TY - JOUR
T1 - The Coulomb interaction in Helium-3
T2 - Interplay of strong short-range and weak long-range potentials
AU - Kirscher, J.
AU - Gazit, D.
N1 - Publisher Copyright:
© 2016 The Authors.
PY - 2016/4/10
Y1 - 2016/4/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84958292262&partnerID=8YFLogxK
U2 - 10.1016/j.physletb.2016.02.011
DO - 10.1016/j.physletb.2016.02.011
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AN - SCOPUS:84958292262
SN - 0370-2693
VL - 755
SP - 253
EP - 260
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
ER -