The Productions and Strong Decays of $D_q(2S)$ and $B_q(2S)$

TL;DR

This paper investigates the production and decay of excited $D_q(2S)$ and $B_q(2S)$ mesons using an improved Bethe-Salpeter approach, providing predictions for their detection in B-factory experiments.

Contribution

It offers new theoretical predictions for the production rates and decay channels of $D_q(2S)$ and $B_q(2S)$ states, aiding experimental identification.

Findings

Predicted branching ratios for $B$ decays to $D_q(2S)$ states are around 10^{-4}.

Identified potential channels for detecting $D_q(2S)$ states at B-factories.

Suggested the $D(2550)^0$ is likely the $D^0(2S)$ state despite decay width discrepancies.

Abstract

We study the productions of first radial excited states $D_q(2S)$ ($q=u, d, s$) and $B_q(2S)$ in exclusive semi-leptonic $B_{q'}$ ($q'=u, d s, c$) decays by the improved Bethe-Salpeter method. These 2S states can be detected through their strong decays to ground mesons, where the strong decays are calculated by the low energy approximation as well as the impulse approximation. Some channels have ratios of order $10^{-4}$: $Br(B^+\to\bar D^0(2S)\ell^+{\nu_\ell})\times Br(\bar D^0(2S)\to \bar D^{*}\pi)\approx(4.9\pm4.0)\times10^{-4}$, $Br(B^0\to D^-(2S)\ell^+{\nu_\ell})\times Br(D^-(2S)\to \bar D^{*}\pi)\approx(4.4\pm3.4)\times10^{-4}$. These channels could be measured by the current B-factories. For $D_s(2S)$, we also obtain a relative large ratio: $Br(B_s^0\to D_s^-(2S)\ell^+{\nu_\ell})\times Br(D_s^-(2S)\to \bar D^{*}\bar K)\approx (9.9\pm14.9)\times10^{-4}$. Although there are discrepancies of the full decay width between the theoretical predictions of ${D}^0(2S)$ and experimental results of $D(2550)^0$, the new detected state $D(2550)^0$ is very likely the ${D}^0(2S)$ state.