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

european physical journal. c, particles and fields

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