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

LOOKING AT THE QCD CORRECTIONS FOR LARGE MtM_t: AN EFFECTIVE LAGRANGIAN POINT OF VIEW

We discuss the QCD corrections to the large-$m_t$ electroweak contributions to $\Delta r$ and to the process $Z\to b \bar b$ as two of the most representative examples. This needs the construction of an effetive field theory below the top quark. We discuss the issue of what $\mu$ scale is the appropriate one at every stage and argue that, while matching corrections do verify the simple prescription of taking $\mu \simeq m_t$ in $\alpha_s(\mu)$, logarithmic (i.e. $\sim \log m_t$) corrections do not, and require the use of the running $\alpha_s(\mu)$ in the corresponding renormalization group equations. In particular we obtain the $\alpha_s$ correction to the non-universal $\log m_t$ contribution to the $Zb\bar b$ vertex.Comment: Latex with macro appended at the beginning of file. Talk given at the Ringberg Workshop ``Perspectives for electroweak interactions in $e^+e^-$ collisions", Ringberg Castle, Germany, February 5--8, 1995. To appear in the proceeding