Effective Theory of 3H and 3He

TL;DR

This paper develops a new perturbative approach in pionless effective field theory to accurately describe Coulomb effects and isospin breaking in trinucleon systems, achieving rapid convergence and precise energy splitting predictions.

Contribution

It introduces a systematic perturbative expansion that isolates Coulomb divergences and demonstrates Coulomb effects as perturbative in the trinucleon regime, improving theoretical predictions.

Findings

Rapid convergence of the perturbative expansion.

Accurate calculation of the 3H-3He binding energy difference.

Coulomb force treated as a perturbative effect in pionless EFT.

Abstract

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV.