Eikonal Particle Scattering and Dilaton Gravity

TL;DR

This paper investigates light charged particles modeled as dilatonic black holes in high-energy scattering, revealing pathologies linked to singularities and exploring effective theories and amplitude calculations in dilaton gravity.

Contribution

It identifies issues in Planckian scattering with nonextremal dilatonic black holes and develops an eikonal amplitude framework incorporating graviton, dilaton, and photon exchanges.

Findings

Pathologies in scattering due to curvature singularities.

Decoupling of electromagnetic and gravitational effects in the eikonal amplitude.

Effective resummation of ladder diagrams yields the scattering amplitude.

Abstract

Approximating light charged point-like particles in terms of (nonextremal) dilatonic black holes is shown to lead to certain pathologies in Planckian scattering in the eikonal approximation, which are traced to the presence of a (naked) curvature singularity in the metric of these black holes. The existence of such pathologies is confirmed by analyzing the problem in an `external metric' formulation where an ultrarelativistic point particle scatters off a dilatonic black hole geometry at large impact parameters. The maladies disappear almost trivially upon imposing the extremal limit. Attempts to derive an effective three dimensional `boundary' field theory in the eikonal limit are stymied by four dimensional (bulk) terms proportional to the light-cone derivatives of the dilaton field, leading to nontrivial mixing of electromagnetic and gravitational effects, in contrast to the case of general relativity. An eikonal scattering amplitude, showing decoupling of these effects, is shown to be derivable by resummation of graviton, dilaton and photon exchange ladder diagrams in a linearized version of the theory, for an asymptotic value of the dilaton field which makes the string coupling constant non-perturbative.