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

Abstract

We present a new lattice determination of some of the parameters appearing both in the Operator Product Expansion (OPE) analysis of the inclusive semileptonic $B$-meson decays and in the Heavy Quark Expansion (HQE) of the pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark masses $m_h$ in the range from $m_c^{\mathrm{phys}}$ to $\simeq 4m_b^{\mathrm{phys}}$. We employed the $N_f=2+1+1$ gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing $a\simeq (0.062,0.082,0.089)$ fm with pion masses in the range $M_{\ddot{I}}€\simeq (210-450)$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3m_c^{\mathrm{phys}}$. The interpolation to the physical $m_b^{\mathrm{phys}}$ is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV (${\overline{m}}_b({\overline{m}}_b)=4.26(18)$ GeV in the $\overline{\mathrm{MS}}$ scheme). The lattice data are analyzed in terms of the HQE and the matrix elements of dimension-4 and dimension-5 operators are extracted with good precision, namely: $\overline{\hat{I}}›=0.552(26)$ GeV, $\hat{I}{¼}_{\ddot{I}}{€}^2=0.321(32)$ GeV${}^2$ and $\hat{I}{¼}_G^2(m_b)=0.253(25)$ GeV${}^2$. The data also allow for an estimate of the dimension-6 operator matrix elements.

arXiv admin note: substantial text overlap with arXiv:1704.06105