We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.

In this paper, for the first time to our knowledge, a method is proposed to compute electromagnetic effects in hadronic processes, such as decays, using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. We present a detailed analysis of the method for the leptonic decays of a pseudoscalar meson. The implementation of our method, although challenging, is within reach of the present lattice technology

We present a lattice QCD computation of the b-quark mass, the B and B_s decay constants, the B-mixing bag parameters for the full four-fermion operator basis as well as determinations for \xi and f_{Bq}\sqrt{B_i^{(q)}} extrapolated to the continuum limit and to the physical pion mass. We used N_f = 2 twisted mass Wilson fermions at four values of the lattice spacing with pion masses ranging from 280 to 500 MeV. Extrapolation in the heavy quark mass from the charm to the bottom quark region has been carried out on ratios of physical quantities computed at nearby quark masses, exploiting the fact that they have an exactly known infinite mass limit. Our results are m_b(m_b, \overline{\rm{MS}})=4.29(12) GeV, f_{Bs}=228(8) MeV, f_{B}=189(8) MeV and f_{Bs}/f_B=1.206(24). Moreover with our results for the bag-parameters we find \xi=1.225(31), B_1^{(s)}/B_1^{(d)}=1.01(2), f_{Bd}\sqrt{\hat{B}_{1}^{(d)}} = 216(10) MeV and f_{Bs}\sqrt{\hat{B}_{1}^{(s)}} = 262(10) MeV. We also computed the bag parameters for the complete basis of the four-fermion operators which are required in beyond the SM theories. By using these results for the bag parameters we are able to provide a refined Unitarity Triangle analysis in the presence of New Physics, improving the bounds coming from B_{(s)}-\bar B_{(s)} mixing

We present unquenched lattice QCD results for the matrix elements of four-fermion operators relevant to the description of the neutral K and D mixing in the Standard Model and its extensions. We have employed simulations with N f = 2+1+1 dynamical sea quarks at three values of the lattice spacings in the interval 0.06 -0.09 fm and pseudoscalar meson masses in the range 210 -450 MeV. Our results are extrapolated to the continuum limit and to the physical pion mass. Renormalization constants have been determined non-perturbatively in the RI-MOM scheme. In particular, for the Kaon bag-parameter, which is relevant for the K 0 − K 0 mixing in the Standard Model, we obtain B RGI K = 0.717(24).