Distinguishing two kinds of scalar mesons from heavy meson decays

In the SU(3) symmetry limit, semileptonic $D^+\to Sl^+ν$ and $B^-\to Sl^-\barν$ decays, with $S=a_0(980)$, $f_0(980)$ and $f_0(600)$, are found to obey different sum rules in the $\bar qq$ and the tetra-quark descriptions for scalar mesons. Thus these sum rules can distinguish the two scenarios for light scalar mesons model-independently. This method also applies to the $\bar B^0\to J/ψ(η_c) S$ decays. Two kinds of SU(3) symmetry breaking effects are found to be under control, which will not spoil our method. The branching fractions of the $D^+\to Sl^+ν$, $B^-\to Sl^-\barν$ and $\bar B^0\to J/ψ(η_c) S$ decays roughly have the order $10^{-4}$, $10^{-5}$ and $10^{-6}$, respectively. The ongoing BES-III and the forthcoming Super B experiments are able to measure these channels and accordingly to provide detailed information of the scalar meson inner structure.

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