Laplace's method for elastic scattering diagrams within multi-particle fields model

TL;DR

This paper applies Laplace's method to simplify complex multidimensional integrals in multi-particle fields models, enabling numerical calculation of elastic proton-proton scattering cross-sections and capturing key features of the scattering behavior.

Contribution

It introduces a novel application of Laplace's method to reduce multidimensional integrals in multi-particle fields models for elastic scattering analysis.

Findings

Successfully reduced multidimensional integrals to one- and two-dimensional forms.

Numerically calculated differential cross-section dσ/dt that qualitatively matches experimental features.

Demonstrated the method's effectiveness in modeling elastic scattering phenomena.

Abstract

We apply the multi-particle fields model to calculate the differential cross-section d{\sigma}/dt of elastic proton-proton scattering. This problem includes the calculation of multidimensional integrals arising from the loop Feynman diagrams. We demonstrated how these integrals can be reduced with Laplace's method to one- and two-dimensional integrals which can be calculated numerically. The obtained result qualitatively describe the minimum in differential cross-section dependency d{\sigma}/dt(t).