NN Scattering Problem

It is shown that chiral perturbation theory (in its original form by Wein-berg) can describe N N scattering with positive as well as negative effective range. Some issues connected with unnaturally large N N 1 S 0 scattering length are discussed. The chiral perturbation theory approach to the low-energy purely pionic processes [1] has been generalised for processes involving an arbitrary number of nucle-ons [2], [3]. Weinberg pointed out that for the n-nucleon problem the power counting should be used for the " effective potentials " and not for the full amplitudes. The effective potential is defined as a sum of time-ordered perturbation theory diagrams for the T-matrix excluding those with purely nucleonic intermediate states. The full S-matrix can be obtained by solving a Lippmann-Schwinger equation (or Schröedinger equation) with this effective potential in place of the interaction Hamiltonian, and with only n-nucleon intermediate states [2]. Using renormalization points also characterised by momenta of order of external momenta p or less, the ultraviolet divergences that arise in calculations using effective theory are absorbed into the parameters of the Lagrangian. After renor-malization, the effective cutoff is of order p [3]. The Lagrangian is rich enough to contain all possible terms which are allowed by assumed symmetries, so all necessary counter-terms are present in the Lagrangian. There has been much recent interest in the chiral perturbation theory approach to nucleon-nucleon scattering problems. While some papers concern different constructive calculational and conceptual problems the authors of [4, 5, 6, 7, 8] came to the conclusion that Weinberg's approach to EFT has severe problems. These arise in the description of interactions with positive effective range. Moreover they conclude " there is no effective field theory of NN scattering with nucleons alone " and