Comments on the Quark Content of the Scalar Meson $f_0(1370)$

Abstract

Based on the measurements of $(D_s^{+},D^{+})\to f_0(1370){\pi }^{+}$ 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 $D_s^{+}\to f_0(1370){\pi }^{+}$. On the other hand, the $s\bar{s}$ component of $f_0(1370)$ should be small enough to avoid excessive $D_s^{+}\to f_0(1370){\pi }^{+}$ induced from the external $W$-emission. Measurement of $f_0(1370)$ production in the decay $D_s^{+}\to K^{+}{K}^{-}{\pi }^{+}$ 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 $D^0\to f_0(1370){\bar{K}}^0\to {\pi }^{+}{\pi }^{-}{\bar{K}}^0$.

Comments: 12 pages, 2 figures