Assessing Theory Uncertainties in EFT Power Countings from Residual Cutoff Dependence

Abstract

I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable predicts the functional form of its residual cutoff dependence on the EFT breakdown scale, low-momentum scales, and 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. For example, in ChiEFT with more than one nucleon, a lack of universally accepted analytic solutions obfuscates the relation between convergence pattern and numerical results, and led to proposals which predict different numbers of Low Energy Coefficients at the same chiral order. The method may provide an independent check whether an observable is renormalised at a given order, and of both the breakdown scale and the momentum-dependent order-by-order convergence pattern of an EFT. Conversely, it may help identify LECs which produce renormalised observables at a given order. I also discuss its underlying assumptions and relation to the RG Equation; useful choices for observables and cutoffs; the momentum window in which the test provides best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting Low Energy Coefficients to data in different or the same channel; caveats and limitations. Since the test is designed to minimise the use of data, it allows one to quantitatively falsify if the EFT has been renormalised consistently, rather than quantifying how an EFT compares to experiment. Its application in particular to the 3P0 and 3P2-3F2 partial waves of NN scattering in ChiEFT may elucidate persistent power-counting issues. Details and a better bibliography can be found in an upcoming publication.