  We present new lattice results of the ETM Collaboration, obtained from
extensive simulations of lattice QCD with dynamical up, down, strange and charm
quarks at physical mass values, different volumes and lattice spacings,
concerning the SM prediction for the so-called intermediate window (W) and
short-distance (SD) contributions to the leading order hadronic vacuum
polarization (LO-HVP) term of the muon anomalous magnetic moment, $a_\mu$.
Results for $a_{\mu}^{\rm LO-HVP,W}$ and $a_{\mu}^{\rm LO-HVP,SD}$, besides
representing a step forward to a complete lattice computation of $a_{\mu}^{\rm
LO-HVP}$ and a useful benchmark among lattice groups, are compared here with
their dispersive counterparts based on experimental data for $e^+e^-$ into
hadrons. The comparison confirms the tension in $a_{\mu}^{\rm LO-HVP,W}$,
already noted in 2020 by the BMW Collaboration, while showing no tension in
$a_{\mu}^{\rm LO-HVP,SD}$.
