2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172728We 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.23 pages, 5 figures, 2 appendices, preprint format. v3: typos fixed, references improved, discussion significantly extended and clarified (including two new appendices)High Energy Physics - PhenomenologyHigh Energy Physics - TheoryNuclear Theorytext