Distinguishing two kinds of scalar mesons from heavy meson decays

Abstract

In the SU(3) symmetry limit, semileptonic $D^{+}\to S{l}^{+}\nu$ and $B^{-}\to S{l}^{-}\bar{\nu }$ decays, with $S=a_0(980)$, $f_0(980)$ and $f_0(600)$, are found to obey different sum rules in the $\bar{q}q$ 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 ${\bar{B}}^0\to J/\psi ({\eta }_c)S$ 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 $D^{+}\to S{l}^{+}\nu$, $B^{-}\to S{l}^{-}\bar{\nu }$ and ${\bar{B}}^0\to J/\psi ({\eta }_c)S$ 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.

Comments: 9 pages, 3 eps figures, published version