Effective Field Theory for Shallow P-Wave States

Abstract

We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.

Trapped two-nucleon system in energy-dependent effective field theory

“…But for higher partial waves, no immediate extension of such a nonperturbative iteration of contact potentials is known to be renormalizable (see Ref. [38] for a latest study), unless a dimeron field is explicitly used [39].…”

Some applications of renormalization group to few-body problems in EFT

“…Both scenarios have been revisited in Ref. [17], the main findings of which are briefly summarized below. The potential of Eq.…”

“…In the current work, following Refs. [14,16,17], we consider fine-tuned systems, for which the P-wave scattering amplitude in Eq. ( 4) features poles located in the validity range of the EFT, k ∼ M lo ≪ M hi .…”

“…However, while in first two references the formulation of the EFT with an auxiliary spin-1 dimer field has been employed, Ref. [17] and the current work considers a formulation without auxiliary fields. We are interested in two fine tuning scenarios.…”

Chiral Effective Field Theory's Impact on Advancing Quantum Monte Carlo Methods

“…The various contributions to the special issue "Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians" commemorate several aspects of Steven Weinberg's legacy in nuclear physics [17,18,19,20,21,22,23]. In this contribution, we present our personal view of the impact that Weinberg's seminal papers had on microscopic studies of nuclear systems with quantum Monte Carlo (QMC) methods.…”