We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_{\mu }^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, $a_{\mu }^{\mathrm{SD}}$ and $a_{\mu }^{\mathrm{W}}$, defined by the RBC/UKQCD Collaboration [Phys. Rev. Lett. 121, 022003 (2018)]. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors 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 $L\simeq 7.6\mathrm{fm}$. For the short-distance window we obtain $a_{\mu }^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\times {10}^{-10}$, which is consistent with the recent dispersive value of $a_{\mu }^{\mathrm{SD}}(e^{+}{e}^{-})=68.4(5)\times {10}^{-10}$ [, Phys. Lett. B 833, 137313 (2022)]. In the case of the intermediate window we get the value $a_{\mu }^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\times {10}^{-10}$, which is consistent with the result $a_{\mu }^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\times {10}^{-10}$ [, Nature (London) 593, 51 (2021)] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of $a_{\mu }^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\times {10}^{-10}$ [, Phys. Rev. D 106, 114502 (2022)]. However, it is larger than the dispersive result of $a_{\mu }^{\mathrm{W}}(e^{+}{e}^{-})=229.4(1.4)\times {10}^{-10}$ by approximately 3.6 standard deviations. The tension increases to approximately 4.5 standard deviations if we average our ETMC result with those by BMW and CLS/Mainz. Our accurate lattice results in the short and intermediate windows point to a possible deviation of the $e^{+}{e}^{-}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.

• Received 29 July 2022
• Accepted 6 March 2023

DOI:https://doi.org/10.1103/PhysRevD.107.074506

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Published by the American Physical Society