Decay constants of $P$-wave heavy-light mesons from unquenched lattice QCD

We review some decays that require knowledge of the decay constants of $0^{+}$ heavy-light mesons. We compute the decay constants of $P$-wave heavy-light mesons from unquenched lattice QCD, with two degenerate flavours of sea quarks, at a single lattice spacing. The lightest sea quark mass used in the calculation is a third of the strange quark mass. For the charm-strange meson we obtain the decay constant: $f_{D_{s{0}^{+}}}=340(110)\mathrm{MeV}$ using our normalization conventions. We obtain the $f_{P_s}^{\mathrm{static}}$ (static-strange $P$-wave) decay constant as $302(39)\mathrm{MeV}$.

Figure 1

Effective mass plot and fitted model for the correlators with heavy $\kappa =0.113$ and light $\kappa =0.1350$.

Figure 2

Mass dependence of the $P$-wave decay constant defined in Eq. (3) at the fixed heavy-quark mass with $\kappa =0.113$, as a function of the bare light quark mass in physical units. The estimate of the decay constant at the mass of the strange quark is also shown.

Figure 3

Mass dependence of the $P$-wave decay constant defined in Eq. (3) at the strange quark mass, as a function of the bare heavy-quark mass in physical units. The vertical line is the estimate for the charm quark mass.