Causality and the effective range expansion
H.-W. Hammer, Dean Lee
TL;DR
This paper generalizes causality bounds and effective range formulas to any dimension and angular momentum, exploring their implications for low-energy scattering and universality, with detailed derivations and examples.
Contribution
It extends Wigner's causality bounds and Bethe's formulas to arbitrary dimensions and angular momenta, providing comprehensive derivations and examples.
Findings
Generalized causality bounds for arbitrary dimensions and angular momentum
Derived integral formulas for the effective range parameter
Discussed implications for low-energy scattering universality
Abstract
We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.
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