Magnetic renormalons in a scalar self-interacting λϕ4 theory

M Correa,M Loewe,R Zamora,D Valenzuela

doi:10.1103/physrevd.99.096024

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.

Highlights

Since the paper by Dyson [1] on the convergence of perturbative series in QED, a seminal article based exclusively on physical arguments, we have learned that power series expansions in quantum field theory, in general, are divergent objects
For weak magnetic field region, using an appropriate expansion for the Schwinger propagators, we find renormalons as poles on the real axis of the Borel plane, of which the position do not depend on the magnetic field, but where the residues acquire a magnetic dependence
We have analyzed the effects of an external constant magnetic field on a typical renormalon-type diagram in the λφ4 theory, using a weak field approximation for the Schwinger propagator

Summary

INTRODUCTION

Since the paper by Dyson [1] on the convergence of perturbative series in QED, a seminal article based exclusively on physical arguments, we have learned that power series expansions in quantum field theory, in general, are divergent objects. In peripheral heavy ion collisions, huge magnetic fields appear [10]. We analyze, in the frame of a self-interacting scalar λφ theory, the influence of the magnetic field on the position of the UV renormalons and their residues in the Borel plane. For this purpose, we will use the weak field expansion for a bosonic Schwinger propagator [11].

MAGNETIC RENORMALON-TYPE CORRECTION TO THE PROPAGATOR

BOREL TRANSFORM

RENORMALONS IN THE VACUUM

MAGNETIC RENORMALONS

CONCLUSIONS