Abstract

We present a precise lattice computation of pseudoscalar and vector heavy-light meson masses for heavy-quark masses ranging from the physical charm mass up to ≃4 times the physical b-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with Nf=2+1+1 dynamical quarks at three values of the lattice spacing (a≃0.062,0.082,0.089  fm) with pion masses in the range Mπ≃210–450  MeV. The heavy-quark mass is simulated directly on the lattice up to ≃3 times the physical charm mass. The interpolation to the physical b-quark mass is performed using the ETMC ratio method, based on ratios of the meson masses computed at nearby heavy-quark masses, and adopting the kinetic mass scheme. The extrapolation to the physical pion mass and to the continuum limit yields mbkin(1  GeV)=4.61(20)  GeV, which corresponds to m¯b(m¯b)=4.26(18)  GeV in the MS¯ scheme. The lattice data are analyzed in terms of the heavy-quark expansion (HQE) and the matrix elements of dimension-four and dimension-five operators are extracted with a good precision, namely, Λ¯=0.552(26)  GeV, μπ2=0.321(32)  GeV2, and μG2(mb)=0.253(25)  GeV2. The data also allow for a rough estimate of the dimension-six operator matrix elements. As the HQE parameters play a crucial role in the inclusive determination of the Cabibbo-Kobayashi-Maskawa matrix elements Vub and Vcb, their precise determination on the lattice may eventually validate and improve the analyses based on fits to the semileptonic moments.