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

Understand

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 $(f_{B_s}/f_B)/(f_{D_s}/f_D) = 1.008 (13)$.