  We propose a new class of universal amplitude ratios which involve the first
terms of the short distance expansion of the correlators of a statistical model
in the vicinity of a critical point. We will describe the critical system with
a conformal field theory (UV fixed point) perturbed by an appropriate relevant
operator. In two dimensions the exact knowledge of the UV fixed point allows
for accurate predictions of the ratios and in many nontrivial integrable
perturbations they can even be evaluated exactly. In three dimensional O(N)
scalar systems feasible extensions of some existing results should allow to
obtain perturbative expansions for the ratios. By construction these universal
ratios are a perfect tool to explore the short distance properties of the
underlying quantum field theory even in regimes where the correlation length
and one point functions are not accessible in experiments or simulations.
