Renormalization of the Off-shell chiral two-pion exchange NN interactions

TL;DR

This paper demonstrates that the renormalization of off-shell chiral two-pion exchange NN interactions depends solely on the on-shell amplitude, ensuring finiteness without additional counterterms, supported by analytical and numerical analysis.

Contribution

It provides an analytical proof that off-shell renormalization relies only on on-shell amplitudes, simplifying the treatment of singular interactions in chiral NN forces.

Findings

Off-shell renormalization depends entirely on on-shell amplitudes.

No new counterterms are needed for off-shell renormalization.

Analytical and numerical validation in the 1S0 channel.

Abstract

The renormalization, finiteness and off-shellness of short distance power like singular interactions is discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding on-shell amplitude without proliferation of new counterterms. We illustrate the result by complementary calculations both in coordinate as well as in momentum space in the simplest 1S0 channel for chiral np interactions including Two Pion Exchange.