# The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

## TL;DR

This paper investigates high-energy scalar particle scattering within an effective quantum gravity framework, developing a systematic method to compute leading and correction eikonal amplitudes using modified perturbation theory and one-loop approximation.

## Contribution

It introduces a novel systematic approach to calculate scattering amplitudes and their corrections in quantum gravity using quasi-potential equations and modified perturbation theory.

## Key findings

- Derived leading eikonal scattering amplitudes.
- Calculated first non-leading corrections.
- Established relations between operator and functional solutions.

## Abstract

The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.