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

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