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.
We present a lattice determination of the vector and scalar form factors of the D → π ν and D → K ν semileptonic decays, which are relevant for the extraction of the CKM matrix elements |V cd | and |V cs | from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 flavors of dynamical quarks, at three different values of the lattice spacing (a 0.062, 0.082, 0.089 fm) and with pion masses as small as 210 MeV. Quark momenta are injected on the lattice using non-periodic boundary conditions. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit we determine the vector and scalar form factors in the whole kinematical region from q 2 = 0 up to q2 accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of q 2 where some deviations are visible. A set of synthetic data points, representing our results for f(q 2 ) for several selected values of q 2 , is provided and also the corresponding covariance matrix is available. At zero 4-momentum transfer we get: f
We present a lattice QCD calculation of the pseudoscalar decay constants f K , f D and f Ds 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 values in the real world. The simulations are based on a unitary setup for the two light mass-degenerate quarks and on a mixed action approach for the strange and charm quarks. We use data simulated at three different values of the lattice spacing in the range 0.06 ÷ 0.09 fm and at pion masses in the range 210 ÷ 450 MeV. Our main results are:
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
We present precise lattice computations for the b-quark mass, the quark mass ratios m b =m c and m b =m s as well as the leptonic B-decay constants. We employ gauge configurations with four dynamical quark flavors, up-down, strange and charm, at three values of the lattice spacing (a ∼ 0.06-0.09 fm) and for pion masses as low as 210 MeV. Interpolation in the heavy quark mass to the bottom quark point is performed using ratios of physical quantities computed at nearby quark masses exploiting the fact that these ratios are exactly known in the static quark mass limit. Our results are also extrapolated to the physical pion mass and to the continuum limit and read m b ðMS; m b Þ ¼ 4.26ð10Þ GeV, m b =m c ¼ 4.42ð8Þ, m b =m s ¼ 51.4ð1.4Þ, f Bs ¼ 229ð5Þ MeV, f B ¼ 193ð6Þ MeV, f Bs =f B ¼ 1.184ð25Þ and ðf Bs =f B Þ=ðf K =f π Þ ¼ 0.997ð17Þ.
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