Subtractive renormalization of the $NN$ scattering amplitude at leading order in chiral effective theory
C.-J. Yang, Ch. Elster, and D. R. Phillips

The leading-order nucleon-nucleon (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$_1$--$^3$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 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.

© 2008 The American Physical Society.