I have the following equation for which I am looking to describe its analytic structure:
$$ \int_{0}^{1} dx [m^{2} - x(1-x)p^{2}]^{\epsilon} $$
where $p^{2} > 0, m^{2} > 0,$ and $|\epsilon| < 1 $. $p^{2}$ is in the complex space. What does the procedure look like to determine any branch cuts or poles for this function? Since $|\epsilon| < 1$ this implies that there will be a branch cut, but I am unfamiliar with how to interpret this for arbitrary values of $|\epsilon| < 1$.
Thanks in advance!