Subtractive renormalization of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="italic">NN</mml:mi></mml:mrow></mml:math>scattering amplitude at leading order in chiral effective theory

Abstract

The leading-order nucleon-nucleon ($\mathit{NN}$) potential derived from chiral perturbation theory consists of one-pion exchange plus short-distance contact interactions. We show that in the ${}^{1}{S}_{0}$ and ${}^{3}{S}_{1}\text{\ensuremath{-}}{}^{3}{D}_{1}$ 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 $\mathit{NN}$ scattering lengths. This procedure leads to a set of integral equations for the partial-wave $\mathit{NN}t$ matrix which gives cutoff-independent results for the corresponding $\mathit{NN}$ phase shifts. This reformulation of the $\mathit{NN}$ 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, from which information on bound-state energies and wave functions can be extracted.