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Analysis of molecular state ${η_cD^*}$ and ${J/ψD^*}$ in the effective Lagrangian approach

Na Li, Ye Xing, Jing-Rui Shi

Abstract

In this work, we investigate the production and decay of the molecular states $cc\bar c\bar q$ with $J^P=1^+$ using the phenomenological analysis and effective Lagrangian approach. Based on an SU(3) flavor symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${η_c D^*}$ and ${J/ψD^*}$. Our results indicate that the production branching ratio from $B_c$ meson is sizable, it can reach the order of $10^{-4}$ for the molecular configuration ${η_cD^*}$, and $10^{-5}$ for molecule ${J/ψD^*}$. In addition, we find that the decay widths of the two molecular configurations ${η_cD^*}$ and ${J/ψD^*}$ are not significant, being at level of $\cal{O}$($\rm {MeV}$).

Analysis of molecular state ${η_cD^*}$ and ${J/ψD^*}$ in the effective Lagrangian approach

Abstract

In this work, we investigate the production and decay of the molecular states with using the phenomenological analysis and effective Lagrangian approach. Based on an SU(3) flavor symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of and . Our results indicate that the production branching ratio from meson is sizable, it can reach the order of for the molecular configuration , and for molecule . In addition, we find that the decay widths of the two molecular configurations and are not significant, being at level of ().

Paper Structure

This paper contains 8 sections, 26 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. molecular state: ${J/\psi D^{*}}$ and ${\eta_c D^{*}}$
  3. phenomenological analysis
  4. The effective Lagrangian approach
  5. Production of the molecular states from $B_c$ meson
  6. Decay of the molecular states
  7. Numerical analysis
  8. Conclusions

Figures (4)

  • Figure 1: The internal W-emission(A) and external W-emission diagram(B) represent the weak processes of the molecular state $T_{\eta_c D^*}$ and $T_{J/\psi D^*}$ production from $B_c$ meson. Diagrams(C,D) are the self-energy and production triangle process of the molecular states $T_{J/\psi D^*}$ and $T_{\eta_c D^*}$ respectively.
  • Figure 2: Diagrams($a$,$a^\prime$,$a^{\prime \prime}$,$b^{\prime \prime}$,$c^{\prime \prime}$) represent two-body decays of the molecular states $T_{\eta_c D^*}$ and $T_{J/\psi D^*}$. Among them, the decay processes depicted in diagrams($a$,$a^\prime$) are dominant, which are the primary focus of the paper, whereas the processes in diagrams($a^{\prime \prime}$,$b^{\prime \prime}$,$c^{\prime \prime}$) are suppressed. Diagrams($b, b^\prime$) and ($c,c^\prime$) picture tree level and one-loop level three-body decays of the molecular states($T_{\eta_c D^*}$ and $T_{J/\psi D^*}$) respectively.
  • Figure 3: In the binding energies $\varepsilon = 5\ \text{MeV}$, the branching ratios of $B^+_c \to K^* T_{cc\bar{c} \bar{q}}$ vary with the scale parameter $\alpha_m$(GeV). The panels correspond to $J/\psi D^*$ molecular configuration (left), and $\eta_c D^*$ molecular configuration (right).
  • Figure 4: In the binding energies $\varepsilon = 5\ \text{MeV}$, the two-body decay widths of $T_{cc\bar{c} \bar{q}}$ vary with the scale parameter $\alpha_m$(GeV). The panels correspond to binding energies $T_{ \eta_c D^*} \to J/\psi D$ (left), $T_{ J/\psi D^*} \to J/\psi D$ (middle), and $T_{ J/\psi D^*} \to \eta_c D^*$ (right).