MSc Defence - Obada Al Ajeh

Investigating the Fierz-Rearrangement Freedom in Chiral Interactions 

Abstract

We investigate the role of contact-operator choices in local chiral two-nucleon interactions. Local chiral interactions are important for nuclear Quantum Monte Carlo calculations because they combine the systematic structure of chiral effective field theory with a form that is more suitable for coordinate-space many-body methods. However, the use of local regulators can break the exact equivalence between different contact-operator bases that would otherwise be related by Fierz rearrangements. In this work, we study how this operator-basis dependence appears in twobody observables and in diagnostics of perturbativeness. We first compare different leading order and next-to-leading order contact-operator combinations using phase shifts and the deuteron binding energy. We then use Weinberg eigenvalues to study the perturbativeness of these interactions and examine how the attractive and repulsive eigenvalue branches depend on the cutoff, chiral order, partial wave, and operator basis. Finally, we apply a variance-based global sensitivity analysis to the deuteron binding energy and to the Weinberg eigenvalues in order to identify which fitted low-energy constants contribute most strongly to the variation of these observables. The results show that the effect of changing the contact-operator is not uniform across all observables. Quantities directly constrained by the fit tend to be more stable, while other observables and diagnostics show clearer basis dependence. The sensitivity analysis further shows that the dominant low-energy constants depend on both the chosen operator basis and the observable being studied. This provides a more detailed view of how regulator choices, contact-operator bases, and fitted short-range coefficients affect local chiral interactions before they are applied in more complicated nuclear systems. 

Examination Committee

• Dr. Robert Wickham, Chair 
• Dr. Alexandros Gezerlis, Advisor  
• Dr. Paul Garrett, Advisory Committee 
• Dr. Eric Poisson, Advisory Committee