Thermomagnetic renormalons in a scalar self-interacting $\lambda \phi^4$ theory

TL;DR

This paper investigates how temperature and weak magnetic fields influence the residues of renormalons in a scalar  theory, revealing opposite effects on their values without changing their pole locations.

Contribution

It extends previous work by including temperature effects in the analysis of thermomagnetic renormalons in a scalar  theory, focusing on residue behavior.

Findings

Residue dependence on temperature and magnetic field is opposite.

Pole locations in the Borel plane remain unchanged.

Detailed technical analysis of residue evolution.

Abstract

In this article we extend a previous discussion about the influence of an external magnetic field on renormalons in a self interacting scalar theory by including now temperature effects, in the imaginary formalism, together with an external weak external magnetic field. We show that the location of poles in the Borel plane does not change, getting their residues, however, a dependence on temperature and on the magnetic field.The effects of temperature and the magnetic field strength on the residues turn out to be opposite. We present a detailed discussion about the evolution of these residues, showing technical details involved in the calculation.