The big news in particle physics in 2021 was that Fermilab’s Muon g−2 experiment raised the deviation in the muon anomalous magnetic moment to 4.2 sigma (LCMF, 07 Apr 2021). The contribution of hadronic vacuum polarization (HVP) was estimated indirectly by estimating the so-called R ratio (R-ratio) with electron-positron collision data (e⁺e⁻), because the calculation using lattice QCD (LQCD) had higher error. But the most accurate LQCD calculation (BMW ’20) reduced the deviation to only 2.2 sigma (LCMF, 10 May 2021). Since then, two new LQCD estimates (CLS ’22 and ETMC ’22) have been published, which combined with the previous one reduce the deviation to 1.5 sigmas in the g−2 value of the muon; in fact, the latest (ETMC ’22) differs by 4.5 sigmas from the e⁺e⁻ estimate. The results obtained with LQCD point to systematic errors in the estimation of HVP using e⁺e⁻ collisions. In addition, the R ratio can also be calculated using QCD on the lattice (R-EMTC ’22); the first results point to a deviation of 3 sigmas between the computational prediction and the experimental estimate. If these results are confirmed in the next few years, one of the most promising signs of new physics beyond the Standard Model would disappear.
The combination BMW ’20 + CLS ’22 + ETMC ’22 leads to a value of ???? = (g−2)/2 for the stub of ????????(HVP,W) = 236.7(8) × 10−10, which is 6.1 sigmas from the prediction using the R-ratio with collisions e⁺e⁻. For now, the individual results do not reach five sigmas, but if as the LQCD simulations with supercomputers improve, at least two achieve it, it will be necessary to consider replacing the estimate with the R-ratio by the estimate with LQCD in the theoretical prediction of the standard model to ????????(HVP). In his case, everything points to a severe setback for the physical signal beyond the standard model using muons. These new results with LQCD have been published in Marco Cè, Antoine Gérardin, …, Hartmut Wittig, “Window observable for the hadronic vacuum polarization contribution to the muon g−2 from lattice QCD,” Phys. Rev. D 106: 114502 (13 Dec 2022), doi: https://doi.org/10.1103/PhysRevD.106.114502, arXiv:2206.06582 [hep-lat] (14 Jun 2022); Constantia Alexandrou, Simone Bacchio, …, Urs Wenger, «Short & intermediate distance HVP contributions to muon g−2: SM (lattice) prediction versus e⁺e⁻ annihilation data,» arXiv:2212.10490 [hep-ph] (20 Dec 2022), doi: https://doi.org/10.48550/arXiv.2212.10490 (EMTC ’22); Constantia Alexandrou, Simone Bacchio, …, Urs Wenger, «Probing the R-ratio on the lattice,» arXiv:2212.08467 [hep-lat] (16 Dec 2022), doi: https://doi.org/10.48550/arXiv.2212.08467 (R-EMTC ’22). It will be necessary to be aware of future progress in this line.