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

## TL;DR

This paper performs a precise lattice QCD computation of heavy-light meson masses across a range of heavy-quark masses, extracting HQE parameters and providing accurate b-quark mass estimates to aid CKM matrix element determinations.

## Contribution

It introduces a novel lattice approach combining the ETMC ratio method and HQE analysis to determine b-quark mass and HQE parameters with high precision from unquenched lattice data.

## Key findings

- Determined the b-quark mass in the kinetic scheme as 4.61(20) GeV.
- Extracted HQE parameters: Λ̄=0.552(26) GeV, μ_π^2=0.321(32) GeV^2, μ_G^2(m_b)=0.253(25) GeV^2.
- Provided estimates for dimension-6 operator matrix elements.

## 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.