In this paper we study two kinds of tau decays: (a) tau- --> (rho pi-,omega pi-, phi pi-, K*0 K-) nu(tau), which belong to Delta S=0 processes and (b) Delta S = 1 processes, like tau- --> (rho K-, omega K-, phi K-, \bar{K*0} pi-) nu(tau), in the framework of resonance chiral theory. We fit the tau- --> omega pi- nu(tau) spectral function and the invariant mass distribution of omega K in the process of tau- --> omega K- nu(tau) to get the values of unknown resonance couplings. Then we make a prediction for branching ratios of all channels.
The recent measurement of the tau -> Ks pion nu_tau spectrum by the Belle Collaboration provides the frame to set forth a theoretical description of the decay, which is based on the contributing vector F_+(s) and scalar F_0(s) form factors. We show that a good representation of data is obtained through the use of form factors calculated within resonance chiral theory and constrained by dispersion relations and short-distance QCD. Hence we obtain a determination of K*(892) parameters and the low-energy parameterization of F_+(s).
Tau decays into hadrons foresee the study of the hadronization of vector and axial-vector QCD currents, yielding relevant information on the dynamics of the resonances entering into the processes. We analyse tau -> (3 pion) nu_tau decays within the framework of the Resonance Chiral Theory, comparing this theoretical scheme with the experimental data, namely ALEPH spectral function and branching ratio. Hence we get values for the mass and on-shell width of the a_1(1260) resonance, and provide the structure functions that have been measured by OPAL and CLEO-II.
$τ\toππν$, $τ\toπKν$, $τ\to Kην$, $τ\to 3πν$ and $τ\to ππKν$ have been investigated using chiral symmetry with dispersion relation in agreement with the unitarity condition.
The decays tau -> 3 pi + nu(tau) are analyzed at one loop order in the framework of Generalized Chiral Perturbation Theory, in order to test the sensitivity to the size of spontaneous chiral symmetry breaking parameters, contained in the S-wave. The latter, due to a kinematical suppression, at threshold, of the P-wave, is relatively large enough to be detectable at high energy machines, through azimuthal left-right asymmetries. This quantity (for the pi- pi- pi+ mode), integrated from threshold to Q^2 = 0.35 GeV^2, varies from (17 +- 3) % in the standard case of large condensate up to (40 +- 5…
We analyze the lowest spectral moments of the left-right two-point correlation function, using all known short-distance constraints and the recently updated ALEPH V-A spectral function from tau decays. This information is used to determine the low-energy couplings L10 and C87 of chiral perturbation theory and the lowest-dimensional contributions to the Operator Product Expansion of the left-right correlator. A detailed statistical analysis is implemented to assess the theoretical uncertainties, including violations of quark-hadron duality.
Using recent precise hadronic tau-decay data on the V-A spectral function and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10 and C_87. At order p^4 we obtain L_10^r(M_rho)=-(5.22+-0.06)10^-3, whereas at order p^6 we get L_10^r(M_rho)=-(4.06+-0.39)10^-3 and C_87^r(M_rho) = (4.89+-0.19)10^-3 GeV^-2.
A sum rule analysis of the hadronic tau-decay data can be used to determine the low-energy constants L10(mu) and C87(mu). These constants are QCD chiral-order parameters, which appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L10(M_rho) = -(5.22\pm 0.06)10^-3. Including in the analysis the order p^6 contributions, we get L10(M_rho) = -(4.06\pm 0.39)10^-3 and C87(M_rho) = (4.89\pm 0.19)10^-3 GeV^-2.
