Causality bounds for neutron-proton scattering

TL;DR

This paper establishes causality and unitarity constraints on low-energy neutron-proton interactions, deriving bounds on interaction ranges and implications for effective field theories and many-body systems.

Contribution

It introduces a general theorem showing zero-range interactions cannot reproduce non-zero partial-wave mixing without violating fundamental principles.

Findings

Interaction length scales can be as large as 5 fm.

Causality bounds influence momentum cutoff choices in EFT.

Large length scales impact universality in Fermi systems.

Abstract

We consider the constraints of causality and unitarity for the low-energy interactions of protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We define and calculate interaction length scales which we call the causal range and the Cauchy-Schwarz range for all spin channels up to J = 3. For some channels we find that these length scales are as large as 5 fm. We investigate the origin of these large lengths and discuss their significance for the choice of momentum cutoff scales in effective field theory and universality in many-body Fermi systems.