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We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, a_^HVP, in the so-called short and intermediate time-distance windows, a_^SD and a_^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 N₅=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 0. 057, 0. 068 and 0. 080 fm with spatial lattice sizes up to L7. 6 fm. For the short-distance window we obtain a_^SD (ETMC) =69. 27 (34) 10^-10, which is consistent with the recent dispersive value of a_^SD (e^+e^-) =68. 4 (5) 10^-10, Phys. Lett. B 833, 137313 (2022). In the case of the intermediate window we get the value a_^W (ETMC) =236. 3 (1. 3) 10^-10, which is consistent with the result a_^W (BMW) =236. 7 (1. 4) 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_^W (CLS) =237. 30 (1. 46) 10^-10, Phys. Rev. D 106, 114502 (2022). However, it is larger than the dispersive result of a_^W (e^+e^-) =229. 4 (1. 4) 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.
Alexandrou et al. (Wed,) studied this question.