Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions

Abstract

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, ${a}_{\ensuremath{\mu}}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}$ and ${a}_{\ensuremath{\mu}}^{\mathrm{W}}$, 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 $\ensuremath{\simeq}0.057$, 0.068 and 0.080 fm with spatial lattice sizes up to $L\ensuremath{\simeq}7.6\text{ }\text{ }\mathrm{fm}$. For the short-distance window we obtain ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the recent dispersive value of ${a}_{\ensuremath{\mu}}^{\mathrm{SD}}({e}^{+}{e}^{\ensuremath{-}})=68.4(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Lett. B 833, 137313 (2022)]. In the case of the intermediate window we get the value ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which is consistent with the result ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Nature (London) 593, 51 (2021)] by the BMW Collaboration as well as with the recent determination by the CLS/Mainz group of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ [, Phys. Rev. D 106, 114502 (2022)]. However, it is larger than the dispersive result of ${a}_{\ensuremath{\mu}}^{\mathrm{W}}({e}^{+}{e}^{\ensuremath{-}})=229.4(1.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ 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 ${e}^{+}{e}^{\ensuremath{-}}$ cross section data with respect to Standard Model predictions in the low- and intermediate-energy regions but not in the high-energy region.