Electroweak matrix elements at large Nc: matching quarks to mesons

I review some progress made on the problem of calculating electroweak processes of mesons at low energy with the use of an approximation to large-Nc QCD which we call the Minimal Hadronic Approximation. An update of results for the matrix elements of the electroweak penguin operators Q7 and Q8 is also given.Comment: 12 pages, 2 figures. Invited talk given at ``The Phenomenology of Large-Nc QCD'', Arizona State U., January 9-11, 2002. A comment and a reference adde

Matching Long and Short Distances in Large-Nc QCD

It is shown, with the example of the experimentally known Adler function, that there is no matching in the intermediate region between the two asymptotic regimes described by perturbative QCD (for the very short-distances) and by chiral perturbation theory (for the very long-distances). We then propose to consider an approximation of large-Nc QCD which consists in restricting the hadronic spectrum in the channels with J^P quantum numbers 0^-, 1^-, 0^+ and 1^+ to the lightest state and treating the rest of the narrow states as a perturbative QCD continuum; the onset of this continuum being fixed by consistency constraints from the operator product expansion. We show how to construct the low-energy effective Lagrangian which describes this approximation. The number of free parameters in the resulting effective Lagrangian can be reduced, in the chiral limit where the light quark masses are set to zero, to just one mass scale and one dimensionless constant to all orders in chiral perturbation theory. A comparison of the corresponding predictions, to O(p^4) in the chiral expansion, with the phenomenologically known couplings is also made.Comment: 35 pages, 9 figures, LaTeX. Added a couple of reference

An example of resonance saturation at one loop

We argue that the large-Nc expansion of QCD can be used to treat a Lagrangian of resonances in a perturbative way. As an illustration of this we compute the L_10 coupling of the Chiral Lagrangian by integrating out resonance fields at one loop. Given a Lagrangian and a renormalization scheme, this is how in principle one can answer in a concrete and unambiguous manner questions such as at what scale resonance saturation takes place.Comment: 9 pages, 5 figures. Enlarged discussion, results unchanged. To be published in Phys. Rev.