Epsilon dichotomy via root numbers of intertwining periods

We give a new proof of the epsilon dichotomy conjecture, stated by Prasad and Takloo-Bighash, for non Archimedean local fields of characteristic zero, when the twisting character is trivial. Our method relies on the functional equation and the analytic properties of intertwining periods, instead of trace formula and type theory. It removes the odd residual characteristic restriction in the previous proof, coming from type theory.