  We show that the signs of the leading irrelevant interactions for Dirac
fermions are constrained by the analytic structure of the S-matrix. If Regge
behavior obtains, negative signs indicate the presence of higher-spin bound
states that spoil the convergence of the dispersion integrals and drive the
corresponding operators relevant. For nucleon-nucleon scattering, the
negativity of some of the low-energy interactions signals the presence of a
spin-1 bound state: the deuteron. We connect the divergence of the dispersion
integral to the "Sommerfeld enhancement" of the cross-section for low-energy
scattering. We also discuss how this illuminates potential pitfalls in using
perturbative methods to understand the dependence of the low-energy nuclear
interaction on the masses of the light quarks. Finally, we suggest the
possibility of applying similar reasoning to the current-current operators in
the electroweak effective lagrangian, where no bound states spoil convergence
of the dispersion relations.
