Identification of $D^*_2(3000)$ as the $D_2^*(2^3P_2)$ and exploring potential of undiscovered $2^+$ mesons via $B$ decays

TL;DR

This work uses a relativistic Bethe–Salpeter framework with the instantaneous Salpeter reduction and a Cornell potential to compute semileptonic and nonleptonic $B$ decays to $J^P=2^+$ charmed mesons. It identifies $D^*_2(3000)$ as the $D_2^*(2P)$ state by matching production in $B$ decays to observed branching ratios, while excluding other candidates like $1F$, $3P$, and $2F$ based on predicted branching suppressions. The study further maps out the discovery potential for undiscovered $2^+$ states ($D^*_2(1F)$, $D^*_2(3P)$, $D^*_2(2F)$) in $B$ decays, highlighting that relativistic partial-wave mixing (P-D-F) and node structures strongly shape decay patterns and mass dependence. The results offer experimentally testable predictions, particularly in semileptonic channels for $2P$, and emphasize mass-sensitive behaviors that could refine spectroscopy in the charmed-meson sector. Overall, the work provides a coherent theoretical framework for identifying excited $2^+$ states and guides future searches at $B$-meson facilities."

Abstract

Following the discovery of the $D^*_2(3000)$, its mass and full width have been extensively studied. Yet its nature remains undetermined to date. Since it was discovered through nonleptonic decay of $B$ meson and the corresponding cascade process, we therefore in this paper investigate the nonleptonic and semileptonic decays of $B$ meson to $J^P = 2^+$ charmed mesons using the Bethe-Salpeter equation approach. Our calculations on nonleptonic $B$ decays reveal that the unconfirmed resonance $D^*_2(3000)$ aligns well with $D^*_2(2^3P_2)$ predictions. Other candidates, including $D^*_2(1^3F_2)$, $D^*_2(3^3P_2)$, and $D^*_2(2^3F_2)$, are excluded due to their very small branching ratios in $B$ decays. Considering that the $D^*_2(1F)$, $D^*_2(3P)$, and $D^*_2(2F)$ have not yet been experimentally observed, we investigate the feasibility of their detection in $B$-meson decays.

Figures (7)

• Figure 1: Feynman diagram for $B^{+}\rightarrow \bar{D}_2^{*0}\ell^+\nu_{\ell}.$
• Figure 2: Feynman diagram for $B^{+}\rightarrow D_2^{*0}\pi^{+}.$
• Figure 3: The radial wave functions of the $2^+$ mesons $\bar{D}_2^{*0}(2460)$ (left), $\bar{D}_2^{*0}(2P)$ (middle) and $\bar{D}_2^{*0}(1F)$ (right), where $q\equiv |\vec{q}|$.
• Figure 4: The radial wave functions of the $2^+$ mesons $\bar{D}_2^{*0}(3P)$ (left), and $\bar{D}_2^{*0}(2F)$ (right), where $q\equiv |\vec{q}|$.
• Figure 5: Electron energy spectra of $(1/\Gamma)(d\Gamma/dx)$ for $B^{+}\to \bar{D}_2^{*0}(2460)\ell^+\nu_{\ell}$ (left), $B^{+}\to \bar{D}_2^{*0}(2P)\ell^+\nu_{\ell}$ (middle), and $B^{+}\to \bar{D}_2^{*0}(1F)\ell^+\nu_{\ell}$ (right).