Santiago Peris

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 JP quantum numbers 0−, 1−, 0+ and 1+ to the lightest state and to treat 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 (p4) in the chiral expansion, with the phenomenologically known couplings is also made.

Electroweak hadronic contributions to the muon (g-2)

We reanalyze the two-loop electroweak hadronic contributions to the muon g−2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Greens function.

Decay of pseudoscalars into lepton pairs and large N(c) QCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colours Nc. When further restricted to the lowest meson dominance approximation to large-Nc QCD, our results agree well with the available experimental data.

A rational approach to resonance saturation in large-Nc QCD

We point out that resonance saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions. These approximants are rational functions which encompass any saturation with a finite number of resonances as a particular example, explaining several results which have appeared in the literature. We review the main properties of Pade Approximants with the help of a toy model for the VV?AA two-point correlator, paying particular attention to the relationship among the Chiral Expansion, the Operator Product Expansion and the resonance spectrum. In passing, we also comment on an old proposal made by Migdal in 1977 which has recently attracted much attention in the context of AdS/QCD models. Finally, we apply the simplest Pade Approximant to the VV?AA correlator in the real case of QCD. The general conclusion is that a rational approximant may reliably describe a Greens function in the Euclidean, but the same is not true in the Minkowski regime due to the appearance of unphysical poles and/or residues.

Duality violations and spectral sum rules

We study the issue of duality violations in the VV−AA vacuum polarization function in the chiral limit. This is done with the help of a model with an expansion in inverse powers of the number of colors, Nc, allowing us to consider resonances with a finite width. Due to these duality violations, the Operator Product Expansion (OPE) and the moments of the spectral function (e.g. the Weinberg sum rules) do not match at finite momentum, and we analyze this difference in detail. We also perform a comparative study of many of the different methods proposed in the literature for the extraction of the OPE parameters and find that, when applied to our model, they all fare quite similarly. In fact, the model strongly suggests that a significant improvement in precision can only be expected after duality violations are included. To this end, we propose a method to parameterize these duality violations. The method works quite well for the model, and we hope that it may also be useful in future determinations of OPE parameters in QCD.

A critical reassessment of Q7 and Q8 matrix elements

Abstract We compare recent theoretical determinations of weak matrix elements of the electroweak penguin operators Q 7 and Q 8 . We pay special attention to the renormalization scheme dependence of these determinations as well as to the influence of higher dimension operators in the different approaches.

The electroweak π+−π0 mass difference and weak matrix elements in the 1/Nc expansion

Abstract The π + − π 0 mass difference generated by the electroweak interactions of the Standard Model is expressed, to lowest order in the chiral expansion and to leading order in α , in terms of an integral involving the same correlation function Π LR ( Q 2 ) which governs the well known electromagnetic π + − π 0 mass difference. We calculate this contribution within the framework of QCD in the limit of a large number of colours N c . We show how this calculation, which requires non-trivial contributions from next-to-leading terms in the 1/ N c expansion, provides an excellent theoretical laboratory for studying issues of long- and short-distance matching in calculations of weak matrix elements of four-quark operators. The electroweak π + − π 0 mass difference turns out to be a physical observable which is under good analytical control and which should, therefore, be an excellent testground of numerical evaluations in lattice-QCD and of model calculations in general.

Large-Nc QCD meets Regge theory: the example of spin-one two-point functions

We discuss the phenomenological implications of assuming a Veneziano-type spectrum for the vector and axial-vector two-point functions in QCD at large Nc. We also compare the phenomenological results with those of Lowest-Meson Dominance, and find that they agree.

Matrix elements of electroweak penguin operators in the 1/Nc expansion

Abstract It is shown that the K → ππ matrix elements of the four-quark operator Q 7 , generated by the electroweak penguin-like diagrams of the Standard Model, can be calculated to first non-trivial order in the chiral expansion and in the 1/ N c expansion. Although the resulting B factors B 7 (1/2) and B 7 (3/2) are found to depend only logarithmically on the matching scale μ , their actual numerical values turn out to be rather sensitive to the precise choice of μ in the GeV region. We compare our results to recent numerical evaluations from lattice-QCD and to other model estimates.

New nonrenormalization theorems for anomalous three point functions

Nonrenormalization theorems involving the transverse, i.e. non anomalous, part of the VVA correlator in perturbative QCD are proven. Some of the consequences and questions they raise are discussed.