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 momenta, one gets QCD constraints on the resonance couplings and, therefore, information on the low-energy constants governing the Goldstone interactions.
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.
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.
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 $…
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.
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.
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.
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…
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…
We present a calculation of the Vector Form Factor at the next-to-leading order in the 1/N_C expansion, within the framework of Resonance Chiral Theory. The calculation is performed in the chiral limit, and with two dynamical quark flavours. The ultraviolet behaviour of quantum loops involving virtual resonance propagators is analyzed, together with the kind of counterterms needed in the renormalization procedure. Using the lowest-order equations of motion, we show that only a few combinations of local couplings appear in the final result. The low-energy limit of our calculation reproduces the…
We use the Interacting Instanton Liquid Model (IILM) as a tool to study the role played by the chiral interactions in the lowest-lying vector and axial vector meson resonances. We find that narrow a1 and rho meson resonances can be generated by instanton-induced chiral forces, even in the absence of confinement. In the IILM, these hadrons are found to have masses only about 30% larger than the experimental value and small width <10-50 MeV. This result suggests that chiral interactions are very important in these systems and provide most of their mass. We explore the decaying patterns of the rh…
Chiral lagrangians provide a model independent description of the strongly interacting symmetry breaking sector. In this work it is first reviewed the LHC sensitivity to the chiral parameters (in the hardest case of non-resonant low-energy WW scattering). Later it is shown how to reproduce or predict the resonance spectrum by means of dispersion theory and the inverse amplitude method. We present a parameter space scan that covers many different strong WW scattering scenarios.
Spectrum of the low-lying $Ω_{cc}$ resonances with negative parity, which are assumed to be dominated by $sccq\bar{q}$ pentaquark components, is investigated using the chiral constituent quark model. Energies of the $Ω_{cc}$ resonances are obtained by considering the hyperfine interaction between quarks by exchanging Goldstone boson. Possible $sccq\bar{q}$ configurations with spin-parity $1/2^{-}$, $3/2^{-}$ and $5/2^{-}$ are taken into account. Numerical results show that the lowest $Ω_{cc}$ resonances with negative parity may lie at $4050 \pm 100$ MeV. In addition, the transitions of the $Ω_…
In the first part of the talk, I discussed results on the determination of the ratios of the light quark masses from large N_c chiral perturbation theory, to be described elsewhere. The following notes contain material from the second part of the talk, which concerns the implications of large N_c for resonance dominance estimates of the low energy coupling constants in chiral perturbation theory.
A chiral Lagrangian with $ SU(3) $ breaking and higher resonances is proposed. In this model, the $ SU(3) $ breaking structure in vector-pseudoscalar sector is realized with the decay constants of pseudoscalar mesons and the masses of vector mesons used as inputs. We examine whether the resulting $ SU(3) $ breaking effect in the charge radii of pseudoscalar mesons is consistent with the experimental facts.
We review our recent study of the pion mass dependence of the rho and sigma resonances generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM) which was modified to properly account for the Adler zero. The method is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the pion mass dependence of the resonance pole positions from the ChPT series up to a given order. We find that the rho-pi-pi coupling constant is almost m_pi independent and that our prediction compare well with some recent lattice results for the rho mas…
We show how parametric resonance mechanism follows quench mechanism in the classical linear sigma model. The parametric resonance amplifies long wavelength modes of the pion for more than $10 fm/c$. The shifting from the quench mechanism to the parametric resonance mechanism is described by a time dependent quantity. After the quench mechanism is over, that quantity has an oscillating part, which causes the parametric resonance. Since its frequency is $2 m_π~(m_π$ : pion mass), very long wavelength modes such as k = 40 MeV of the pion are amplified by the parametric resonance.
