$D^*_{(s)}\to P$ form factors and their applications to semi-leptonic and non-leptonic weak decays

TL;DR

This work computes the $D^{*}_{(s)}\to P$ transition form factors within the covariant light-front quark model to enable systematic predictions of both semi-leptonic and non-leptonic weak decays. By evaluating $V(q^2)$, $A_0(q^2)$, $A_1(q^2)$, and $A_2(q^2)$ and extrapolating to the full kinematic range with a three-parameter form, the authors obtain decay observables such as branching ratios, the longitudinal polarization fraction $f_L$, and the forward-backward asymmetry $A_{FB}$ for channels like $D^{*}_{(s)}\to \pi, K, \eta_q, \eta_s$ with final states including $\ell=e,\mu$ and hadrons $P V$ or $P P$. They find the largest semi-leptonic BRs for $D^{*+}_{s}\to \eta\ell^{+}\nu_{\ell}$ and $D^{*+}_{s}\to \eta\rho^{+}$, both near $\mathcal{O}(10^{-6})$, and provide detailed $f_L$ and $A_{FB}$ predictions, including LFU patterns and $q^2$-dependent behavior. The results, together with projected event yields at STCF, CEPC, FCC-ee, and HL-LHC, offer concrete targets for future experiments to test SM predictions and constrain possible new physics in charmed vector meson decays.

Abstract

Similar to other heavy flavor mesons, the weak decays of $D^*_{(s)}$ mesons can provide a platform to verify the standard model, explore new physics, and understand the mechanisms of weak interactions. At present, the theoretical and experimental studies on $D^*_{(s)}$ mesons are relatively limited. In addition to the dominant electromagnetic decays, the $D^*_{(s)}$ weak decays should be feasible to explore the $D^*_{(s)}$ mesons. In this study, we used the covariant light-front quark model to study the form factors of the transitions $D^*_{(s)}\to π, K, η_{q,s}$, then calculated the branching ratios of the semi-leptonic decays $D^*_{(s)}\to P\ell^{+}ν_{\ell}$ and the non-leptonic decays $D^*_{(s)}\to PP, PV$ with $P=π, K, η^{(\prime)}, V=ρ, K^*, φ$ and $\ell=e, μ$. The channels $D_{s}^{*+}\toη\ell^{+}ν_{\ell}$ and $D^{*+}_{s}\to ηρ^{+}$ possess the largest branching ratios, which can reach an order of $10^{-6}$ among these decays, and are most likely to be accessible in experiments at future high-luminosity colliders. Furthermore, we predict and discuss the longitudinal polarization fraction $f_{L}$ and the forward-backward asymmetry $A_{FB}$ for the considered semi-leptonic $D^*_{(s)}$ decays.

Figures (1)

• Figure 1: Feynman diagrams for $D^*_{(s)}$ decay (left) and transition (right) amplitudes, where $P^{\prime(\prime\prime)}$ is the incoming (outgoing) meson momentum, $p^{\prime(\prime\prime)}_1$ is the quark momentum, $p_2$ is the anti-quark momentum and X denotes the vector or axial-vector transition vertex.