QCD-Gravity double copy in Regge asymptotics: from $2\rightarrow n$ amplitudes to radiation in shockwave collisions

TL;DR

This paper explores the deep connections between QCD and gravity through the double copy framework, applying dispersive techniques to derive evolution equations and analyzing multi-particle production in shockwave collisions.

Contribution

It introduces a novel application of the double copy relation to Regge asymptotics, deriving gravitational analogs of QCD evolution equations and linking gluon and graviton shockwave propagators.

Findings

Derived the gravitational Lipatov equation from QCD methods.

Established double copy relations between gluon and graviton shockwave propagators.

Outlined extensions for multi-particle production in gravitational shockwave collisions.

Abstract

These lectures discuss multi-particle production in QCD and in gravity at ultrarelativistic energies, their double copy relations, and strong parallels in emergent shockwave dynamics. Dispersive techniques are applied to derive the BFKL equation for multi-gluon production in Regge asymptotics. Identical methods apply in gravity and are captured by a gravitational Lipatov equation. The building blocks in both cases are Lipatov vertices and reggeized propagators satisfying double copy relations; in gravity, Weinberg's soft theorem is recovered as a limit of the Lipatov framework. BFKL evolution in QCD generates wee parton states of maximal occupancy characterized by an emergent semi-hard saturation scale. Renormalization group equations in the Color Glass Condensate (CGC) EFT describe wee parton correlations and their rapidity evolution. A shockwave picture of deeply inelastic scattering and hadron-hadron collisions follows, with multi-particle production described by Cutkosky's rules in strong time-dependent fields. Gluon radiation in the CGC EFT has a double copy in gravitational shockwave collisions, with a similar correspondence applicable between gluon and graviton shockwave propagators. Possible extensions of this semi-classical double copy are outlined for computing multi-particle production in gravitational shockwave collisions, self-force and tidal contributions, and classical and quantum noise in the focusing of geodesics.