The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials

TL;DR

This paper demonstrates a consistent renormalization of Helium-3 using pionless effective field theory, effectively handling the interplay of strong short-range and weak long-range Coulomb interactions without isospin-breaking three-nucleon forces.

Contribution

It provides a non-perturbative and perturbative renormalization approach for Helium-3, emphasizing the importance of regularization methods in effective field theory.

Findings

Successful renormalization at leading and next-to-leading order

Demonstration of scheme independence through cutoff variation

Highlighting the role of regularization in theoretical consistency

Abstract

Quantum chromodynamics and the electroweak theory at low energies are prominent instances of the combination of a short-range and a long-range interaction. For the description of light nuclei, the large nucleon-nucleon scattering lengths produced by the strong interaction, and the reduction of the weak interaction to the Coulomb potential, play a crucial role. Helium-3 is the first bound nucleus comprised of more than one proton in which this combination of forces can be studied. We demonstrate a proper renormalization of Helium-3 using the pionless effective field theory as the formal representation of the nuclear regime as strongly interacting fermions. The theory is found consistent at leading and next-to-leading order without isospin-symmetry-breaking 3-nucleon interactions and a non-perturbative treatment of the Coulomb interaction. The conclusion highlights the significance of the regularization method since a comparison to previous work is contradictory if the difference in those methods is not considered. With a perturbative Coulomb interaction, as suggested by dimensional analysis, we find the Helium-3 system properly renormalized, too. For both treatments, renormalization-scheme independence of the effective field theory is demonstrated by regulating the potential and a variation of the associated cutoff.