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Quantum chromodynamics and the electroweak theory at low energies areprominent instances of the combination of a short-range and a long-rangeinteraction. For the description of light nuclei, the large nucleon-nucleonscattering lengths produced by the strong interaction, and the reduction of theweak interaction to the Coulomb potential, play a crucial role. Helium-3 is thefirst bound nucleus comprised of more than one proton in which this combinationof forces can be studied.  We demonstrate a proper renormalization of Helium-3 using the pionlesseffective field theory as the formal representation of the nuclear regime asstrongly interacting fermions. The theory is found consistent at leading andnext-to-leading order without isospin-symmetry-breaking 3-nucleon interactionsand a non-perturbative treatment of the Coulomb interaction. The conclusionhighlights the significance of the regularization method since a comparison toprevious work is contradictory if the difference in those methods is notconsidered.  With a perturbative Coulomb interaction, as suggested by dimensionalanalysis, we find the Helium-3 system properly renormalized, too.  For both treatments, renormalization-scheme independence of the effectivefield theory is demonstrated by regulating the potential and a variation of theassociated cutoff.

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