Progress on computing the hadronic vacuum polarization contribution to the muon anomalous magnetic moment with staggered fermions

Abstract

We give an update of our calculation of the light-quark, connected, hadronic vacuum polarization contribution to the muon anomalous magnetic moment, or muon $g-2$. The update includes preliminary results on a $2 + 1 + 1$ highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, $0.042$ fm lattice spacing, and volume $144^3 \times 288$. We discuss code and algorithm improvements for these calculations to compute the vector-vector correlation function more efficiently.

Figures (5)

• Figure 1: The summand in Eq. (\ref{['eq:t-m amu']}). No LMA (left), total (middle), LMA only (right). Odd-parity, excited state oscillations intrinsic to staggered fermions are readily apparent.
• Figure 2: Comparision of the summand in Eq. \ref{['eq:t-m amu']} between our old method and new method for the $64^3$ ensemble.
• Figure 3: Statistical errors on the summand in Eq. (\ref{['eq:t-m amu']}). Comparison between number of hits (left) and comparison between old and new method (right).
• Figure 4: LL contribution from contracting the meson fields with, and without, sparsening the low-modes.
• Figure 5: Summand in Eq. (\ref{['eq:t-m amu']}) for the $144^3$ ensemble (left) and uncorrected results for the intermediate window value. The new point at $a=0.042$ fm (see Table \ref{['tab:144c intermediate win']}) is compared with our earlier results Aubin:2022hgm (right). Errors shown are statistical only.