Eur. Phys. J. A (2020) 56: 118
https://doi.org/10.1140/epja/s10050-020-00129-5

Regular Article –Theoretical Physics

A consistency test of EFT power countings from residual cutoff dependence

¹ Department of Physics, Institute for Nuclear Studies, George Washington University, Washington, DC, 20052, USA
² Department of Physics, Duke University, Box 90305, Durham, NC, 27708, USA

^* e-mail: hgrie@gwu.edu

Received: 3 November 2019
Accepted: 23 March 2020
Published online: 21 April 2020

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 breakdown scale of an Effective Field Theory (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. For example, in Chiral Effective Field Theory () 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 (LECs) at the same chiral order, and at times even predicts a different ordering long-range contributions. The method may provide an independent check whether an observable is properly renormalised at a given order, and allows one to estimate both the breakdown scale and the momentum-dependent order-by-order convergence pattern of an EFT. Conversely, it may help identify those LECs (and long-range pieces) which produce renormalised observables at a given order. I also discuss its underlying assumptions and relation to the Wilsonian Renormalisation Group Equation; useful choices for observables and cutoffs; the momentum window in which the test likely provides best signals; its dependence on the values and forms of cutoffs as well as on the EFT parameters; the impact of fitting LECs to data in different or the same channel; and caveats as well as 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. This complements other tests which quantify how an EFT compares to experiment. Its application in particular to the and – partial waves of scattering in may elucidate persistent power-counting issues.