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The role of the $f_0(1710)$ and $a_0(1710)$ resonances in the $D^0 \to ρ^0 φ$, $ωφ$ decays

Natsumi Ikeno, Wen-Hao Jia, Wei-Hong Liang, Eulogio Oset

TL;DR

This work explains why D^0 → ρ^0 φ occurs more readily than D^0 → ω φ by invoking an indirect production path: external emission creates K^{*+}K^{*-}, which then rescatter into VV final states via strong interactions described by the local hidden gauge approach. The resulting coupled-channel dynamics generate the resonances f_0(1710) and a_0(1710), whose couplings to ρ^0 φ and ω φ dominate the transitions, respectively; solving the Bethe–Salpeter equation yields T ≈ [I − VG]^{−1}V with poles matching these states. The calculated ratio R_b = Γ_{D^0→ρφ} / Γ_{D^0→ωφ} improves from ~1.5–2.0 to ≈ 1.97 when the VV channels are fully treated, and a further ρ-mass convolution brings R_b to ≈ 1.47, in line with experimental measurements within uncertainties. The results underscore the significant role of the a_0(1710) in shaping D^0 decay patterns and offer a pathway to constrain its mass and couplings through future precision data.

Abstract

We study the $D^0 \to ρ^0 φ$, $ωφ$ decays which proceed in a direct mode via internal emission with equal rates. Yet, the experimental branching ratio for the $ρ^0 φ$ mode is twice as big as that for the $ωφ$ mode. We find a natural explanation based on the extra indirect mechanism where $K^{*+} K^{*-}$ is produced via external emission and that channel undergoes final state interaction with other vector--vector channels to lead to the $ρ^0 φ$, $ωφ$ final states, with transition amplitudes dominated by the $a_0(1710)$ resonance, recently discovered, and $f_0(1710)$ respectively. The large coupling of the $a_0(1710)$ to the $ρ^0 φ$ channel is mostly responsible for this large ratio of the production rates.

The role of the $f_0(1710)$ and $a_0(1710)$ resonances in the $D^0 \to ρ^0 φ$, $ωφ$ decays

TL;DR

This work explains why D^0 → ρ^0 φ occurs more readily than D^0 → ω φ by invoking an indirect production path: external emission creates K^{*+}K^{*-}, which then rescatter into VV final states via strong interactions described by the local hidden gauge approach. The resulting coupled-channel dynamics generate the resonances f_0(1710) and a_0(1710), whose couplings to ρ^0 φ and ω φ dominate the transitions, respectively; solving the Bethe–Salpeter equation yields T ≈ [I − VG]^{−1}V with poles matching these states. The calculated ratio R_b = Γ_{D^0→ρφ} / Γ_{D^0→ωφ} improves from ~1.5–2.0 to ≈ 1.97 when the VV channels are fully treated, and a further ρ-mass convolution brings R_b to ≈ 1.47, in line with experimental measurements within uncertainties. The results underscore the significant role of the a_0(1710) in shaping D^0 decay patterns and offer a pathway to constrain its mass and couplings through future precision data.

Abstract

We study the , decays which proceed in a direct mode via internal emission with equal rates. Yet, the experimental branching ratio for the mode is twice as big as that for the mode. We find a natural explanation based on the extra indirect mechanism where is produced via external emission and that channel undergoes final state interaction with other vector--vector channels to lead to the , final states, with transition amplitudes dominated by the resonance, recently discovered, and respectively. The large coupling of the to the channel is mostly responsible for this large ratio of the production rates.
Paper Structure (6 sections, 20 equations, 3 figures, 3 tables)

This paper contains 6 sections, 20 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Role of $VV$ interaction in the $D^0 \to \rho^0 \phi$, $\omega \phi$ decays
  3. Results with full amplitudes and $\rho$ mass distribution
  4. Full amplitudes in coupled channels
  5. Convolution of $\Gamma_{D^0 \to \rho \phi}$ with the $\rho$ mass distribution
  6. Conclusions

Figures (3)

  • Figure 1: Diagram for $D^0 \to \phi \rho^0$, $\phi \omega$ at the quark level, involving internal emission. The $W \bar{s} u$ vertex is Cabibbo suppressed.
  • Figure 2: Mechanism of $K^{*+} K^{*-}$ production through external emission.
  • Figure 3: Mechanism for $D^0 \to \rho^0 \phi, \, \omega \phi$ through $K^{*+}K^{*-}$ production and final state interaction.