We show that the f_0(980) and a_0(980) states appearing in scattering and production processes can be described quite well by the two-channel Oller-Oset-Peláez (OOP) version of unitarized chiral theories. It is impossible, however, to deduce a conclusion on the nature of them from the fitting to experimental data alone. Using explicit N_c dependence of parameters in OOP amplitudes we demonstrate that light scalar resonances are not of q\bar q states but dynamical rescattering effects generated under chiral symmetry, unitarity and channel couplings.
We review recent work on thermal resonances and their connection with chiral symmetry and $U(1)_A$ restoration within the QCD phase diagram. In particular, the $f_0(500)$ and $K_0^* (700)$ states generated from $ππ$ and $πK$ scattering within Unitarized Chiral Perturbation Theory (ChPT) at finite temperature allow one to describe scalar susceptibilities, which combined with Ward Identities yield interesting conclusions regarding the interplay between chiral and $U(1)_A$ restoration, key to understand the nature of the transition
We discuss the renormalization of the $1^{--}$ vector meson propagator within Resonance chiral theory at one loop. Using the particular form of the interaction Lagrangian we show that additional poles of the renormalized propagator corresponding to $1^{+-}$ degrees of freedom can be generated. We give a concrete example of such an effect.
Baryon chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom is considered. Using the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective field theory with a systematic power counting is obtained. As applications we discuss the mass of the nucleon, the pion-nucleon sigma term, and the pole of the $Δ$ propagator.
We modify a chiral effective lagrangian recently suggested to describe interactions of the light pseudoscalars with mesons containing a heavy quark, so as to incorporate light vector resonances, such as $ρ$, etc. The modification uses the hidden gauge symmetry approach. As a preliminary example we present an application to the semileptonic $D\to K^\star$ decay.
Quantum loops in the Resonance Chiral Theory are needed to improve the implementation of non-perturbative QCD. Furthermore, the one-loop computations can predict chiral low-energy couplings at next-to-leading order, a very appealing task. We present a first calculation of the vector form factor of the pion at subleading order in the 1/N_C expansion. From the analysis of the result at large energies we justify the requirement of considering short-distance constraints from form factors with resonances in the final state. The long-distance limit of our results allows to get a next-to-leading orde…
We review our recent one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. By unitarizing these amplitudes we are able to generate dynamically the lightest resonances in meson-meson scattering. We thus obtain a remarkable description of the meson-meson scattering data right from threshold up to 1.2 GeV, in terms of chiral parameters in good agreement with previous determinations.
We study the relation of vector Proca field formalism and antisymmetric tensor field formalism for spin-one resonances in the context of the large N_C inspired chiral resonance Lagrangian systematically up to the order O(p6) and give a transparent prescription for the transition from vector to antisymmetric tensor Lagrangian and vice versa. We also discuss the possibility to describe the spin-one resonances using an alternative "mixed" first order formalism, which includes both types of fields simultaneously, and compare this one with the former two. We also briefly comment on the compatibilit…
We review the unitarization of Chiral Perturbation Theory with dispersion relations and how it describes meson-meson scattering data, generating light resonances whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.
Equivalence of the hidden local symmetry formulation with non-minimal interactions and the anti-symmetric tensor field method of $ρ$ and $a_1$ mesons in the chiral lagrangian is shown by using the auxiliary field method. Violation of the KSRF I relation, which becomes important in the application of chiral lagrangian to {\em non QCD-like} technicolor models can be parametrized by non-minimal coupling in the hidden local symmetry formalism keeping low energy theorem of hidden local symmetry. We also obtain explicit correspondence of parameters in both formulations.
