Cause of deterioration of N^3LO predictions at ~100 MeV in Long–Yang MWPC

Determine whether the decline in order-by-order improvement observed near a laboratory scattering energy of approximately 100 MeV for neutron–proton scattering observables computed up to next-to-next-to-next-to-leading order in the modified Weinberg power counting of Long and Yang—where sub-leading potential corrections are included perturbatively—is caused by overfitting of the calibrated low-energy constants or by an inherent deficiency in the modified Weinberg power counting itself.

Background

The paper computes neutron–proton scattering observables up to N^3LO using a renormalization-group invariant modified Weinberg power counting (MWPC) by Long and Yang, in which one-pion exchange is treated non-perturbatively in specific channels and higher-order corrections enter via distorted-wave perturbation theory. Low-energy constants (LECs) are calibrated to selected Nijmegen phase shifts, and calculations are performed for two cutoffs (500 and 2500 MeV).

The authors report steady order-by-order convergence and realistic descriptions up to roughly 60 MeV. However, around 100 MeV, some N^3LO predictions do not improve over N^2LO for differential cross sections and certain polarizations. They explicitly state uncertainty about the origin of this deterioration, raising two possibilities: overfitting of LECs or an underlying issue with the adopted MWPC. Identifying the cause is important for assessing the robustness and predictive power of RG-invariant chiral EFT in this energy regime.