Analyticity, Unitarity and One-loop Graviton Corrections to Compton Scattering

TL;DR

This paper calculates one-loop graviton corrections to low-energy Compton scattering, confirming the Gerasimov-Drell-Hearn sum rule's validity and exploring high-energy effects like black hole production and string trajectories.

Contribution

It provides the first verification of the sum rule at one-loop level for graviton corrections and discusses high-energy phenomena affecting UV divergences.

Findings

One-loop graviton correction agrees with perturbative computations.

Sum rule remains valid at one-loop level, contrary to previous claims.

High-energy effects may soften UV divergences.

Abstract

We compute spin-flip cross section for graviton photoproduction on a spin-1/2 target of finite mass. Using this tree-level result, we find one-loop graviton correction to the spin-flip low-energy forward Compton scattering amplitude by using Gerasimov-Drell-Hearn sum rule. We show that this result agrees with the corresponding perturbative computations, implying the validity of the sum rule at one-loop level, contrary to the previous claims. We discuss possible effects from the black hole production and string Regge trajectory exchange at very high energies. These effects seem to soften the UV divergence present at one-loop graviton level. Finally, we discuss the relation of these observations with the models that involve extra dimensions.