Rescattering-induced $D\to SS$ weak decays

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 ${\sigma }_0/f_0(500)$. 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 $\mathcal{B}(D_s^{+}\to {\sigma }_0{a}_0^{+})=(1.0\pm 0.2_{-0.2}^{+0.1})\times 10^{-2}$, $\mathcal{B}(D^{+}\to {\sigma }_0{a}_0^{+})=(1.1\pm 0.2_{-0.2}^{+0.1})\times 10^{-3}$, and $\mathcal{B}(D^0\to {\sigma }_0{a}_0^0)=(0.9\pm 0.2_{-0.3}^{+0.2})\times 10^{-5}$. 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 $(3.4\pm 0.3_{-0.9}^{+0.4})\times 10^{-4}$. These results highlight rescattering-induced $D\to SS$ decays as promising channels for experimental studies at BESIII, Belle(-II), and LHCb.

13 pages, 2 figures, 2 tables, published edition

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