Factorization and Decay Constants $f_{D_s^*}$ and $f_{D_s}$

TL;DR

This paper calculates the decay constants of $D_s$ and $D_s^{*}$ mesons using factorization, considering non-factorizable effects, different form factors, and penguin contributions, providing estimates with uncertainties.

Contribution

It introduces a comprehensive calculation of $D_s$ and $D_s^{*}$ decay constants including non-factorizable effects and various form factor models, which was not extensively done before.

Findings

Estimated $f_{D_s} = 233 ext{--}255$ MeV with uncertainties.

Estimated $f_{D_s^{*}} = 346 ext{--} 428$ MeV with uncertainties.

Found the ratio $f_{D_s^{*}}/f_{D_s} eq 1$, indicating differences in decay dynamics.

Abstract

We calculate the decay constants of $D_s$ and $D_s^{*}$ with $\bar{B}^0 \ra D^{+}\ell^{-}\nu$ and $\bar{B}^0 \ra D^{+}D_s^{-(*)}$ decays. In our analysis we take the factorization method including non-factorizable term contributions and used two different form factor behaviours (constant and monopole-type) for $F_0(q^2)$. We also consider the QCD-penguin and Electroweak-penguin contributions in hadronic decays within the NDR renormalization scheme at NLO calculation. We estimate the decay constant of the $D_s$ meson to be $233\pm49$ ${\rm MeV}$ for (pole/pole)-type form factor and $255\pm54$ ${\rm MeV}$ for (pole/constant)-type form factor. For $D_s^{*}$ meson, we get $f_{D_s^{*}} = 346 \pm 82$ ${\rm MeV}$, and $f_{D_s^{*}}/f_{D_s} = 1.43 \pm 0.45$ for (pole/constant)-type form factor.