For the integrand function $$\frac{e^{-A\sqrt{s}}}{(\sqrt{s}+B)(s-C)\sqrt{s+\theta_c}}$$, I defined the integral path as in the picture. Is it correct? There are two discontinuity points between $\gamma_4$ and $\gamma_5$, $\gamma_7$ and $\gamma_8$ with respect to the argument. I think the paths (branch cuts) for $\sqrt{s}$ and $\sqrt{s-\theta_c}$ are distinguished and can not be unified into one.
