Comparison of the hadronic vacuum polarization between hadronic $\tau$-decay data and lattice QCD

TL;DR

This study compares the hadronic vacuum polarization from lattice QCD with that from tau decay data, finding good overall agreement but notable differences in specific four-pion contributions.

Contribution

It provides a detailed comparison between lattice QCD and tau decay data for HVP, including various dispersive and perturbative approaches, highlighting areas of agreement and discrepancy.

Findings

Good overall agreement between lattice and tau-based HVP results.

Discrepancies observed in four-pion mode contributions, especially for the 2π−π+π0 mode.

Dispersive methods using tau data and e+e− cross sections yield consistent results in most cases.

Abstract

We compare the isospin-one, vector-current hadronic vacuum polarization (HVP) obtained from isospin-symmetric lattice QCD with that obtained from a dispersive representation employing inclusive hadronic $\tau$ decay data corrected for isospin breaking. We consider the subtracted HVP evaluated at squared Euclidean momenta ranging from $0.5$ GeV$^2$ to $12$ GeV$^2$, together with the light-quark-connected HVP contribution to the muon anomalous magnetic moment and the short-, intermediate- and long-distance RBC/UKQCD window components thereof. Dispersive contributions from the region of hadronic invariant masses above the $\tau$ mass are evaluated using perturbative QCD. We also consider dispersive determinations using $\tau$ data only for contributions from two-pion, or two-pion and four-pion, modes, and evaluating the remaining contributions using exclusive-mode $e^+e^-\to\mbox{hadrons}$ cross sections up to about 2 GeV, lessening the dependence on perturbation theory. We find generally good agreement between lattice and $\tau$-based results. However, a comparison of $\tau$-based window-quantity contributions for the two four-pion modes to expectations for those contributions based on the Pais relations and $e^+e^-$ four-pion cross sections, reveals significant differences for the $2\pi^-\pi^+\pi^0$ mode.