The classical two-loop amplitude at leading logarithmic accuracy for graviton emission in multi-Regge kinematics

Abstract

Using the gravitational shockwave formalism, we compute the classical part of the $\mathcal{O}(G^{7/2})$ five-point amplitude at leading logarithmic accuracy describing the emission of a graviton in the collision of two massless scalars in multi-Regge kinematics (MRK). The result splits into a two-particle reducible term and a three-particle reducible one, the latter being the radiative counterpart of the $H$-diagram with the emission taken in MRK limit. The same amplitude can be equivalently calculated as the ultrarelativistic limit of the corresponding massive amplitude by applying the optical theorem according to the conjectured universality of the leading logarithmic amplitudes in classical gravity.