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, $a_{\hat{I}}{¼}^{\mathrm{HVP}}$, in the so-called short and intermediate time-distance windows, $a_{\hat{I}}{¼}^{\mathrm{SD}}$ and $a_{\hat{I}}{¼}^{\mathrm{W}}$, defined by the RBC/UKQCD Collaboration [1]. 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 $L\simeq 7.6$~fm. For the short distance window we obtain $a_{\hat{I}}{¼}^{\mathrm{SD}}(\mathrm{ETMC})=69.27(34)\cdot 10^{-10}$, which is consistent with the recent dispersive value of $a_{\hat{I}}{¼}^{\mathrm{SD}}(e^{+}{e}^{-})=68.4(5)\cdot 10^{-10}$ [2]. In the case of the intermediate window we get the value $a_{\hat{I}}{¼}^{\mathrm{W}}(\mathrm{ETMC})=236.3(1.3)\cdot 10^{-10}$, which is consistent with the result $a_{\hat{I}}{¼}^{\mathrm{W}}(\mathrm{BMW})=236.7(1.4)\cdot 10^{-10}$ [3] by the BMW collaboration as well as with the recent determination by the CLS/Mainz group of $a_{\hat{I}}{¼}^{\mathrm{W}}(\mathrm{CLS})=237.30(1.46)\cdot 10^{-10}$ [4]. However, it is larger than the dispersive result of $a_{\hat{I}}{¼}^{\mathrm{W}}(e^{+}{e}^{-})=229.4(1.4)\cdot 10^{-10}$ [2] 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.

78 pages, 22 figures, 14 tables. Analysis improved with more data and fits, presentation reorganized, more material in appendices, fixed typos