# Complete set of essential parameters of an effective theory

## TL;DR

This paper identifies the complete set of essential parameters in an effective scalar field theory, distinguishing them from redundant ones, to facilitate proper renormalization and theoretical consistency.

## Contribution

It systematically determines the full set of essential coupling constants in effective scalar theories, clarifying which parameters are necessary for renormalization.

## Key findings

- Distinguished essential from redundant parameters in effective theories
- Provided a method to select parameters relevant for renormalization
- Focused on scalar field theories with arbitrary high-dimensional operators

## Abstract

The present paper continues the series [V. V. Vereshagin, True self-energy function and reducibility in effective scalar theories, Phys. Rev. D 89, 125022 (2014); A. Vereshagin and V. Vereshagin, Resultant parameters of effective theory, Phys. Rev. D 69, 025002 (2004); K. Semenov-Tian-Shansky, A. Vereshagin, and V. Vereshagin, S-matrix renormalization in effective theories, Phys. Rev. D 73, 025020 (2006)] devoted to the systematic study of effective scattering theories. We consider matrix elements of the effective Lagrangian monomials (in the interaction picture) of arbitrary high dimension D and show that the full set of corresponding coupling constants contains parameters of both kinds: essential and redundant. Since it would be pointless to formulate renormalization prescriptions for redundant parameters, it is necessary to select the full set of the essential ones. This is done in the present paper for the case of the single scalar field.