Universal features of 2→ N scattering in QCD and gravity from shockwave collisions

A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is Γ^μν= 1/2C^μ C^ν- 1/2N^μ N^ν, where Γ^μν is the gravitational Lipatov vertex in the 2→ 3 graviton scattering amplitude, C^μ its Yang-Mills counterpart, and N^μ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing 2→ N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian 2→ N graviton scattering. We construct a quantitative correspondence between a semi-classical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to R_S,L, R_S,H ≪ b, with R_S,L, R_S,H the respective emergent Schwarzchild radii generated in shockwave collisions and b is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2→ N amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering.