Renormalization of pionless effective field theory in the A-body sector

TL;DR

This paper develops a renormalization method for pionless effective field theory applicable to large many-body nuclear systems, ensuring consistent parameter adjustments across different A-body sectors within many-body perturbation theory.

Contribution

It introduces a renormalization procedure that produces A-independent counterterms, facilitating the application of EFT to complex many-body nuclear systems.

Findings

Counterterms are independent of the A-body sector.

The procedure is demonstrated within the random phase approximation.

This work advances practical EFT applications in many-body physics.

Abstract

Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive meaningful estimations of observable. In this paper, a renormalization procedure is designed in connection with many-body approximations applicable to large-A systems and formulated within the frame of many-body perturbation theory. The procedure is shown to generate counterterms that are independent of the targeted A-body sector. As an example, the procedure is applied to the random phase approximation. This work constitutes one step towards the design of a practical EFT for many-body systems.