Light-quark contribution to the leading hadronic vacuum polarization term of the muon g-2 from twisted-mass fermions

We present a lattice calculation of the leading hadronic vacuum polarization (HVP) contribution of the light u- and d-quarks to the anomalous magnetic moment of the muon, a(mu)(HVP) (ud), adopting the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with N-f = 2 + 1 + 1 dynamical quarks at three values of the lattice spacing (a similar or equal to 0.062, 0.082, 0.089 fm) with pion masses in the range M-pi similar or equal to 210-450 MeV. Thanks to several lattices at fixed values of the light-quark mass and scale but with different sizes we perform a careful investigation of finite-volume effects (FVEs), which represent one of main source of uncertainty in modern lattice calculations of a(mu)(HVP)(ud). In order to remove FVEs we develop an analytic representation of the vector correlator, which describes the lattice data for time distances larger than similar or equal to 0.2 fm. The representation is based on quark-hadron duality at small and intermediate time distances and on the two-pion contributions in a finite box at larger time distances. After removing FVEs we extrapolate the corrected lattice data to the physical pion point and to the continuum limit taking into account the chiral logs predicted by Chiral Perturbation Theory (ChPT). We obtain a(mu)(HVP)(ud) = 619.0(17.8) x 10(-10). Adding the contribution of strange and charm quarks, obtained by ETMC, and an estimate of the isospin-breaking corrections and quark-disconnected diagrams from the literature we get a(mu)(HVP) (udsc) = 683(19) x 10(-10), which is consistent with recent results based on dispersive analyses of the experimental cross section data for e(+)e(-) annihilation into hadrons. Using our analytic representation of the vector correlator, taken at the physical pion mass in the continuum and infinite volume limits, we provide the first eleven moments of the polarization function and we compare them with recent results of the dispersive analysis of the pi(+)pi(-) channels. We estimate also the light-quark contribution to the missing part of a(mu)(HVP) not covered in the MUonE experiment.