Distinguishing two kinds of scalar mesons from heavy meson decays

TL;DR

This paper proposes a model-independent method using sum rules in heavy meson decays to distinguish between two scalar meson structures, with potential for experimental verification at BES-III and Super B.

Contribution

It introduces a novel sum rule approach to differentiate scalar meson models in heavy meson decays, applicable across various decay channels and robust against symmetry-breaking effects.

Findings

Sum rules differ for $ar qq$ and tetra-quark models in semileptonic decays.

Branching fractions are estimated as $10^{-4}$, $10^{-5}$, and $10^{-6}$ for different decay modes.

Method is experimentally feasible with current and upcoming facilities.

Abstract

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