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

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).

Comments: v2: Revised, 31 pages, 8 figures, in English and Ukrainian; v3: substantially revised, 15 pages, 8 figures, in English only