Current-current operator evolution in the chiral limit

We consider the strong interaction corrections to current-current hadronic operators in the chiral limit. High-momentum contributions are computed in perturbative QCD with massless quarks while low-momentum contributions are estimated in a truncated non-linear σ-model for massless pseudoscalars. In the large-N approximation, the ambiguity on the momentum matching around the confining scale is removed by using the effective color-singlet gauge boson exchanged between the two currents as a universal probe.