Residual Cut-Off Dependence and Power Counting: The Deuteron as a Case Study Knowns, Unknowns and Known Unknowns About Regulator Dependence

Effective field theories (EFTs) require regularization and renormalization to gain predictive power. While regularization is inconsequential from the point of view of the observable predictions of EFT-in a renormalized theory predictions are regulator-independent once the cutoff is removed-the particular details of regulator dependence might provide interesting insights into the inner workings of an EFT. In fact, the analysis of regulator dependence has been frequently suggested as a tool to study the ordering scheme or power counting of EFTs. We show here the quantitative differences betweeen inferred residual cutoff dependence from different regulators, thereby showing that cutoff variations might provide limited information about uncertainties and power counting (at least in practical settings).