Subleading contributions to the three-nucleon contact interaction

TL;DR

This paper derives a minimal, symmetry-constrained form of the three-nucleon contact interaction with two derivatives, providing a local potential in configuration space and identifying key operators for four-nucleon interactions.

Contribution

It introduces a minimal, symmetry-consistent formulation of the three-nucleon contact interaction with derivatives, and clarifies the structure of four-nucleon contact operators.

Findings

Derived a local three-nucleon potential with 13 low-energy constants.

Identified only one independent operator for leading four-nucleon contact interaction.

Provided a symmetry-constrained minimal Lagrangian form.

Abstract

We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities and Poincare' covariance. The resulting interaction, depending on 13 unknown low-energy constants, leads to a three-nucleon potential which we give in a local form in configuration space. We also consider the leading (no-derivative) four-nucleon interaction and show that there exists only one independent operator.