Rigorous limits on the interaction strength in quantum field theory

Abstract

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 $\ensuremath{\simeq}10(d\ensuremath{-}1)$ for $1<d<1.7$. This puts strong limits on unparticle self-interaction cross sections at the LHC.