Straight-line particle path approximation for high-energy hadron scattering in quantum field theory

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

“…As a result we have the eikonal representation of elastic scattering amplitude with eikonal phase function χ 0 (|r ⊥ |, s) in Eq. (31). It is important note that the nonlocal potential differs from the local by terms of order O 1 p in the high energy limit p → ∞.…”

“…Use this exact form of the Yukawa as a quasi-potential and replace into Eqs. (29) and (30), for the leading eikonal amplitude and its first correction, we get (see Appendix C)…”

“…When substituting the Newtonian potential (40) into Eqs. (29) and (30), the vertex factor for graviton exchange between "nucleons" should be added by V Newton with sV Newton [21,62], the definition of the non-relativistic potential (see Eq. (D.7) in Appendix D) and graviton still has a mass μ and perform some calculations for the leading eikonal behavior and the first correction of the scattering amplitude (see Eqs.…”

“…An approach that has probed the first of these features with some success is the one that based on the reggeized string exchange amplitudes with subsequent reduction to the gravitational eikonal limit including the leading order corrections [18]. In articles [19][20][21] the high energy scattering amplitude of two "nucleons" in the quantum gravity is constructed by extending the functional integration method [22][23][24][25][26][27][28] which has been used effectively in quantum electrodynamics [29][30][31][32][33][34][35][36][37][38]. A straightline path approximation was used to calculate the functional integrals which occur.…”