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We present a new rearrangement of short-range interactions in the $^1S_0$nucleon-nucleon channel within Chiral Effective Field Theory. This is intendedto reproduce the amplitude zero (scattering momentum $\simeq$ 340 MeV) atleading order, and it includes subleading corrections perturbatively in a waythat is consistent with renormalization-group invariance. Systematicimprovement is shown at next-to-leading order, and we obtain results that fitempirical phase shifts remarkably well all the way up to the pion-productionthreshold. An approach in which pions have been integrated out is included,which allows us to derive analytic results that also fit phenomenologysurprisingly well.

The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory