Gauge invariance in the presence of a cutoff

Abstract

We use the method of gauging equations to construct the electromagnetic current operator for the two-nucleon system in a theory with a finite cutoff. The employed formulation ensures that the two-nucleon T-matrix and corresponding five-point function, in the cutoff theory, are identical to the ones formally defined by a reference theory without a cutoff. A feature of our approach is that it effectively introduces a cutoff into the reference theory in a way that maintains the long-range part of the exchange current operator; for applications to effective field theory (EFT), this property is usually sufficient to guarantee the predictive power of the resulting cutoff theory. In addition, our approach leads to Ward-Takahashi (WT) identities that are linear in the interactions. From the point of view of EFT's where such a WT identity is satisfied in the reference theory, this ensures that gauge invariance in the cutoff theory is maintained order by order in the expansion.

15 pages, 2 figures

References in corpus (4)

• A gauge invariant chiral unitary framework for kaon photo- and electroproduction on the proton
• Gauge-invariant approach to meson photoproduction including the final-state interaction
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• On the Wilsonian renormalization group equation for nuclear current operators

Cited by in corpus (6)

• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Pion photoproduction in a dynamical coupled-channels model
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• Gauge-invariant formulation of $NN\to NN\gamma$
• Threshold neutral pion photoproduction off the tri-nucleon to O(q^4)
• Renormalisation-group analysis of electromagnetic couplings in the pionless effective field theory