Rescattering-induced $D\to SS$ weak decays

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 $\sigma_0/f_0(500)$. 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, $D \to \pi\eta^{(\prime)} \to \sigma_0 a_0$ and $D \to a_1(1260)\eta \to \sigma_0 a_0$, mediated by pion exchange in $\pi\eta^{(\prime)}$ and $a_1(1260)\eta$ scatterings, respectively, are identified as the leading mechanisms. Our calculations yield branching fractions ${\cal B}(D_s^+ \to \sigma_0 a_0^+) = (1.0 \pm 0.2^{+0.1}_{-0.2}) \times 10^{-2}$, ${\cal B}(D^+ \to \sigma_0 a_0^+) = (1.1 \pm 0.2^{+0.1}_{-0.2}) \times 10^{-3}$, and ${\cal B}(D^0 \to \sigma_0 a_0^0) = (0.9 \pm 0.2^{+0.2}_{-0.3}) \times 10^{-5}$. 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.