Comments on the Quark Content of the Scalar Meson $f_0(1370)$
Abstract
Description
Based on the measurements of $(D_s^+,D^+)\to f_0(1370)π^+$ we determine, in a model independent way, the allowed $s\bar s$ content in the scalar meson $f_0(1370)$. We find that, on the one hand, if this isoscalar resonance is a pure $n\bar n$ state [ $n\bar n\equiv(u\bar u+d\bar d)/\sqrt{2} ]$, a very large $W$-annihilation term will be needed to accommodate $D_s^+\to f_0(1370)π^+$. On the other hand, the $s\bar s$ component of $f_0(1370)$ should be small enough to avoid excessive $D_s^+\to f_0(1370)π^+$ induced from the external $W$-emission. Measurement of $f_0(1370)$ production in the decay $D_s^+\to K^+K^-π^+$ will be useful to test the above picture. For the decay $D^0\to f_0(1370)\bar K^0$ which is kinematically barely or even not allowed, depending on the mass of $f_0(1370)$, we find that the finite width effect of $f_0(1370)$ plays a crucial role on the resonant three-body decay $D^0\to f_0(1370)\bar K^0\toπ^+π^-\bar K^0$.
12 pages, 2 figures
12 pages, 2 figures