Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters

TL;DR

This paper introduces a Wilsonian renormalization group method for the Lippmann-Schwinger equation with multiple cutoffs, deriving integro-differential equations and solving them perturbatively for low-energy nucleon-nucleon interactions.

Contribution

It presents a novel approach to handle multiple cutoff parameters in the Lippmann-Schwinger equation within the Wilsonian RG framework, with explicit perturbative solutions.

Findings

Derived integro-differential equations for cutoff-dependent potentials.

Obtained perturbative solutions for low-energy S-wave potentials.

Discussed implications for effective field theory in nucleon-nucleon scattering.

Abstract

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.