A $N_f = 2 + 1 + 1$ "twisted" determination of the $b$-quark mass, $f_{B}$ and $f_{B_s}$

TL;DR

This paper uses lattice QCD with twisted mass Wilson fermions to precisely determine the b-quark mass and B-meson decay constants, employing simulations at multiple lattice spacings and pion masses, and extrapolating to physical values.

Contribution

The study introduces a novel combined chiral, continuum, and heavy-quark mass extrapolation method using ratios with known static limits for accurate b-quark mass and decay constants.

Findings

b-quark mass: 4.29(13) GeV

Decay constants: f_B=196(9) MeV, f_{B_s}=235(9) MeV

Decay constant ratios consistent with previous results

Abstract

We present a lattice QCD determination of the $b$-quark mass and of the $f_{B_s}$ and $f_B$ decay constants performed with $N_f = 2 + 1 + 1$ twisted mass Wilson fermions. We have used simulations at three values of the lattice spacing generated by ETMC with pion masses ranging from 210 to 440 MeV. To obtain physical quantities we performed a combined chiral and continuum limit and an extrapolation in the heavy quark mass from the charm to the $b$-quark region using suitable ratios calculated at nearby heavy-quark masses having an exactly known static limit. Our results are: $m_b(m_b) = 4.29 (13)$ GeV, $f_B = 196 (9)$ MeV, $f_{B_s} = 235 (9)$ MeV, $f_{B_s} / f_B = 1.201 (25)$, $(f_{B_s}/f_B)/(f_K/f_\pi) = 1.007 (16)$ and $(f_{B_s}/f_B)/(f_{D_s}/f_D) = 1.008 (13)$.