Signs of analyticity in fermion scattering

Allan Adams; Alejandro Jenkins; Donal O'Connell

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arXiv · 0802.4081

Signs of analyticity in fermion scattering

Allan Adams·Alejandro Jenkins·Donal O'Connell

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Abstract

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.

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Allan Adams, Alejandro Jenkins, Donal O'Connell. 2008-10-31. Signs of analyticity in fermion scattering. https://arxiv.org/abs/0802.4081

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