Ph.D. Thesis: Chiral Effective Field Theory Beyond the Power-Counting Regime

TL;DR

This thesis introduces new methods to identify the power-counting regime in chiral effective field theory, enabling the use of lattice QCD data beyond traditional limits and revealing an intrinsic energy scale in nucleon-pion interactions.

Contribution

It develops techniques to determine the optimal regularization scale in chiral EFT, allowing reliable extrapolations outside the conventional power-counting regime.

Findings

Existence of an optimal regularization scale confirmed.

Robust chiral extrapolation procedure validated.

Evidence for an intrinsic energy scale in nucleon-pion interactions.

Abstract

Novel techniques are presented, which identify the power-counting regime (PCR) of chiral effective field theory, and allow the use of lattice quantum chromodynamics results that extend outside the PCR. By analyzing the renormalization of low-energy coefficients of the chiral expansion of the nucleon mass, the existence of an optimal regularization scale is realized. The techniques developed for the nucleon mass renormalization are then applied to a test case: performing a chiral extrapolation without prior phenomenological bias. The robustness of the procedure for obtaining an optimal regularization scale and performing a reliable chiral extrapolation is confirmed. The procedure developed is then applied to the magnetic moment and the electric charge radius of the nucleon. The consistency of the results for the value of the optimal regularization scale provides strong evidence for the existence of an intrinsic energy scale in the nucleon-pion interaction.