Rescattering-induced $$D\rightarrow SS$$ weak decays

Abstract We investigate two-body non-leptonic $$D\rightarrow SS$$ D → S S weak decays, where S denotes a light scalar meson such as $$a_0/a_0(980),$$ a 0 / a 0 ( 980 ) , $$f_0/f_0(980),$$ f 0 / f 0 ( 980 ) , or $$\sigma _0/f_0(500).$$ 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, $$D \rightarrow \pi \eta ^{(\prime )} \rightarrow \sigma _0 a_0$$ D → π η ( ′ ) → σ 0 a 0 and $$D \rightarrow a_1(1260)\eta \rightarrow \sigma _0 a_0,$$ D → a 1 ( 1260 ) η → σ 0 a 0 , mediated by pion exchange in $$\pi \eta ^{(\prime )}$$ π η ( ′ ) and $$a_1(1260)\eta $$ a 1 ( 1260 ) η scatterings, respectively, are identified as the leading mechanisms. Our calculations yield branching fractions $${\mathcal {B}}(D_s^+ \rightarrow \sigma _0 a_0^+) = (1.0 \pm 0.2^{+0.1}_{-0.2}) \times 10^{-2},$$ B ( D