A novel computational paradigm for a precise determination of the hadronic contribution to $(g_\mu-2)$ from lattice QCD

TL;DR

This paper introduces a multi-level Monte Carlo integration method to significantly reduce statistical errors in lattice QCD calculations of the hadronic contribution to the muon g-2, enabling more precise Standard Model predictions.

Contribution

The paper proposes and tests a multi-level Monte Carlo technique that exponentially reduces variance in lattice QCD correlation functions, improving the precision of hadronic contribution calculations.

Findings

Multi-level Monte Carlo reduces statistical errors in lattice QCD.

Feasibility demonstrated on a 3fm lattice with 0.065fm spacing.

Accelerates convergence of long-distance correlator contributions.

Abstract

The hadronic contribution to the muon anomalous magnetic moment $a_\mu=(g_\mu-2)/2$ has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty of the ongoing E989 experiment. That is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty based on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. In this talk we present our proposal to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We report the results of our feasibility tests for the computation of the Hadronic Vacuum Polarization on a lattice with a linear extension of 3~fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to $a_\mu$.