Abstract
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 dynamical quarks at three values of the lattice spacing (a ≃ 0.062, 0.082, 0.089 fm) with pion masses in the range Mπ ≃ 210-450 MeV. The strange and charm quark masses are tuned at their physical values. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: aμs(αem2) = (53.1 ± 2.5) · 10− 10, aμs(αem3) = (−0.018 ± 0.011) · 10− 10 and aμc(αem2) = (14.75 ± 0.56) · 10− 10, aμc(αem3) = (−0.030 ± 0.013) · 10− 10 for the strange and charm contributions, respectively.
Highlights
The theoretical predictions for the hadronic contributions have been traditionally obtained from experimental data using dispersion relations for relating the Hadronic Vacuum Polarization (HVP) function to the experimental cross section data for e+e− annihilation into hadrons [6, 7]
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections
Our findings demonstrate that the expansion method of refs. [27, 28], which has been already applied successfully to the calculation of e.m. and strong isospin breaking (IB) corrections to meson masses [28, 29] and leptonic decays of pions and kaons [30, 31], works as well in the case of the HVP contribution to aμ
Summary
The hadronic contribution ahμad to the muon anomalous magnetic moment at order αe2m can be related to the Euclidean space-time HVP function Π(Q2) by [8,9,10]. In eq (2.1) the subtracted HVP function ΠR(Q2) ≡ Π(Q2) − Π(0) appears. This is due to the fact that the photon wave function renormalization constant absorbs the value of the photon self energy at Q2 = 0 in order to guarantee that the e.m. coupling αem is the experimental one in the limit Q2 → 0. The HVP function ΠR(Q2) can be determined from the vector current-current Euclidean correlator V (t) defined as. In what follows we will limit ourselves to the connected contributions to ahμad. For sake of simplicity we drop the label f and the suffix (conn), but it is understood that hereafter we refer to the connected part of ahμad for a generic quark flavor f
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