$D_{(s)}(2S)$ and $D^{*}_{(s)}(2S)$ production in nonleptonic $B_{(s)}$ weak decays

TL;DR

This study computes nonleptonic decays of $B_{(s)}$ mesons into first radially excited charmed states $D_{(s)}(2S)$ and $D^{*}_{(s)}(2S)$ using the covariant light-front quark model. It delivers transition form factors for both ground and radially excited states, analyzes SU(3) flavor breaking, and predicts branching ratios for a wide set of channels, highlighting sizable rates for many $D(2S)$ and $D^{*}(2S)$ modes that current experiments could probe. The results are broadly consistent with relativistic quark model and RIQM predictions, while showing notable deviations from the Bethe–Salpeter method in the excited-state sector. A key finding is that polarization remains dominantly longitudinal across many channels, suggesting robust qualitative behavior despite quantitative differences in form factors. These predictions provide guidance for LHCb and Belle II to explore the spectrum and properties of first radially excited charmed mesons.

Abstract

Recently, many new excited states of heavy mesons have been discovered in recent experiments, including radially excited states. The production processes of these states from the $B_{(s)}$ meson have drawn significant interest. In this paper, we use the covariant light-front approach to study the nonleptonic $B_{(s)}$ meson decays to the first radially excited states $D_{(s)}(2S)$ and $D^{*}_{(s)}(2S)$. Our results reveal that many channels exhibit large branching ratios in the range $10^{-5}\sim 10^{-4}$, even up to $10^{-3}$ for individual channels, which are detectable by current experiments. Our predictions for the decays $B_{(s)}\to D^{(*)}_{(s)}(2S)(π,ρ,K^{(*)})$ are larger than those given by the Bethe-Salpeter (BS) equation method, but agree well with the relativistic quark mode (RQM) and the relativistic independent quark model (RIQM) calculations. For comparison, we also present the branching ratios of the decays $B_{(s)}\to D^{(*)}_{(s)}(1S)(π,ρ,K^{(*)})$, which are comparable with other theoretical results and the data. Although the branching ratios of the decays $B_{(s)} \to D^{*}_{(s)}(1S)(ρ,K^*)$ are much larger than those of the decays $B_{(s)} \to D^{*}_{(s)}(2S)(ρ,K^*)$, the polarization properties between them are similar, that is, the longitudinal polarization fractions are dominant and can amount roughly to $90\%$.

Figures (3)

• Figure 1: Feynman diagrams for $B_{(s)}$ 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.
• Figure 2: Form factors $F_{1}(q^2)$ and $F_{0}(q^2)$ of the transitions $B_{(s)}\rightarrow D_{(s)}(1S,2S)$.
• Figure 3: Form factors $V(q^2)$, $A_{0}(q^2)$, $A_{1}(q^2)$ and $A_{2}(q^2)$ of the transitions $B_{(s)}\rightarrow D^{*}_{(s)}(1S,2S)$.