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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 thefactorizable contribution in QCD facorization scheme but also thenonfactorizable hard spectator corrections in QCDF and pQCD approach. We getconsistent result with the experimental data of $B_s^0 \to J/\psi f_0(980)$ andpredict the branching ratio of $B_s^0 \to J/\psi \sigma$. We suggest two waysto determine $f_0-\sigma$ mixing angle $\theta$. Using the experimentalmeasured 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. Wesuggest another way to determine $f_0-\sigma$ mixing angle $\theta$ using bothof experimental measured decay branching ratios $B_s^0 \to J/\psi f_0(980)(\sigma)$ to avoid theoretical uncertainties.

Determination of $f_0-\sigma$ mixing angle through $B_s^0 \to J/\Psi~f_0(980)(\sigma)$ decays