Chiral effective action of QCD: Precision tests, questions and electroweak extensions

This talk first discusses some aspects of the chiral expansion with three light flavours related to the (non) applicability of the OZI rule. Next, the extension of ChPT to an effective theory of the full standard model is considered. Some applications of a systematic description of the coupling constants by sum rules (e.g. to the determination of quark masses and $K_{l3}$ decays) are presented.Comment: 6 pages, plenary talk at the International Conference on QCD and Hadronic physics, Beijing 16-20 June 200

N_f Dependence of the Quark Condensate from a Chiral Sum Rule

How fast does the quark condensate in QCD-like theories vary as a function of $N_f$ is inferred from real QCD using chiral perturbation theory at order one-loop. A sum rule is derived for the single relevant chiral coupling-constant, $L_6$. A model independent lower bound is obtained. The spectral function satisfies a Weinberg-type superconvergence relation. It is discussed how this, together with chiral constraints allows a solid evaluation of $L_6$, based on experimental $\pi\pi-K\bar K$ S-wave T-matrix input. The resulting value of $L_6$ is compatible with a strong $N_f$ dependence possibly suggestive of the proximity of a chiral phase transitionComment: 22 pages, 4 figures. A few improvements and corrections mad

Chiral perturbation theory: a basic introduction

Chiral perturbation theory is a very general expansion method which can be applied to any dynamical system which has continuous global symmetries and in which the ground state breaks some of these spontaneously. In these lectures we explain at a basic level and in detail how such symmetries are identified in the case of the QCD Lagrangian and describe the steps which are involved in practice in the construction of a low-energy effective theory for QCD.Comment: Lectures given at the FANTOM study week, Emmen May 24-28 2004. 17 pages, 4figures. v2: eq. (62) correcte

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $\pi\pi$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $\sigma\gamma$ electromagnetic form factor. Finally, and evaluation of the contribution of $\gamma\pi\pi$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.Comment: 53 pages, 18 figure

Virtual quarks, vacuum stability and scalar meson physics

Results are reviewed, which provide relations between the response (and eventual instability) of the chiral QCD vacuum to an increase of the number of massless quarks in the theory and the observed violations of the large $N_c$ expansion in the scalar meson sector, by combining chiral perturbation theory expansions in $m_s$ with sum rule methods. An approach based on the construction of scalar form-factors was recently confirmed by an independent approach which uses the $\pi K$ scattering amplitudes.Comment: 7 pages, Talk given at " Chiral fluctuations in hadronic matter international workshop", Orsay, September 26-28, 200

Form factors of the isovector scalar current and the ηπ\eta\pi scattering phase shifts

A model for S-wave $\eta\pi$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $K\bar{K}$ channel. The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $\eta\pi\to\eta\pi$, $\eta\pi\to K\bar{K}$ amplitudes and approximately for $K\bar{K}\to K\bar{K}$. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omn\`es problem, thus allowing to compute the $\eta\pi$ and $K\bar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $a_0(980)$, $a_0(1450)$ resonances, as well as the chiral results of the $\eta\pi$ and $K\bar{K}$ scalar radii which are predicted to be remarkably small at $O(p^4)$. This $T$-matrix model could be used for a unified treatment of the $\eta\pi$ final-state interaction problem in processes such as $\eta'\to \eta \pi\pi$, $\phi\to\eta\pi\gamma$, or the $\eta\pi$ initial-state interaction in $\eta\to3\pi$.Comment: 33 pages, 14 figures. v2: Some clarifications and corrections of typo

Radiative corrections in weak semi-leptoni processes at low energy: a two-step matching determination

We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the Standard Model. For this purpose, we follow a two-step procedure. A first matching, from the Standard Model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual $\log(M\_Z/M\_\rho)$ approximation.Comment: 28 pages, late

Listening to features

This work explores nonparametric methods which aim at synthesizing audio from low-dimensionnal acoustic features typically used in MIR frameworks. Several issues prevent this task to be straightforwardly achieved. Such features are designed for analysis and not for synthesis, thus favoring high-level description over easily inverted acoustic representation. Whereas some previous studies already considered the problem of synthesizing audio from features such as Mel-Frequency Cepstral Coefficients, they mainly relied on the explicit formula used to compute those features in order to inverse them. Here, we instead adopt a simple blind approach, where arbitrary sets of features can be used during synthesis and where reconstruction is exemplar-based. After testing the approach on a speech synthesis from well known features problem, we apply it to the more complex task of inverting songs from the Million Song Dataset. What makes this task harder is twofold. First, that features are irregularly spaced in the temporal domain according to an onset-based segmentation. Second the exact method used to compute these features is unknown, although the features for new audio can be computed using their API as a black-box. In this paper, we detail these difficulties and present a framework to nonetheless attempting such synthesis by concatenating audio samples from a training dataset, whose features have been computed beforehand. Samples are selected at the segment level, in the feature space with a simple nearest neighbor search. Additionnal constraints can then be defined to enhance the synthesis pertinence. Preliminary experiments are presented using RWC and GTZAN audio datasets to synthesize tracks from the Million Song Dataset.Comment: Technical Repor