Rigorous Limits on the Interaction Strength in Quantum Field Theory

We derive model-independent, universal upper bounds on the Operator Product Expan-sion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension d scalar primaries is found to be bounded by ' 10(d − 1) for 1 < d < 1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC