The resultant parameters of effective theory

TL;DR

This paper systematically studies the formulation of effective field theories, focusing on constructing essential parameters for general scattering theories without high-spin massless particles, and classifies their combinations in renormalized S-matrix calculations.

Contribution

It introduces a detailed classification of Hamiltonian coupling constant combinations relevant for effective scattering theories without massless particles of spin greater than 1/2.

Findings

Classification of parameter combinations for renormalized S-matrix

Identification of essential parameters in effective theories

Framework applicable to theories without high-spin massless particles

Abstract

This is the 4-th paper in the series devoted to a systematic study of the problem of mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of essential parameters in the case of the most general effective scattering theory containing no massless particles with spin J > 1/2. We perform the detailed classification of combinations of the Hamiltonian coupling constants and select those which appear in the expressions for renormalized S-matrix elements at a given loop order.