Whether new data on $D_s\to f_0(980)e^{+}{\nu }_e$ can be understood if $f_0(980)$ consists of only the conventional $q\bar{q}$ structure

Abstract

Only two isospin-singlet scalar mesons $f_0(600)$ ($\sigma$) and $f_0(980)$ exist below 1 GeV, so that it is natural to suppose that they are two energy eigenstates which are mixtures of $\frac{1}{\sqrt{2}}(u\bar{u}+d\bar{d})$ and $s\bar{s}$. Is this picture right? Generally, it is considered that $f_0(600)$ mainly consists of $\frac{1}{\sqrt{2}}(u\bar{u}+d\bar{d})$, if so, the dominant component of $f_0(980)$ should be $s\bar{s}$. The recent measurement of the CLEO collaboration on the branching ratio of $D_s\to f_0(980)e^{+}{\nu }_e$ provides an excellent opportunity to testify the structure of $f_0(980)$, namely whether the data can be understood as long as it consists of mainly the conventional $q\bar{q}$ structure. We calculate the form factors of $D_s\to f_0(980)$ in the light-front quark model (LFQM) and the corresponding branching ratio of the semileptonic decay. By fitting the data, we obtain the mixing angle $\varphi$. The obtained mixing angle shows that the $s\bar{s}$ component in $f_0(980)$ may not be dominant.

Comments: 13pages, 3 figures; some changes were made, references added. Accepted by PRD