Violations of local duality in the heavy quark sector

We examine the origin of possible failures of the quark-hadron local duality. In particular, we consider a correlator of two currents comprising heavy quark operators, and compare the evaluation by the Operator Product Expansion with the result obtained inserting an infinite set of hadronic states, in the Nc → ∞ limit. Whereas the smeared spectral functions agree with each other, their local behaviour is different. The difference manifests itself in the form of a term O(Λϵ) (ϵ being the residual energy) that is not present in the expansion in powers of Λϵ predicted by the OPE.