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

Abstract

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_{\hat{I}}{¼}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, $a_{\hat{I}}{¼}^{\mathrm{SD}}$ and $a_{\hat{I}}{¼}^{\mathrm{W}}$. 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 $a_{\hat{I}}{¼}^{\mathrm{SD}}=69.27(34)\cdot 10^{-10}$, in agreement with the dispersive determination based on experimental $e^{+}{e}^{-}$ data. For the intermediate window we get instead $a_{\hat{I}}{¼}^{\mathrm{W}}=236.3(1.3)\cdot 10^{-10}$, which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of $3.6\ddot{I}ƒ$.

10 pages, 4 figures, 1 table, LATTICE 2022