Tau decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate these processes. Within an effective field theory-like framework, namely Resonance Chiral Theory, we analyse the decays ot the tau into K K pion modes and compare the results with CLEO and BaBar data. In this way, we provide bounds on the couplings entering our Lagrangian and predict the corresponding spectral functions. As a main result -an…
The hadronic tau decay $τ^- \to ν_τηπ^- π^0$ occurs through V-A weak current. In this decay mode, the vector current contribution is intrinsic parity violating and the axial current contribution is G parity violating. The latter contribution is suppressed due to tiny isospin breaking. We have computed both vector and axial vector form factors using a chiral Lagrangian with vector mesons including the effect of isospin breaking and intrinsic parity violation. A numerical result of the invariant mass distribution is shown and the structure of $ρ$ resonance can be seen in the distribution with re…
Within the resonance chiral theory, we have studied the process of a tau lepton decaying into a vector resonance plus a pseudo-Goldstone meson and a tau neutrino. Two kinds of processes are discussed: (a) tau- --> (rho pi-,omega pi-, phi pi-, K*0 K-) nu(tau), belonging to Delta S=0 processes and (b) Delta S = 1 processes, such as tau- --> (rho K-, omega K-,phi K-,\bar{K*0} pi-) nu(tau). To fit the tau- --> omega pi- nu(tau) spectral function and the decay distribution of tau- --> omega K- nu(tau) to get unknown resonance couplings, we then make a prediction for branching ratios of all channels…
The doubly charged scalar boson (H^{\pm\pm}) is introduced in several models of the new physics beyond the standard model. The H^{\pm\pm} has Yukawa interactions with two left-handed charged leptons or two right-handed charged leptons depending on the models. We study kinematical properties of H^{\pm\pm} decay products through tau leptons in order to discriminate the chiral structures of the new Yukawa interaction. The chirality of tau leptons can be measured by the energy distributions of the tau decay products, and thus the chiral structure of the new Yukawa interaction can be traced in the …
In a small window of phase space, chiral perturbation theory can be used to make standard model predictions for tau decays into two and three pions. For $τ\to 2πν_τ$, we give the analytical result for the relevant form factor $F_V$ up to two loops, then calculate the differential spectrum and compare with available data. For $τ\to 3 πν_τ$, we have calculated the hadronic matrix element to one loop. We discuss the decomposition of the three pion states into partition states and we give detailed predictions for the decay in terms of structure functions. We also compare with low energy prediction…
We have considered a supersymmetric scenario in which the minimal supersymmetric standard model is augmented with a right-chiral neutrino superfield for each generation. Such a scenario can have a lightest supersymmetric particle (LSP) dominated by the right-chiral sneutrino state and the lighter stau as the next-to-lightest supersymmetric particle (NLSP). This can easily be motivated by assuming a high scale framework of supersymmetry breaking like minimal supergravity (mSUGRA). Due to the extremely small neutrino Yukawa coupling, the decay of the NLSP to the LSP is suppressed and consequentl…
We present a partial upgrade of the Monte Carlo event generator TAUOLA with the two and three hadron decay modes using the theoretical models based on Resonance Chiral Theory. These modes account for 88% of total hadronic width of the tau meson. First results of the model parameters have been obtained using BaBar data for three pion mode.
Hadronic tau decay data provides access to the light quark vector (V) and axial vector (A) spectral functions. This makes possible investigations of the dynamics of QCD at intermediate scales and improved determinations of certain QCD/Standard Model parameters. We discuss three such applications: (1) the investigation of the nature of duality violation in QCD at intermediate scales (and its relation to the determination of alpha_s); (2) the extraction of m_s from flavor-breaking differences of flavor 'ud' and 'us' data; and (3) the determination of the dimension D=6 term in the OPE for the fla…
We review the main components that have to be considered, within Resonance Chiral Theory, in the study of processes whose dynamics is dominated by hadron resonances. We show its application in the study of the tau -> (3 pion) nu_tau decay.
We discuss semileptonic and leptonic B decays, B to D^{(*)} tau nu and B to tau nu, in the chiral U(1)' models which were proposed by the present authors in the context of the top forward-backward asymmetry (A^t_FB) observed at the Tevatron. In these models, extra Higgs doublets with nonzero U(1)' charges are required in order to make the realistic mass matrix for up-type quarks. Then the extra (pseudo)scalars contribute to A^t_FB with large flavor-changing Yukawa couplings involving top quark. The contribution of the charged Higgs to A^t_FB is negligible, but it may significantly affect B dec…
A general expression of the axial-vector current is presented, in which both the effects of the chiral symmetry breaking and the spontaneous chiral symmetry breaking are included. A new resonance formula of the axial-vector meson is derived and in the limit of $q^{2}\rightarrow 0$ this formula doesn't go back to the ``chiral limit``. The studies show that the dominance of the axial-vector meson is associated with the satisfaction of PCAC. The dominance of pion exchange is companied by the strong anomaly of PCAC.
