A bstract We present a lattice QCD determination of the b quark mass and of the B and B ~( s )decay constants, performed with N ~( f )= 2 twisted mass Wilson fermions, by simulating at four values of the lattice spacing. In order to study the b quark on the lattice, two methods are adopted in the present work, respectively based on suitable ratios with exactly known static limit and on the interpolation between relativistic data, evaluated in the charm mass region, and the static point, obtained by simulating the HQET on the lattice. The two methods provide results in good agreement. For the b quark mass in the $ overline {ext{MS}} $ scheme and for the decay constants we obtain $ {overline m_b}left( {{{overline m }_b}} ight) $ = 4 . 29(14) GeV, f ~( B )= 195(12) MeV, f ~( Bs )= 232(10) MeV and f ~( Bs ) /f ~( B )= 1 . 19(5). As a byproduct of the analysis we also obtain the results for the f ~( D )and f ~( Ds )decay constants: f ~( D )= 212(8) MeV, f ~( Ds )= 248(6) MeV and f ~( Ds ) /f ~( D )= 1 . 17(5).
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