A new resummation scheme in scalar field theories

TL;DR

This paper introduces a novel resummation scheme for scalar field theories that combines parquet techniques and flow equations, improving approximation accuracy and ensuring renormalizability for numerical analysis.

Contribution

It proposes a hierarchical resummation method that enhances Bethe--Salpeter kernel approximations and integrates flow equations for a self-consistent, renormalizable framework.

Findings

Enhanced accuracy of Bethe--Salpeter kernel approximations

Achieved renormalization within the resummation scheme

Developed a self-consistent system for propagator and kernel calculations

Abstract

A new resummation scheme in scalar field theories is proposed by combining parquet resummation techniques and flow equations, which is characterized by a hierarchy structure of the Bethe--Salpeter (BS) equations. The new resummation scheme greatly improves on the approximations for the BS kernel. Resummation of the BS kernel in the $t$ and $u$ channels to infinite order is equivalent to truncate the effective action to infinite order. Our approximation approaches ensure that the theory can be renormalized, which is very important for numerical calculations. Two-point function can also be obtained from the four-point one through flow evolution equations resulting from the functional renormalization group. BS equations of different hierarchies and the flow evolution equation for the propagator constitute a closed self-consistent system, which can be solved completely.