In this work, we perform a detailed study of the $τ^-\toπ^-π^0γν$ decay process within the resonance chiral theory. We pay special attention to the triple-product asymmetry in the $τ^-\toπ^-π^0γν$ process. The minimal resonance chiral Lagrangian and the odd-intrinsic parity resonance operators are simultaneously included to calculate the decay amplitudes. Various invariant-mass distributions in the $π^-π^0$, $π^-γ$ and $π^0γ$ systems are studied and they reveal different resonance dynamics. We further predict the intriguing nonzero triple-product asymmetry distributions, which may provide usef…
Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Ex…
The saturation of QCD chiral sum rules is reanalyzed in view of the new and complete analysis of the ALEPH experimental data on the difference between vector and axial-vector correlators (V-A). Ordinary finite energy sum rules (FESR) exhibit poor saturation up to energies below the tau-lepton mass. A remarkable improvement is achieved by introducing pinched, as well as minimizing polynomial integral kernels. Both methods are used to determine the dimension d=6 and d=8 vacuum condensates in the Operator Product Expansion, with the results: {O}_{6}=-(0.00226 \pm 0.00055) GeV^6, and O_8=-(0.0053 …
Exclusive semi-leptonic decays of the tau lepton offer a clean probe to study the hadronization of QCD currents in its non-perturbative regime and learn about resonance dynamics, which drives strong interactions in these processes. In this theory outlook, I will use the simplest non-trivial di-pion tau decays to illustrate briefly recent theoretical progress on these analyses and their comparison to data.
We analyze how the recent precise hadronic tau-decay data on the V-A spectral function and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory (ChPT), can be used to improve the knowledge of some of the low-energy constants of ChPT. In particular we find the most precise values of L_{9,10} (or equivalently l_{5,6}) at order p^4 and p^6 and the first phenomenological determination of C_87 (c_50).
We analyse tau -> (3 pions) nu_tau decays within the framework of the resonance chiral theory of QCD. We have worked out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, and the new coupling constants that arise have been constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values for the mass and on-shell width of the a_1(…
tau -> (3 pions) nu_tau decays are analysed within the framework of the resonance effective theory of QCD. We work out the relevant Lagrangian that describes the axial-vector current hadronization contributing to these processes, in particular the local a_1(1260)-rho(770)-Goldstone interactions. The new coupling constants are constrained by imposing the asymptotic behaviour of the corresponding spectral function within QCD. Hence we compare the theoretical framework with the experimental data, obtaining a good quality fit from the ALEPH spectral function and branching ratio. We also get values…
QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the ${\cal{O}}(p^4)$ Lagrangian of chiral perturbation theory, $\bar{L}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress pote…
We study two and three meson decays of the tau lepton within the framework of the Resonance Chiral Theory, that is based on the following properties of QCD: its chiral symmetry in the massless case, its large-N_C limit, and the asymptotic behaviour it demands to the relevant form factors. Most of the couplings in the Lagrangian are determined this way rendering the theory predictive. Our outcomes can be tested thanks to the combination of a very good experimental effort (current and forthcoming, at B- and tau-charm-factories) and the very accurate devoted Monte Carlo generators.
The τ\to (a_1 h)^- ν_τ decays of the τ-lepton are studied using the method of phenomenological chiral Lagrangians. The expression of weak hadronic currents between pseudoscalar and axial-vector meson states is obtained. Calculated partial widths for these decays are compared with the available experimental data.
We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite.
A combination of finite energy sum rule techniques and Chiral Perturbation Theory (ChPT) is used in order to exploit recent ALEPH data on the non-strange tau vector (V) and axial-vector (A) spectral functions with respect to an experimental determination of the ChPT quantity L_{10}. A constrained fit of R_{τ,V-A}^(k,l) inverse moments (l<0) and positive spectral moments (l>=0) adjusts simultaneously L_{10} and the nonperturbative power terms of the Operator Product Expansion. We give explicit formulae for the first k=0,1 and l=-1,-2 strange and non-strange inverse moment chiral sum rules to on…
Evidence of a new particle with mass ~125 GeV decaying into a pair of tau leptons at the Large Hadron Collider spurs interest in ascertaining its spin in this channel. Here we present a comparative study between spin-0 and spin-2 nature of this new particle, using spin correlations and decay product directions. The TauSpinner algorithm is used to re-weight distributions from qqbar -> gamma/Z -> tau+ tau- sample to simulate a spin-2 state exchange. The method is based on supplementing the Standard Model matrix elements with those arising from presence of a new interaction. Studies with simulate…
