Thermal Renormalons in Scalar Field Theory

TL;DR

This paper investigates how thermal effects influence renormalon singularities in scalar  theory, revealing temperature-dependent residues while pole positions stay fixed, using Thermofield Dynamics.

Contribution

It demonstrates the temperature dependence of residues of thermal renormalons in scalar  theory through a specific diagram analysis.

Findings

Residues of renormalon poles depend on temperature.

Pole positions remain unchanged with temperature.

Thermofield Dynamics effectively analyzes thermal renormalons.

Abstract

In the frame of the scalar theory $g \phi ^{4}$, we explore the occurrence of thermal renormalons, i. e. temperature dependent singularities in the Borel plane. The discussion of a particular renormalon type diagram at finite temperature, using Thermofield Dynamics, allows us to establish that these singularities actually get a temperature dependence. This dependence appears in the residues of the poles, remaining their positions unchanged with temperature.