A Consistency Test of EFT Power Countings from Residual Cutoff Dependence

Understand

A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented.

• The Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the breakdown scale of an EFT, on the low-momentum scales, and on the order of the calculation.
• Passing this test is a necessary but not sufficient consistency criterion for a suggested power counting whose exact nature is disputed.
• In Chiral Effective Field Theory (ChiEFT) with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the convergence pattern in results.