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.
|Original language||American English|
|Number of pages||8|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 10 Apr 2016|
Bibliographical noteFunding Information:
JK gratefully acknowledges the hospitality of the Ohio State University, discussions with N. Barnea, H. Deleon, R.J. Furnstahl, U. van Kolck, S. König, J. Vanasse, and the financial support of the Minerva Foundation . DG was supported, in part, by BMBF ARCHES . Both authors are grateful for U. van Kolck's and B. Bazak's comments on the manuscript.
© 2016 The Authors.