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We present a new lattice determination of some of the parameters appearingboth in the Operator Product Expansion (OPE) analysis of the inclusivesemileptonic $B$-meson decays and in the Heavy Quark Expansion (HQE) of thepseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a latticeQCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quarkmasses $m_h$ in the range from $m_c^{\rm phys}$ to $\simeq 4m_b^{\rm phys}$. Weemployed the $N_f = 2+1+1$ gauge configurations of the European Twisted MassCollaboration (ETMC) 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 $\simeq3m_c^{\rm phys}$. The interpolation to the physical $m_b^{\rm phys}$ isperformed using the ETMC ratio method and adopting the kinetic mass scheme. Weobtain $m_b^{\rm kin}(1~\mbox{GeV}) = 4.61 (20)$ GeV($\overline{m}_b(\overline{m}_b) = 4.26 (18)$ GeV in the $\overline{\rm MS}$scheme). The lattice data are analyzed in terms of the HQE and the matrixelements of dimension-4 and dimension-5 operators are extracted with goodprecision, 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 foran estimate of the dimension-6 operator matrix elements.

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