We have established a new convergent scheme to treat analyticallynucleon-nucleon interactions from a chiral effective field theory. TheKaplan-Savage-Wise (KSW) amplitudes are resummed to fulfill the unitarity orright hand cut to all orders below pion production threshold. This is achievedby matching order by order in the KSW power counting the general expression ofa partial wave with resummed unitarity cut, with the inverses of the KSWamplitudes. As a result, a new convergent and systematic KSW expansion isderived for an on-shell interacting kernel \cR in terms of which the partialwaves are computed. The agreement with data for the S-waves is fairly good upto laboratory energies around 350 MeV and clearly improves and reestablishesthe phenomenological success of the KSW amplitudes when treated within thisscheme.
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