We study heavy-light baryon resonances with quantum numbers J^P=1/2^- in terms of the non-linear chiral SU(3) Lagrangian. Within the chi-BS(3) approach a parameter-free leading order prediction is obtained for the scattering of Goldstone bosons off heavy-light baryon resonances with J^P=1/2^+. The three states Lambda_{c1}(2593), Lambda_{c0}(2880) and Xi_{c1}(2790) discovered by the CLEO collaboration are recovered. We suggest the existence of resonance states that form an anti-quindecimplet, two sextet and two anti-triplet representations of the SU(3) group. In particular, narrow states with a…
We study the problems related to the renormalization of propagators in Resonance Chiral Theory, concentrating on the case of vector $1^{--}$ resonances in the antisymmetric tensor formalism. We have found that renormalization of the divergences of the self-energy graphs needs new type of kinetic counterterms with two derivatives which are not present in the original leading order Lagrangian. The general form of the propagator for antisymmetric tensor fields could then contain not only poles corresponding to the original $1^{--}$ resonance states but also to the additional states with opposite …
We discuss the formation of s- and d-wave baryon resonances as predicted by the chiral SU(3) symmetry of QCD. Based on the leading order term of the chiral Lagrangian a rich spectrum of molecules is generated, owing to final-state interactions. The spectrum of s- and d-wave baryon states with zero and non-zero charm is remarkably consistent with the empirical pattern. In particular, the recently announced Sigma_c(2800) of the BELLE collaboration is reproduced with realistic mass and width parameters. Similarly, the d-wave states Lambda_c(2625) and Xi_c(2815) are explained naturally to be chira…
This PhD thesis is a first step towards the control of the quantum corrections in the Resonance Chiral Theory, the suggested framework to handle QCD in the resonance region. After a theoretical introduction, Chapter 3 is devoted to calculate the vector form factor of the pion at the next-to-leading order in the 1/N(C) expansion. The ultraviolet behaviour of the calculation is analyzed, together with the needed counterterms in the renormalization procedure. The long-distance limit allows to determine the resonance contribution to the low-energy constants of Chiral Perturbation Theory at the NLO…
As an alternative to the two-quark condensate we propose a specific four-quark condensate as an order parameter of chiral symmetry restoration. We show that this four-quark condensate is closer connected to observable quantities. Within a resonance gas model we calculate the in-medium changes of two- and four-quark condensate as functions of temperature and baryo-chemical potential. In this way we estimate the line of chiral symmetry restoration in the temperature-potential plane and also as a function of energy and baryon density. It turns out that the line determined from the vanishing of th…
We calculate the width of the Roper resonance at next-to-leading order in a systematic expansion of baryon chiral perturbation theory with pions, nucleons, and the delta and Roper resonances as dynamical degrees of freedom. Three unknown low-energy constants contribute up to the given order. One of them can be fixed by reproducing the empirical value for the width of the Roper decay into a pion and a nucleon. Assuming that the remaining two couplings of the Roper interaction take values equal to those of the nucleon, the result for the width of the Roper decaying into a nucleon and two pions i…
In this talk we report on the use of a chiral unitary approach for the interaction of the octets of meson and baryon and the octet of mesons with the decuplet of baryons. Two octets of $J^π=1/2^-$ baryon states and a singlet are generated dynamically in the first case, resulting in the case of strangeness $S=-1$ in two poles of the scattering matrix close to the nominal $Λ(1405)$ resonance. In the second case many resonances are also generated, among them an exotic baryon with S=1 corresponding to a $ΔK$ resonance. We make suggestions of experiments which could show evidence for the existence …
The use of the equations of motion and meson field redefinitions allows the development of a simplified resonance chiral theory lagrangian: terms including resonance fields and a large number of derivatives can be reduced into corresponding O(p2) resonance operators, containing the lowest possible number of derivatives. This is shown by means of the explicit computation of the pion vector form-factor up to next-to-leading order in 1/Nc. The study of the renormalization group equations for the corresponding couplings demonstrates the existence of an infrared fixed point in the resonance theory.…
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.