Measurements of tau lepton, because of its long lifetime, large mass and parity sensitive couplings lead to broad physics interest. From the perspective of high-energy experiments such as at LHC, knowledge of tau lepton properties offers an important ingredient of new physics signatures. From the perspective of lower energies, tau lepton decays constitute an excellent laboratory for hadronic interactions. At present,hundreds of millions of tau decays have been amassed by both Belle and BaBar experiments. It is of utmost importance to represent such data in a form as useful for general applicat…
Hadronization in tau -> K K pi nu_tau decays is driven by both vector and axial-vector currents that we study, guided by the following principles: The 1/N_C expansion -worked out at leading order, considering only the contribution of the lightest spin one resonances-, approximate chiral symmetry at low energies and the appropriate asymptotic behaviour we demand to the associated form factors. All these features are implemented in the resonance theory. Most of its couplings are determined by imposing the short-distance requirements of vector and axial-vector spectral functions within QCD. We pl…
An intrinsic parity violating hadronic tau lepton decay is investigated. $τ\to ππην$ is the process in which the dominant contribution to the amplitude is due to the intrinsic parity violation. To predict the hadronic invariant mass spectra and to compare them with experimental data, we extend the chiral Lagrangian with vector mesons so that it incorporates the intrinsic parity violating terms and $ϕ$ and $η^\prime$ mesons. The coefficients of the intrinsic parity violating terms will be determined by fitting the branching fractions for $V^I \rightarrow P γ$, $V^I \rightarrow 3 P$ and $P \to V…
I discuss the recent attempts to build an effective chiral Lagrangian incorporating massive resonance states. A useful approximation scheme to organize the resonance Lagrangian is provided by the large-Nc limit of QCD. Integrating out the resonance fields, one recovers the usual chiral perturbation theory Lagrangian with explicit values for the low-energy constants, parameterized in terms of resonance masses and couplings. The resonance chiral theory generates Green functions that interpolate between QCD and chiral perturbation theory. Analyzing these Green functions, both for large and small …
The conditions for the independence of decays of the spin-1/2 resonances on the production mechanism of the resonances and on polarizations of the incoming and outgoing particles are derived and applied in the case of several tau-lepton decays. The necessity for inclusion of the influence of the production mechanism in the evaluation of the lepton flavour violating decays is stressed.
The QCD sum rule approach is employed in order to study chiral properties of positive- and negative-parity nucleon resonances. It is pointed out that nucleons with an ``exotic'' chiral property, which can be represented by local five-quark operators, can be paired with a standard nucleon forming a single chiral multiplet. The sum rules of the five-quark operators, however, are shown not to couple strongly to chirally-``exotic'' nucleon resonances at the mass region of less than 2 GeV.
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $Δ(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $Δ$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
We consider the sneutrino resonance reaction l^+ l^- -> sneutrino -> tau^+ tau^- in the MSSM without R-parity. We introduce new CP-violating and CP-conserving tau-spin asymmetries which are generated already at the tree-level if there is sneutrino - sneutrino-bar mixing and that are forbidden in the SM. It is remarkable that these spin asymmetries can reach ~75% around resonance for a sneutrino mass splitting of Δm ~ Γand ~10% for a splitting as low as Δm ~ 0.1Γ, where Γis the sneutrino width. We show that they are easily detectable already at LEP2 so long as the beam energy is within ~10 GeV …
Using recent precise hadronic tau-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energy constants appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L_10^r(M_rho) = -(5.22\pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06\pm 0.39)10^{-3} and…
Current theoretical studies on the $σ$ and $κ$ resonances are reviewed. It is emphasized that all evidences accumulated so far are consistent with the picture that the $σ$ meson is the chiral partner of the Nambu--Goldstone bosons in a linear realization of chiral symmetry.
The contributions of the lightest tensor-meson resonances to the low-energy coupling constants of second order chiral perturbation theory with two flavours are evaluated and compared with the available phenomenological information as well as with similar results for other resonances.
The divergent part of the generating functional of the Resonance Chiral Theory is evaluated up to one loop when one multiplet of scalar an pseudoscalar resonances are included and interaction terms which couple up to two resonances are considered. Hence we obtain the renormalization of the couplings of the initial Lagrangian and, moreover, the complete list of operators that make this theory finite, at this order.
