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$\bar{B}_s \to f_0(980)$ form factors and the width effect from light-cone sum rules

In this paper we calculate the $\bar{B}_s \to f_0(980)$ form factors from light-cone sum rules with $B$ meson DAs. With adopting the quark-antiquark configuration of light scalar mesons,the high twist two-particle and the three-particle contributions are found to be $\sim 25\%$ individual, and totally they give about $50\%$ correction to certain form factors in the considered energy regions. We further explore the light-cone sum rules approach to study the $S-$wave $\bar{B}_s \to KK$ form factors,the $f_0+f'_0+f''_0$ resonance model is proposed and the result shows that the background effect from $f'_0+f''_0$ accounts $\sim 5\%$. As a by-product, we extract the strong coupling $|g_{f_0 KK }| = 1.08^{+0.05}_{-0.14}$ GeV with taking the $\bar{B}_s \to f_0(980)$ form factors calculated previous under the narrow width approximation.