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We present new lattice results of the ETM Collaboration, obtained fromextensive simulations of lattice QCD with dynamical up, down, strange and charmquarks at physical mass values, different volumes and lattice spacings,concerning the SM prediction for the so-called intermediate window (W) andshort-distance (SD) contributions to the leading order hadronic vacuumpolarization (LO-HVP) term of the muon anomalous magnetic moment, $a_\mu$.Results for $a_{\mu}^{\rm LO-HVP,W}$ and $a_{\mu}^{\rm LO-HVP,SD}$, besidesrepresenting a step forward to a complete lattice computation of $a_{\mu}^{\rmLO-HVP}$ and a useful benchmark among lattice groups, are compared here withtheir dispersive counterparts based on experimental data for $e^+e^-$ intohadrons. 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$a_{\mu}^{\rm LO-HVP,SD}$.

Short \& intermediate distance HVP contributions to muon g-2: SM (lattice) prediction versus $e^+e^-$ annihilation data