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

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 $m_c^{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}$ to $\simeq 4m_b^{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}$. We employed the $N_f=2+1+1$ gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing $a \simeq (0.062, 0.082, 0.089)$fmwithpionmassesintherange$M_\pi \simeq (210 - 450)$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3m_c^{\rm phys}$\mathrm{.}Theinterpolationtothephysical$m_b^{\rm phys}$ is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain $m_b^{\mathrm{k}\mathrm{i}\mathrm{n}}(1GeV)=4.61(20)$ GeV (${\bar{m}}_b({\bar{m}}_b)=4.26(18)$ GeV in the $\overline{\mathrm{M}\mathrm{S}}$ 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: $\bar{\mathrm{\Lambda }}=0.552(26)$ 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 an estimate of the dimension-6 operator matrix elements.