2019/12/18 by Felipe J. Llanes–Estrada, Llanes-Estrada, Felipe J., Raúl Roldán-González +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1912.08747
openalex publication_date 2019/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scattering off the edge of a composite particle or finite-range interaction can precede that off its center. An effective theory treatment with pointlike particles and contact interactions must find that the scattered experimental wave is slightly advanced, in violation of causality (the fundamental underlying theory being causal). In practice, partial-wave or other projections of multivariate amplitudes exponentially grow with imaginary E, so that upper complex-plane analyticity is not sufficient to obtain a dispersion relation for them, but only for a slightly modified function (the modified relations additionally connect different J). This limits the maximum precision of certain dispersive approaches to compositeness based on Cauchy's theorem leading to partial-wave dispersion relations. This may be of interest to some dispersive tests of the Standard Model with hadrons, and to unitarization methods used to extend electroweak effective theories. Interestingly, the Inverse Amplitude Method is safe (as the inverse amplitude has the opposite, convergent behavior allowing contour closure). Generically, one-dimensional sum rules such as for the photon vacuum polarization, one-dimensional form factors or the Adler function, to name a few, are not affected by this uncertainty. Likewise, fixed-t dispersion relations were cleverly constructed to avoid it and consequences therefrom are solid.