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

¹ Dipartimento di Fisica, Università di Torino and INFN Sezione di Torino
² Departamento de Fisica Teòrica, Universitat de València and IFIC, Universitat de València-CSIC
³ Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre

^* Speaker, e-mail: aurora.melis@ific.uv.es. Acknowledges financial support from “La Caixa-Severo Ochoa” scholarship.

Published online: 26 March 2018

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 $m_c^{\text{phys}}$ to ≃ $4m_b^{\text{phys}}$. 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 ≃ (0.062,0.082,0.089) fm with pion masses in the range M_π ≃ (210 - 450) MeV. The heavy-quark mass is simulated directly on the lattice up to ≃ $3m_c^{\text{phys}}$. The interpolation to the physical $m_b^{\text{phys}}$ is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain $m_b^{\text{kin}}$ (1 GeV) = 4.61(20) GeV (m̅_b(m̅_b) = 4.26(18) GeV in the 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: $\overline{\Lambda }=0.552\left(26\right)\text{GeV,}{\mu }_{\pi }^2=0.321\left(32\right)\text{Ge}{\text{V}}^{\text{2}}$ and ${\mu }_G^2\left(m_b\right)=0.253\left(25\right)\text{Ge}{\text{V}}^{\text{2}}$. The data also allow for an estimate of the dimension-6 operator matrix elements.