Charmed meson resonances with quantum numbers J^P=0^+ and J^P=1^+ are generated in terms of chiral coupled-channel dynamics. At leading order in the chiral expansion a parameter-free prediction is obtained for the scattering of Goldstone bosons off charmed pseudo-scalar and vector mesons. The recently announced narrow open charm states observed by the BABAR and CLEO collaborations are reproduced. We suggest the existence of states that form an anti-triplet and a sextet representation of the SU(3) group. In particular, so far unobserved narrow isospin-singlet states with negative strangeness ar…
The features of the Resonance Chiral Theory (RChT) related to the description of the lightest scalar resonances, sigma, f0(980) and a0(980), are discussed. Major attention is paid to the fits of the invariant mass distributions in the radiative decays of the phi(1020) meson. The study of the scalar sector in RChT is motivated by the success of the theory predictive power in numerous processes with other types of resonances. We conclude that RChT is sufficiently flexible to describe these decays, however the further quantitative improvement is required. The technical work-outs and related impor…
The all--important consequence of Chiral Dynamics for $ππ$ scattering is the Adler zero, which forces $ππ$ amplitudes to grow asymptotically. The continuation of this subthreshold zero into the physical regions requires a $P$--wave resonance, to be identified with the $ρ$. It is a feature of $ππ$ scattering that convergent dispersive integrals for the $I=1$ channel are essentially saturated by the $ρ$--resonance and are much larger than those with $I=2$ quantum numbers. These facts predict the parameters $\overline{\ell}_1$, $\overline{\ell}_2$ of the Gasser--Leutwyler Chiral Lagrangian, as we…
The phi(1020) radiative decays form a good playground for study of the low-lying a0(980) and f0(980) scalar mesons. The complicated interplay of kaon loop mechanism, isoscalar meson mixing and momentum dependence of the effective couplings manifests itself in the invariant mass distributions in the phi(1020) -> pi0 pi0 gamma and pi eta gamma spectra. These distributions are fitted in framework of Resonance Chiral Theory.
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.
A review on the requirements of chiral symmetry on effective quark models is presented. The connection between the pion Salpeter amplitude and the mass gap equation is discussed. Hadronic scattering, notably, $ππ$ scattering is presented. The constraints imposed by chiral symmetry between difractive quark scattering and quark-quark annihilation is presented. Hadronic coupled channels as a consequence of quark-quark annihilation are discussed together with the $^3P_0$ mecahnism. Graphical-rules diagrams are intoduced as a means to evaluate hadronic coupled channel transition potentials. Their r…
The formulas for the temperature dependences of the non-strange and strange quark condensates are derived by taking into account the contribution of the massive resonances. Critical temperature of the chiral symmetry restoration transition is established to be 190 MeV if only meson resonances are considered, and 175 MeV if both meson and baryon resonances are taken into account.
We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. On the ot…
With an effective chiral flavour SU(3) model we show the effect of hadronic resonances on the QCD phase diagram. We state that varying the resonance couplings to the scalar and vector fields affects the order and location of the phase transition, the possible existence of a critical end point (CEP), and the thermodynamic properties. We present (strange) quark number susceptibilities at zero baryochemical potential and at three different points at the phase transition. Comparing results to lattice QCD, we state that reasonable large vector couplings limit the phase transition to a smooth crosso…
The use of the equations of motion and meson field redefinitions allows the simplification of the subleading operators required in the one-loop resonance chiral theory calculation of the pi pi vector form-factor. The study of the renormalization group equations of the relevant parameters shows the existence of an infrared fixed point for all the couplings. It is important to remark that this result does not rely on the high-energy form-factor constraints, which are often considered in other works. The possibility of developing a perturbative 1/Nc expansion in the slow running region around the…
Guided by the large-Nc limit of QCD, we construct the most general chiral resonance Lagrangian that can generate chiral low-energy constants up to O(p^6). By integrating out the resonance fields, the low-energy constants are parametrized in terms of resonance masses and couplings. Information on those couplings and on the low-energy constants can be extracted by analysing QCD Green functions of currents both for large and small momenta. The chiral resonance theory generates Green functions that interpolate between QCD and chiral perturbation theory. As specific examples we consider the VAP and…
