We present a lattice QCD determination of the vector and scalar form factors of the semileptonic K → π ν decay which are relevant for the extraction of the CKM matrix element |V us | from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical fermions, which include in the sea, besides two light mass degenerate quarks, also the strange and the charm quarks. We use data simulated at three different values of the lattice spacing and with pion masses as small as 210MeV. Our final result for the vector form factor at zero momentum transfer is f + (0) = 0.9709(46), where the uncertainty is both statistical and systematic combined in quadrature. Using the latest experimental value of f + (0)|V us | from K 3 decays, we obtain |V us | = 0.2230(11), which allows to test the unitarity constraint of the Standard Model below the permille level once the determination of |V ud | from superallowed nuclear β decays is adopted. A slight tension with unitarity at the level of ∼ 2 standard deviations is observed. Moreover we present our results for the semileptonic scalar f 0 (q 2 ) and vector f + (q 2 ) form factors in the whole range of values of the squared four-momentum transfer q 2 measured in K 3 decays, obtaining a very good agreement with the momentum dependence of the experimental data. We provide a set of synthetic data points representing our results for the vector and scalar form factors at the physical point for several selected values of q 2 .2

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Electromagnetic corrections to the leptonic decay rates of charged pseudoscalar mesons: lattice resultsV. Lubicz (a,b) , G. Martinelli (c) , C.T. Sachrajda (d) , F. Sanfilippo (d) , S. Simula * (b) , N. Tantalo (e) , C. Tarantino (a,b)

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moments of the electron, a HVP e , the muon, a HVP µ , and the tau, a HVP τ , including both the isospin-symmetric QCD term and the leading-order strong and electromagnetic isospinbreaking corrections. Moreover, the contribution to a HVP µ not covered by the MUonE experimen, a HVP MUonE , is provided. We get a HVP e = 185.8 (4.2) • 10 −14 , a HVP µ = 692.1 (16.3) • 10 −10 , a HVP τ =335.9 (6.9)•10 −8 and a HVP MUonE = 91.6 (2.0)•10 −10 . Our results are obtained in the quenched-QED approximation using the QCD gauge configurations generated by the European (now Extended) Twisted Mass Collaboration (ETMC) with N f = 2 + 1 + 1 dynamical quarks, at three values of the lattice spacing varying from 0.089 to 0.062 fm, at several values of the lattice spatial size (L 1.8 ÷ 3.5 fm) and with pion masses in the range between 220 and 490 MeV.

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