Smearing of causality by compositeness divides dispersive approaches into exact ones and precision-limited ones

Scattering off the edge of a composite particle or finite-range interaction can precede that its center. An effective theory treatment with pointlike particles and contact interactions must find scattered experimental wave is slightly advanced, in violation causality (the fundamental underlying being causal). In practice, partial-wave other projections multivariate amplitudes exponentially grow Im(E), so analyticity not sufficient to obtain dispersion relation for them, but only modified function relations additionally connect different J). This limit precision certain dispersive approaches compositeness based on Cauchy's theorem. Awareness this may be interest some tests Standard Model hadrons, unitarization methods used extend electroweak theories. Interestingly, Inverse Amplitude Method safe (as inverse amplitude has opposite, convergent behavior allowing contour closure). Generically, one-dimensional sum rules such as photon vacuum polarization, form factors Adler are affected by uncertainty; nor fixed-t relations, cleverly constructed avoid it whose consequences solid.