Multi-level computation of the hadronic vacuum polarization contribution to $(g_\mu-2)$

Understand

The first results from the Fermilab E989 experiment have confirmed the long-standing tension between the experimental determination of the muon anomalous magnetic moment $a_\mu=(g_\mu-2)/2$ and its SM determination using the dispersive approach.

• In order to match the expected final precision from E989, the current uncertainty on ab initio determinations using lattice QCD must be decreased by a factor 5-15, a goal which is hampered by the signal-to-noise ratio problem of the electromagnetic current correlator.
• Multi-level Monte Carlo integration with fermions is a method which reduces the variance of correlators exponentially in the distance of the fields.
• Here we demonstrate that the variance reduction in a realistic two-level simulation with a pion mass of 270 MeV, linear size of 3 fm and lattice spacing around 0.065 fm is sufficient to compute the tail of the current correlator with the statistical accuracy required for the hadronic vacuum polarization contribution to $a_\mu$.