Masses and decay constants of D(s)* and B(s)* mesons with Nf = 2 + 1 + 1 twisted mass fermions

TL;DR

This paper uses lattice QCD with twisted mass fermions to calculate the masses and decay constants of vector mesons D* and B*, providing results close to experimental values and exploring heavy-quark mass ratios.

Contribution

It presents a novel lattice QCD calculation of D* and B* meson properties with Nf=2+1+1 dynamical quarks, including ratios of vector to pseudoscalar quantities across a range of heavy-quark masses.

Findings

Ratios of vector to pseudoscalar masses close to 1 for B mesons.

Computed decay constants for D* and B* mesons with high precision.

Results consistent with experimental data and theoretical predictions.

Abstract

We present a lattice calculation of the masses and decay constants of $D_{(s)}^*$ and $B_{(s)}^*$ mesons using the gauge configurations produced by the European Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ dynamical quarks at three values of the lattice spacing $a \sim (0.06 - 0.09)$ fm. Pion masses are simulated in the range $M_\pi \simeq (210 - 450)$ MeV, while the strange and charm sea-quark masses are close to their physical values. We compute the ratios of vector to pseudoscalar masses and decay constants for various values of the heavy-quark mass $m_h$ in the range $0.7 m_c^{\mathrm{phys}} \lesssim m_h \lesssim 3 m_c^{\mathrm{phys}}$. In order to reach the physical b-quark mass, we exploit the Heavy Quark Effective Theory prediction that, in the static limit of infinite heavy-quark mass, the considered ratios are equal to one. At the physical point our results are: $M_{D^*} / M_{D} = 1.0769(79)$, $M_{D^*_{s}} / M_{D_{s}} = 1.0751(56)$, $ f_{D^*} / f_{D} = 1.078(36),$ $f_{D^*_{s}} / f_{D_{s}} = 1.087(20)$, $M_{B^*} / M_{B} = 1.0078(15)$, $M_{B^*_{s}} / M_{B_{s}} = 1.0083(10)$, $f_{B^*} / f_{B} = 0.958(22)$ and $f_{B^*_{s}} / f_{B_{s}} = 0.974(10)$. Combining them with the experimental values of the pseudoscalar meson masses (used as input to fix the quark masses) and the values of the pseudoscalar decay constants calculated by ETMC, we get: $M_{D^*} = 2013(14)~\mathrm{MeV}$, $ M_{D_s^*} = 2116(11)~\mathrm{MeV}$, $f_{D^*} = 223.5(8.4)~\mathrm{MeV}$, $f_{D_s^*} = 268.8(6.6)~\mathrm{MeV}$, $M_{B^*} = 5320.5(7.6)~\mathrm{MeV}$, $M_{B_s^*} = 5411.36(5.3)~\mathrm{MeV}$, $f_{B^*} = 185.9(7.2)~\mathrm{MeV}$ and $f_{B_s^*} = 223.1(5.4)~\mathrm{MeV}$.