Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature

TL;DR

This paper provides explicit analytic expressions for the evolution of renormalon residues in a scalar  theory under thermal, thermomagnetic, and thermoelectric effects across all temperature ranges, without approximations.

Contribution

It introduces a unified analytic approach to study renormalons in scalar theories with external fields at any temperature, extending previous low/high temperature analyses.

Findings

Residues depend on temperature and external fields.

Pole locations in the Borel plane remain unchanged.

Analytic expressions are valid for all temperature ranges.

Abstract

In this article we revisit the discussion of renormalons in the frame of a scalar self-interacting $\lambda \phi^{4}$ theory in the presence of thermomagnetic effects, i.e magnetic and thermal effects. Our results for the evolution of the residues is now given by an explicit analytic expression, valid for all values of temperature, without the necessity of separating the discussion in a low- and a high temperature region analyses. We carry out the same discussion for the case of an external constant electric field, obtaining also in this case an analytic expression for the whole range o temperature. In both cases, the location of the poles in the Borel plane does not change with respect to the vacuum case. Their residues, however, acquire a dependence on temperature and the external field. Results are presented for the evolution of residues in the thermomagnetic and thermoelectric cases. We show a comparison with our previous results in the thermomagnetic case, presenting also in detail the mathematical techniques needed for our analytic expressions to be valid in the whole range of temperature.