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

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 $\simeq 4$ 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 ($a\simeq 0.062,0.082,0.089$ fm) with pion masses in the range $M_{\pi }\simeq 210-450$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3$ 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 $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV, which corresponds to ${\overline{m}}_b({\overline{m}}_b)=4.26(18)$ GeV in the $\overline{MS}$ scheme. The lattice data are analyzed in terms of the Heavy Quark Expansion (HQE) and the matrix elements of dimension-4 and dimension-5 operators are extracted with a good precision, namely: $\overline{\Lambda }=0.552(26)$ GeV, ${\mu }_{\pi }^2=0.321(32)$ GeV${}^2$ and ${\mu }_G^2(m_b)=0.253(25)$ GeV${}^2$. The data also allow for a rough estimate of the dimension-6 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.

31 pages, 12 figures, 6 tables

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