Rigorous limits on the interaction strength in quantum field theory

We derive model-independent, universal upper bounds on the operator product expansion 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 operator product expansion coefficient of three identical dimension d scalar primaries is found to be bounded by similar or equal to 10(d - 1) for 1 < d < 1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.