Universal features of $ 2\to N$ scattering in QCD and gravity from shockwave collisions

Abstract

A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is $\Gamma^{\mu\nu}= \frac12C^\mu C^\nu- \frac12N^\mu N^\nu$, where $\Gamma^{\mu\nu}$ is the gravitational Lipatov vertex in the $2\to 3$ graviton scattering amplitude, $C^\mu$ its Yang-Mills counterpart, and $N^\mu$ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing $2\to N$ 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 $2\to N$ 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 $R_{S,L}$, $R_{S,H}$ $ \ll 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 $2\rightarrow N$ amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering.