A nonperturbative parametrization and scenario for EFT renormalization

TL;DR

This paper introduces a universal, nonperturbative parametrization of T-matrices in effective field theory, revealing a scale invariant and challenging traditional renormalization approaches with new predictions for contact potentials.

Contribution

It proposes a universal form for nonperturbatively renormalized T-matrices and identifies a scale invariant under the renormalization group, offering new insights into EFT renormalization.

Findings

Identifies a universal, scale-invariant renormalization group fixed point.

Derives effective range parameters in a nonperturbative contact potential scenario.

Challenges conventional wisdoms in EFT renormalization.

Abstract

We present a universal form of the $T$-matrices renormalized in nonperturbative regime and the ensuing notions and properties that fail conventional wisdoms. A universal scale is identified and shown to be renormalization group invariant. The effective range parameters are derived in a nonperturbative scenario with some new predictions within the realm of contact potentials. Some controversies are shown to be due to the failure of conventional wisdoms.