  We derive model-independent, universal upper bounds on the Operator Product
Expansion (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.
