Rescattering corrections and self-consistent metric in Planckian scattering

TL;DR

This paper extends the ACV approach to transplanckian scattering by developing a self-consistent metric that includes rescattering corrections, allowing for large-angle scattering and UV-safe solutions with calculable trajectory shifts and delays.

Contribution

It introduces a refined reduced-action model with an improved eikonal representation that describes large-angle scattering and incorporates UV-safe rescattering solutions into the metric.

Findings

Rescattering solutions are UV-safe and regular.

Particles experience calculable trajectory shifts and time delays.

The model describes scattering up to order R^2/b^2 in the expansion.

Abstract

Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles' motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles' shock-waves undergo calculable trajectory shifts and time delays during the scattering process --- which turns out to be consistently described by both action and metric, up to relative order $R^2/b^2$ in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutions --- not fully investigated here --- are also presented.