True self energy function and reducibility in effective scalar theories. (Revised)

TL;DR

This paper clarifies the structure of the true self-energy function in effective scalar theories, showing how it is determined by minimal coupling constants and simplifying the renormalization process for multi-leg graphs.

Contribution

It introduces a revised, clearer formulation of the self-energy function and its renormalization in effective scalar theories, correcting previous ambiguities and typos.

Findings

The true self-energy is fixed by minimal coupling constants.

Higher-leg graphs receive finite corrections.

No renormalization prescriptions are needed for higher derivatives on-shell.

Abstract

This is the revised version of Sect. I - IV of the paper https://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. The thing is that in https://doi.org/10.1103/PhysRevD.89.125022 the text was insufficiently clear and, in addition, it contained (through my fault) a few typos. This is the reason why I decided to offer a revised version. Original abstract: This is the eighth paper in the series devoted to the systematic study of effective theories. Below, I discuss the renormalization of the one-loop two-leg functions in multicomponent effective scalar theory. It is shown that only a part of numerous contributions that appear in the general expression for a two-leg graph can be considered as the true self-energy function. This part is completely fixed by the values of minimal coupling constants; it is the only one that should be taken into account in the conventional process of the summation of Dyson's chain that results in explicit expression for the full propagator. The other parts provide the well-defined finite corrections for the graphs with the number of legs n > 2. It is also shown that there is no need to attract the renormalization prescriptions for the higher derivatives of the two-leg function on the mass shell; the requirements of finiteness and diagonability turn out to be quite sufficient.