Signs of analyticity in fermion scattering

Details Signs of analyticity in fermion scattering Signs of analyticity in fermion scattering

2008-02-28

arxiv.org/abs/0802.4081v3

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages, 5 figures, 2 appendices, preprint format. v3: typos fixed, references improved, discussion significantly extended an

Scientific paper

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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