Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory

TL;DR

This paper presents a subtractive renormalization method for NN scattering in chiral effective theory that yields cutoff-independent phase shifts using only scattering lengths, simplifying calculations and enabling bound state analysis.

Contribution

It introduces a subtractive renormalization approach for NN scattering at leading order, relying solely on scattering lengths, improving the practicality and physical transparency of the calculations.

Findings

Renormalization achieved with a single subtraction in specific channels.

Results are cutoff-independent and depend only on observable scattering lengths.

Method allows analytical continuation to study bound states.

Abstract

The leading-order nucleon-nucleon (NN) potential derived from chiral perturbation theory consists of one-pion exchange plus a short-distance contact interaction. We show that in the 1S0 and 3S1-3D1 channels renormalization of the Lippmann-Schwinger equation for this potential can be achieved by performing one subtraction. This subtraction requires as its only input knowledge of the NN scattering lengths. This procedure leads to a set of integral equations for the partial-wave NN t-matrix which give cutoff-independent results for the corresponding NN phase shifts. This reformulation of the NN scattering equation offers practical advantages, because only observable quantities appear in the integral equation. The scattering equation may then be analytically continued to negative energies, where information on bound-state energies and wave functions can be extracted.