Relativity constraints on the two-nucleon contact interaction

TL;DR

This paper develops a relativistically invariant contact Lagrangian for two-nucleon interactions at order Q^2, identifying necessary terms for Poincare covariance and implications for multi-nucleon systems.

Contribution

It constructs the most general relativistically invariant contact Lagrangian at order Q^2, including additional terms required for Poincare covariance beyond the non-relativistic limit.

Findings

Identifies a complete set of contact interaction terms at order Q^2.

Shows the necessity of additional Poincare-covariant terms for multi-nucleon systems.

Highlights the impact of these terms on EFT calculations of nuclear observables.

Abstract

We construct the most general, relativistically invariant, contact Lagrangian at order Q^2 in the power counting, Q denoting the low momentum scale. A complete, but non-minimal, set of (contact) interaction terms is identified, which upon non-relativistic reduction generate 2 leading independent operator combinations of order Q^0 and 7 sub-leading ones of order Q^2 - a result derived previously in the heavy-baryon formulation of effective field theories (EFT's). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, in order to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number A>2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.