Time windows of the muon HVP from twisted-mass lattice QCD

TL;DR

This paper calculates the muon HVP contribution to its anomalous magnetic moment using lattice QCD, focusing on short and intermediate time windows, and compares results with experimental data and other lattice studies.

Contribution

It provides a lattice QCD determination of the muon HVP contribution in specific time windows using physical quark masses and multiple lattice spacings, highlighting agreement and discrepancies with dispersive methods.

Findings

Short window result agrees with experimental data.

Intermediate window result differs from dispersive determination by 3.6 sigma.

Uses gauge ensembles with physical quark masses and multiple lattice spacings.

Abstract

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_{\mu}^{\rm HVP}$, in the so-called short and intermediate time-distance windows, $a_{\mu}^{\rm SD}$ and $a_{\mu}^{\rm W}$. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_\mu^{\rm SD} = 69.27\,(34) \cdot 10^{-10}$, in agreement with the dispersive determination based on experimental $e^+ e^-$ data. For the intermediate window we get instead $a_\mu^{\rm W} = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of $3.6\,\sigma$.