# Magnetic renormalons in a scalar self interacting $\lambda \phi^{4}$ theory

## TL;DR

This paper investigates how external magnetic fields affect renormalons in a scalar $bb$ theory, revealing new magnetic-dependent residues at weak fields and their disappearance at strong fields, with comparisons to thermal effects.

## Contribution

It introduces the analysis of magnetic field effects on renormalons in $bb$ theory, highlighting the emergence and disappearance of poles under different magnetic regimes.

## Key findings

- New renormalons appear as poles with magnetic-dependent residues at weak fields.
- In the strong magnetic limit, these new poles vanish in the lowest Landau level approximation.
- The magnetic effects on renormalons are compared with thermal effects from previous studies.

## Abstract

We present an analysis about the influence of an external magnetic field on renormalons in a self interacting theory $\lambda \phi ^{4}$. In the weak magnetic field region, using an appropriate expansion for the Schwinger propagator's, we find new renormalons as poles on the real axis of the Borel plane, whose position do not depend on the magnetic field, but where the residues acquire in fact a magnetic dependence. In the strong magnetic limit, working in the lowest Landau level approximation (LLLA), these new poles are not longer present. We compare the magnetic scenario with previous results in the literature concerning thermal effects on renormalons in this theory.