Anomalous mapping between pionfull and pionless EFT's

TL;DR

This paper investigates the unexpected dominant role of certain box diagram contributions in the connection between pionfull and pionless effective field theories for nuclear forces, revealing an anomalous mapping within the non-relativistic regime.

Contribution

It identifies the dominant 2N-reducible component in the box diagram responsible for the anomalous mapping between pionfull and pionless EFTs, providing insights for renormalization strategies.

Findings

The 2N-reducible part of the box diagram dominates over the 2N-irreducible part.

Anomalous mapping occurs within the non-relativistic regime.

A natural renormalization strategy for pionfull theory is proposed.

Abstract

The pion contributions to the coupling $C_0$ of pionless EFT are studied via both non-relativistic and relativistic forms of chiral effective field theory for nuclear forces. A definite item in the $2N$-reducible component of the box diagram is shown to be dominant over the $2N$-irreducible (potential) ones due to the pinching of low-lying nucleon poles, and this anomalous mapping between pionless and pionfull EFT's occurs right within the non-relativistic regime. A natural strategy for renormalization of the pionfull theory emerges as a byproduct through the interactive analysis of the box diagram. Such mapping perspective may shed some light on the efficient organization of the pionfull effective field theory for nuclear forces.