}$, achieving a 0.8% relative uncertainty. The paper highlights the influence of lattice artifacts, finite-size effects, and isospin-breaking corrections on the precision of the computed $a_\mu$. The paper shows discrepancies with other model predictions such as R-ratio based evaluations, emphasizing the need for continued cross-verification between lattice QCD methods and phenomenological approaches.

Implications and Future Directions

The continued refinement of $a_\mu^\mathrm{LO-HVP}$ through lattice QCD is paramount, given its implications in detecting potential physics beyond the Standard Model. Future work is likely to focus on further reducing uncertainties by improving lattice techniques—especially concerning light quark contributions— and by adopting refined scale setting and flavor-symmetry breaking schemes. As computational resources expand, these methods enable researchers to validate or refute current theoretical and experimental tensions surrounding the muon $g-2$ anomaly.

This paper exemplifies the synergy between advanced computational techniques and theoretical physics in addressing longstanding challenges in particle physics, underscoring lattice QCD's vital role in precision physics.