Power Counting of Contact-Range Currents in Effective Field Theory

Abstract

We analyze the power counting of two-body currents in nuclear effective field theories (EFTs). We find that the existence of non-perturbative physics at low energies, which is manifest in the existence of the deuteron and the 1S0 NN virtual bound state, combined with the appearance of singular potentials in versions of nuclear EFT that incorporate chiral symmetry, modifies the renormalization-group flow of the couplings associated with contact operators that involve nucleon-nucleon pairs and external fields. The order of these couplings is thereby enhanced with respect to the naive-dimensional-analysis estimate. Consequently, short-range currents enter at a lower order in the chiral EFT than has been appreciated up until now, and their impact on low-energy observables is concomitantly larger. We illustrate the changes in the power counting with a few low-energy processes involving external probes and the few-nucleon systems, including electron-deuteron elastic scattering and radiative neutron capture by protons.

5 pages. Minor revisions. Conclusions unchanged. Version to appear in Physical Review Letters

References in corpus (8)

• Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation
• Electromagnetic two-body currents of one- and two-pion range
• Short-range nuclear forces in singlet channels
• Renormalization of Singular Potentials and Power Counting
• Thermal neutron captures on $d$ and ${}^3$He
• Chiral effective theory predictions for deuteron form factor ratios at low Q^2
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• On the Wilsonian renormalization group equation for nuclear current operators

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