Smoothness of Classical Limit in KMOC Formalism

In this paper, we revisit the smoothness of the classical limit of inclusive observables in the formalism developed by Kosower, Maybee and O’Connell (KMOC). Building on the earlier work [1-3], we prove that the classical limit of three classes of inclusive observables, namely scattering angle, radiative field and angular impulse is smooth and does not suffer from any so-called super-classical divergences at all orders in perturbation. Our analysis goes some way in showing that KMOC formalism can be used to compute classical radiation by simply focusing on all the terms that scale as ${\mathrm{\hslash }}^0$ as all the terms that scale with inverse power of $\mathrm{\hslash }$ vanish.