Renormalization of One Meson Exchange Potentials and Their Currents

TL;DR

This paper investigates the renormalization of one meson exchange potentials and currents in nucleon-nucleon interactions, demonstrating that appropriate boundary conditions lead to results largely independent of nucleon substructure and meson details, simplifying calculations while maintaining gauge invariance.

Contribution

It introduces a renormalization scheme for meson exchange potentials that reduces sensitivity to nucleon substructure and meson details, simplifying calculations and preserving gauge invariance.

Findings

Phase shifts and deuteron properties are insensitive to nucleon substructure.

The scheme achieves good agreement with low energy data.

Gauge invariance is maintained throughout the renormalization process.

Abstract

The Nucleon-Nucleon One Meson Exchange Potential, its wave functions and related Meson Exchange Currents are analyzed for point-like nucleons. The leading Nc contributions generate a local and energy independent potential which presents 1/r^3 singularities, requiring renormalization. We show how invoking suitable boundary conditions, neutron-proton phase shifts and deuteron properties become largely insensitive to the nucleon substructure and to the vector mesons. Actually, reasonable agreement with low energy data for realistic values of the coupling constants (e.g. SU(3) values) is found. The analysis along similar lines for the Meson Exchange Currents suggests that this renormalization scheme implies tremendous simplifications while complying with exact gauge invariance at any stage of the calculation.