6533b853fe1ef96bd12ad53b

RESEARCH PRODUCT

Extraction of heavy-quark-expansion parameters from unquenched lattice data on pseudoscalar and vector heavy-light meson masses

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description

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 $\ensuremath{\simeq}4$ times the physical $b$-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with ${N}_{f}=2+1+1$ dynamical quarks at three values of the lattice spacing ($a\ensuremath{\simeq}0.062,0.082,0.089\text{ }\text{ }\mathrm{fm}$) with pion masses in the range ${M}_{\ensuremath{\pi}}\ensuremath{\simeq}210--450\text{ }\text{ }\mathrm{MeV}$. The heavy-quark mass is simulated directly on the lattice up to $\ensuremath{\simeq}3$ 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 ${m}_{b}^{\mathrm{kin}}(1\text{ }\text{ }\mathrm{GeV})=4.61(20)\text{ }\text{ }\mathrm{GeV}$, which corresponds to ${\overline{m}}_{b}({\overline{m}}_{b})=4.26(18)\text{ }\text{ }\mathrm{GeV}$ in the $\overline{\mathrm{MS}}$ 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, $\overline{\mathrm{\ensuremath{\Lambda}}}=0.552(26)\text{ }\text{ }\mathrm{GeV}$, ${\ensuremath{\mu}}_{\ensuremath{\pi}}^{2}=0.321(32)\text{ }\text{ }{\mathrm{GeV}}^{2}$, and ${\ensuremath{\mu}}_{G}^{2}({m}_{b})=0.253(25)\text{ }\text{ }{\mathrm{GeV}}^{2}$. 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 ${V}_{ub}$ and ${V}_{cb}$, their precise determination on the lattice may eventually validate and improve the analyses based on fits to the semileptonic moments.