A note on nonperturbative renormalization of effective field theory

TL;DR

This paper investigates the nonperturbative renormalization of effective field theories for nucleon-nucleon scattering, revealing fundamental mismatches that challenge traditional counterterm methods.

Contribution

It uncovers intrinsic structural mismatches between EFT power counting and divergence structures, demonstrating limitations of conventional renormalization techniques in nonperturbative regimes.

Findings

Identifies intrinsic structures in nonperturbative T-matrix renormalization.

Shows conventional counterterm algorithms are inadequate for EFT in nonperturbative regimes.

Provides rigorous solutions using algebraic Lippmann-Schwinger equations.

Abstract

Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of $T$-matrices are unraveled using rigorous solutions and an inverse form of algebraic Lippmann-schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for $NN$ scattering in nonperturbative regimes.