Within Chiral Perturbation Theory, we study elastic pion scattering in the I=0, J=2, channel, whose main features are the f2(1270) resonance and the vanishing of the lowest order. By means of a chiral model that includes an explicit resonance coupled to pions, we describe the data and calculate the resonance contribution to the O(p^4) and O(p^6) chiral parameters. We also generalize the Inverse Amplitude Method to higher orders, which allows us to study channels with vanishing lowest order. In particular, we apply it to the I=0,J=2 case, finding a good description of the f2(1270) resonance, as…
Parameters of the effective chiral lagrangian (EChL) of orders $O(p^4)$ and $O(p^6)$ are extracted from low--energy behaviour of dual resonance models for $ ππ$ and $πK$ scattering amplitudes. Dual resonance models are considered to be good candidates for the resonance spectrum and for hadronic scattering amplitudes in the large $N_c$ limit of QCD. We discuss dual resonance models in the presence of spontaneous and explicit chiral symmetry breaking. Obtained parameters of the EChL are used to estimate chiral corrections up to the sixth order to various low--energy characteristics of $ππ$ and $…
The mass spectrum of Delta resonances is compared to predictions based on three quark-model variants, to predictions assuming that chiral symmetry is restored in high-mass baryon resonances, and to predictions derived from AdS/QCD. The latter approach yields a nearly perfect agreement when the confinement property of QCD is modeled by a soft wall in AdS.
The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-Nc chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/Nc expansion.
The tau -> pi pi pi nu_tau decay is driven by the hadronization of the axial-vector current. Within the resonance chiral theory, and considering the large-Nc expansion, this process has been studied in Ref.[1]. In the light of later developments we revise here this previous work by including a new off-shell width for the lightest a_1 resonance that provides a good description of the tau -> pi pi pi nu_tau spectrum and branching ratio. We also consider the role of the rho(1450) resonance in these observables. Thus we bring in an overall description of the tau -> pi pi pi nu_tau process in excel…
We discuss the sensitivity of the $e^+ e^- \rightarrow W^+ W^-$ cross section at a future $e^+ e^-$ collider with $\sqrt{s}=500$GeV to the non-decoupling effects of a techni-$ρ$ like vector resonance. The non-decoupling effects are parametrized by the chiral coefficients of the electroweak chiral perturbation theory. We define renormalization scale independent chiral coefficients by subtracting the Standard Model loop contributions. We also estimate the size of the decoupling effects of the techni-$ρ$ resonance by using a phenomenological Lagrangian including the vector resonance.
We calculate the width of the delta resonance at leading two-loop order in baryon chiral perturbation theory. This gives a correlation between the leading pion-nucleon-delta and pion-delta couplings, which is relevant for the analysis of pion-nucleon scattering and other processes.
Strong anomaly of the PCAC is found in $τ\rightarrowωππν$ and $ωρν$ in the chiral limit. It originates in WZW anomaly. Theoretical result of $τ\rightarrowωππν$ agrees with data well and the measurement of $τ\rightarrowωρν$ will confirm the strong anomaly of PCAC. The strong anomaly of PCAC is studied.
Until present the study of the form factors associated to the vector and axial-vector components of the hadronic weak current has been carried out with a plethora of modelizations of the underlying strong interactions. While of importance to get an understanding of the dynamics involved, the amount and quality of the experimental data start to show some discrepancies with the analysed models. Moreover, and from a theoretical point of view, most of these models are not consistent with quantum chromodynamics (QCD). We propose a QCD-based model-independent procedure to analyse those decays throug…
We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.
We discuss recent results regarding the interplay between chiral and $U(1)_A$ symmetry restoration, both from the point of view of Ward Identities relating meson susceptibilities and quark condensates, and from the behaviour of light meson resonances at finite temperature
A proper estimation of the chiral low-energy constants of Chiral Perturbation Theory is a very important task. To this end resonance chiral Lagrangians have been used fruitfully. We have studied the determination of chiral couplings at next-to-leading (NLO) order in the 1/N(C) expansion, keeping full control of the renormalization scale dependence. We find that, by imposing short-distance constraints coming from QCD, resonance saturation at NLO in 1/N(C) is satisfied. In other words, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly…
We analyse the hadronization structure of both vector and axial-vector currents leading to tau -> KKpi nu_tau decays. At leading order in the 1/Nc expansion, and considering only the contribution of the lightest resonances, we work out, within the framework of the resonance chiral Lagrangian, the structure of the local vertices involved in those processes. The couplings in the resonance theory are constrained by imposing the asymptotic behaviour of vector and axial-vector spectral functions ruled by QCD. In this way we predict the hadron spectra and conclude that, contrarily to previous assert…
It is shown that the implementation of the Large--$N_c$ approximation helps to get insight into the structure of, in principle, any QCD-like theory. As an example, we will compute the NLO corrections to $L_{10}$ in the chiral limit with a Lagrangian with Resonances.
The precision obtainable in phenomenological applications of Chiral Perturbation Theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-Nc resonance lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/Nc expansion within the framework of Resonance Chi…
