Rescattering-induced $D\to SS$ weak decays

TL;DR

This work addresses why D decays to scalar-scalar final states can occur at observable rates despite the suppression of short-distance amplitudes. It develops a formalism where long-distance final-state interactions, implemented as triangle rescattering diagrams with intermediate states such as pi eta and a1 eta and mediated by meson exchanges, generate the D to SS decay amplitudes; eta-eta' mixing and SU(3) flavor breaking are incorporated, along with loop regularization and hadronic couplings. The main result is that rescattering dominates these decays and yields concrete branching fractions: D_s+ -> sigma0 a0+ around 1.0e-2, D+ -> sigma0 a0+ around 1.1e-3, D0 -> sigma0 a0^0 around 9e-6, and D_s+ -> f0 a0+ around 3.4e-4, with near-threshold suppression for the f0 a0+ channel. These findings indicate rescattering-induced D -> SS decays are experimentally accessible and provide insight into the nature of light scalar mesons and long-distance hadronic weak dynamics.

Abstract

We investigate two-body non-leptonic $D\to SS$ weak decays, where $S$ denotes a light scalar meson such as $a_0/a_0(980)$, $f_0/f_0(980)$, or $σ_0/f_0(500)$. Short-distance topologies from $W$-boson emission and annihilation (exchange) are found to be negligible, while long-distance final-state interactions provide the dominant contributions. In particular, triangle rescattering processes, $D \to πη^{(\prime)} \to σ_0 a_0$ and $D \to a_1(1260)η\to σ_0 a_0$, mediated by pion exchange in $πη^{(\prime)}$ and $a_1(1260)η$ scatterings, respectively, are identified as the leading mechanisms. Our calculations yield branching fractions ${\cal B}(D_s^+ \to σ_0 a_0^+) = (1.0 \pm 0.2^{+0.1}_{-0.2}) \times 10^{-2}$, ${\cal B}(D^+ \to σ_0 a_0^+) = (1.1 \pm 0.2^{+0.1}_{-0.2}) \times 10^{-3}$, and ${\cal B}(D^0 \to σ_0 a_0^0) = (0.9 \pm 0.2^{+0.2}_{-0.3}) \times 10^{-5}$. For the Cabibbo-allowed decay mode $D_s^+ \to f_0 a_0^+$, the near-threshold condition $m_{D_s}\simeq m_{f_0}+m_{a_0}$ limits the phase space, suppressing the branching fraction to $(3.4\pm0.3^{+0.4}_{-0.9})\times 10^{-4}$. These results highlight rescattering-induced $D\to SS$ decays as promising channels for experimental studies at BESIII, Belle(-II), and LHCb.

Figures (2)

• Figure 1: Triangle rescattering diagrams are considered, where (a,b) correspond to $D_s^+ \to (\pi^+\eta^{(\prime)}, a_1^+\eta) \to \sigma_0 a_0^+$ mediated by charged pion exchange, while (a,c) represent $D_s^+ \to (\pi^+\eta^{(\prime)}, K^+\bar{K}^0) \to f_0 a_0^+$ mediated by $\pi^+$ and $K^+(\bar{K}^0)$ exchanges, respectively.
• Figure 2: Triangle rescattering diagrams, where (a) and (b) illustrate the decays $D^{+(0)}\to (\pi^{+(0)}\eta,\pi^{+(0)}\eta^\prime)\to\sigma_0 a_0^{+(0)}$ and $D^{+(0)}\to a_1^{+(0)}\eta\to \sigma_0 a_0^{+(0)}$, respectively, mediated by pion exchange in the triangle loops.