Abstract:

A remarkable double-copy relation of Einstein gravity to QCD in Regge asymptotics is Ξ“πœ‡β’πœˆ=1/2πΆπœ‡β’πΆπœˆβˆ’1/2β’π‘πœ‡β’π‘πœˆ, where Ξ“πœ‡β’πœˆ is the gravitational Lipatov vertex in the 2β†’3 graviton scattering amplitude, πΆπœ‡ its Yang-Mills counterpart, and π‘πœ‡ the QED bremsstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing the 2→𝑁 scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2D effective field theory framework describing trans-Planckian 2→𝑁 graviton scattering. We construct a quantitative correspondence between a semiclassical 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 𝑅𝑆,𝐿, 𝑅𝑆,𝐻β‰ͺ𝑏, where 𝑅𝑆,𝐿, 𝑅𝑆,𝐻 are 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 the 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.

H. Raj, R. Venugopalan, β€žUniversal features of 2 β†’ N scattering in QCD and gravity from shockwave collisionsβ€œ, Phys. Rev. D 109, 044064 (2024).

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.109.044064

Related to Project C05, Co6