Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N$^3$LO

We predict neutron-proton scattering cross-sections and polarization observables up to next-to-next-to-next-to leading order in a renormalization-group invariant description of the strong nucleon-nucleon interaction. Low-energy constants are calibrated to phase shifts, sub-leading corrections are computed in distorted-wave perturbation theory, and we employ momentum-cutoff values 500 and 2500 MeV. We find a steady order-by-order convergence and realistic descriptions of scattering observables up to a laboratory scattering energy of approximately 100 MeV. We also compare perturbative and non-perturbative calculations for phase shifts and cross sections and quantify how unitarity is gradually restored at higher orders. The perturbative approach offers an important diagnostic tool for any power counting and our results suggest that the breakdown scale in chiral effective field theory might be significantly lower than estimates obtained in non-perturbative calculations.