Effective field theory of 3He

TL;DR

This paper develops an effective field theory approach to study 3He as a three-body bound state, incorporating Coulomb interactions and revealing the Efimov effect persists with Coulomb forces.

Contribution

It extends the EFT framework to include Coulomb interactions in 3He, demonstrating the necessity of a three-body force at leading order and analyzing the Efimov effect with Coulomb forces.

Findings

Three-body force is required at leading order for 3He.

The Efimov effect persists with Coulomb interactions.

The difference in three-body force strengths between 3He and triton is quantified.

Abstract

3He and the triton are studied as three-body bound states in the effective field theory without pions. We study 3He using the set of integral equations developed by Kok et al. which includes the full off-shell T-matrix for the Coulomb interaction between the protons. To leading order, the theory contains: two-body contact interactions whose renormalized strengths are set by the NN scattering lengths, the Coulomb potential, and a three-body contact interaction. We solve the three coupled integral equations with a sharp momentum cutoff, Lambda, and find that a three-body interaction is required in 3He at leading order, as in the triton. It also exhibits the same limit-cycle behavior as a function of Lambda, showing that the Efimov effect remains in the presence of the Coulomb interaction. We also obtain the difference between the strengths of the three-body forces in 3He and the triton.