  We study $B_s^0 \to J/\psi f_0(980)$ decays, the quark content of $f_0(980)$
and the mixing angle of $f_0(980)$ and $\sigma(600)$. We calculate not only the
factorizable contribution in QCD facorization scheme but also the
nonfactorizable hard spectator corrections in QCDF and pQCD approach. We get
consistent result with the experimental data of $B_s^0 \to J/\psi f_0(980)$ and
predict the branching ratio of $B_s^0 \to J/\psi \sigma$. We suggest two ways
to determine $f_0-\sigma$ mixing angle $\theta$. Using the experimental
measured branching ratio of $B_s^0 \to J/\psi f_0(980) $, we can get the
$f_0-\sigma$ mixing angle $\theta$ with some theoretical uncertainties. We
suggest another way to determine $f_0-\sigma$ mixing angle $\theta$ using both
of experimental measured decay branching ratios $B_s^0 \to J/\psi f_0(980)
(\sigma)$ to avoid theoretical uncertainties.
