Is there a way to define the following multivalued function as a single valued function where the branch cuts are taken to be $z =x+iy \in \{(x,y):|x|<a, \hspace{3mm}y = i\pi n \}$ and $n$ an integer:
\begin{align} f(z) = \ln \left[ \frac{\cosh z + \sqrt{\cosh^2z - \cosh^2a}}{e^z \cosh a} \right] \end{align}