We investigate the $a_0(980)$ resonance within chiral effective field theory through a three-coupled-channel analysis, namely $πη$, $K\bar{K}$ and $πη'$. A global fit to recent lattice finite-volume energy levels from $πη$ scattering and relevant experimental data on a $πη$ event distribution and the $γγ\toπη$ cross section is performed. Both the leading and next-to-leading-order analyses lead to similar and successful descriptions of the finite-volume energy levels and the experimental data. However, these two different analyses yield different $πη$ scattering phase shifts for the physical masses for the $π, K, η$ and $η'$ mesons. The inelasticities, the pole positions in the complex energy plane and their residues are calculated both for unphysical and physical meson masses.
Both scalar and vector light resonances can be generated from the unitarization of one-loop chiral perturbation theory. This amounts to using in a dispersion relation the chiral expansion, which incorporates the correct QCD quark mass dependence. We can thus predict the quark mass dependence of the poles associated to those light resonances. Our results compare well with some recent lattice results for the rho(770) mass and can be used as a benchmark for future lattice results on the rho(770) or the f0(600) also known as the sigma.
The leading one-loop corrections to the gravitational form factors of the delta resonance are calculated in the framework of chiral effective field theory. Various contributions to the energy-momentum tensor and the renormalization of the low-energy constants are worked out. Using the small scale expansion, expressions for static quantities are obtained and the real and imaginary parts of the gravitational form factors are calculated numerically.
In this work we address the question of how well the chiral crossover transition can be understood in terms of a noninteracting hadron resonance gas model. Using the latest results on the variation of hadron masses as a function of the pion mass from lattice quantum chromodynamics, we study the temperature dependence of the renormalized chiral condensate in 2+1 flavor QCD. Furthermore, we suggest a better criterion to estimate of the pseudocritical temperature, which gives $T_c = 161.2 \pm 1.7$ MeV, which is much improved compared to all the earlier results within the hadron resonance gas mode…
The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance.
The Lattice results for the pion and kaon decay constants are analysed within the Resonance Chiral Theory framework in the large NC limit. The approximately linear behaviour of the observable at large light-quark mass is explained through the interaction with the lightest multiplet of scalar resonances. The analysis of the Lattice results allows to obtain the resonance mass MS=1049 +- 25 MeV and the Chiral Perturbation Theory parameters at leading order in 1/NC.
There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presented
Explicit expressions for pion correlators are derived in position-space, employing Chiral Perturbation Theory (ChPT). Resonance exchange contributions are included to test the range of applicability of the leading-order ChPT expressions. The obtained results will be useful for a forthcoming Lattice-QCD study of double parton distributions in the pion.
We calculate the magnetic moments of the N(1535) resonance using the chiral unitary model, where the resonance is dynamically generated in the scatterings of the lowest-lying mesons and baryons. We obtain the magnetic moments of the resonance as +1.1 and -0.25 for p(1535) and n(1535), respectively, in units of the nuclear magneton. We discuss the origin of these numbers within the chiral unitary model, then we compare the present results with those of the quark model and the chiral doublet model. The possibility to observe the magnetic moments in experiments is also investigated.
The dimensionless parameter $ξ= M_π^2/(16 π^2 F_π^2)$, where $F_π$ is the pion decay constant and $M_π$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calcula…
We stress, on theoretical and phenomenological grounds, the importance of the $Δ(1232)$-resonance in a chiral effective field theory approach applied to the study of $πN$ scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from $πN$ scattering data.
We study the chiral behavior of the nucleon and $Δ$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $πN$ and $πΔ$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $πN…
Heavy baryon chiral perturbation theory is briefly reviewed, paying particular attention to the role of the spin 3/2 delta resonances. The concept of resonance saturation for the baryonic sector is critically discussed. Starting from a relativistic formulation of the pion-nucleon-delta system, the heavy baryon chiral lagrangian including spin 3/2 resonances is constructed by means of a 1/m-expansion. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $M_π$ and the delta-nucleon mass difference $Δ$.
We study the resonance properties within chiral perturbation theory by explicitly taking into account the U_A(1) anomaly effect. This assures we have the appropriate degrees of freedom of low energy QCD in the large Nc limit. We calculate the various resonance properties, such as mass, width and residues, for the physical case, i.e. Nc=3. Then we extrapolate the values of Nc to study the trajectories of resonance poles.
Chiral quark models with Polyakov loop at finite temperature have been often used to describe the phase transition. We show how the transition to a hadron resonance gas is realized based on the quantum and local nature of the Polyakov loop.
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.
We present a detailed analysis of S-wave Kpi scattering up to 2 GeV, making use of the resonance chiral Lagrangian predictions together with a suitable unitarisation method. Our approach incorporates known theoretical constraints at low and high energies. The present experimental status, with partly conflicting data from different experiments, is discussed. Our analysis allows to resolve some experimental ambiguities, but better data are needed in order to determine the cross-section in the higher-energy range. Our best fits are used to determine the masses and widths of the relevant scalar re…
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 …
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.
Baryon resonances with even and odd parity are collectively investigated from the viewpoint of chiral symmetry(ChS). We propose a quartet scheme where Delta's and N^*'s with even and odd parity form a chiral multiplet. This scheme gives parameter-free constraints on the baryon masses in the quartet, which are consistent with observed masses with spin 1/2, 3/2, 5/2. The scheme also gives selection rules in the one-pion decay: The absence of the parity non-changing decay N(1720) -> pi Delta(1232) is a typical example which should be confirmed experimentally to unravel the role of ChS in baryon r…
We discuss baryon resonances which are dynamically generated in hadron dynamics based on chiral coupled channels approach. With the dynamical description of the baryon resonance, we discuss the origin of the resonance pole, finding that for the description of N(1535) some other components than meson and baryon are necessary. Since the chiral unitary model provides a microscopic description in terms of constituent hadrons, it is straightforward to calculate transition amplitudes and form factors of resonances without introducing further parameters. Finally we briefly discuss few-body nuclear ka…
We consider the electromagnetic transition form factors of the Roper resonance in the framework of an effective field theory of pions, nucleons and delta and Roper resonances as explicit degrees of freedom. Due to the lack experimental data in the region of applicability of low energy effective field theory we fit available free coupling constants and compare obtained results compare to the predictions of a theoretical model.
A calculation for the one-loop pion vector form-factor in Resonance Chiral Theory is provided in this talk. The amplitude is computed up to next-to-leading order in 1/Nc and, by means of high-energy constraints, we are able to produce a prediction for the corresponding O(p4) Chiral Perturbation Theory low energy constant L9(mu)=(7.6+- 0.6) 10^{-3} at the scale mu=770 MeV.
We perform a relativistic chiral effective field theory calculation of the radiative pion photoproduction ($γp \to π^0 p γ'$) in the $Δ$-resonance region, to next-to-leading order in the ``delta-expansion''. This work is aimed at a model-independent extraction of the $Δ^+$ magnetic moment from new precise measurements of this reaction. It also predicts the chiral behavior of $Δ$'s magnetic moment, which can be used to extrapolate the recent lattice QCD results to the physical point.
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.
We analyze s-wave pion-nucleon scattering in a unitarized chiral effective Lagrangian including all dimension two contact terms. We find that both the S11(1535) and the S11(1650) are dynamically generated, but the S31(1620) is not. We further discuss the structure of these dynamically generated resonances.
Several conceptual points concerning the inclusion of the $Δ$(1232) resonance in the framework of chiral effective-field theory are discussed, with an emphasis on the problem of power counting in the baryon sector in general. I also formulate a new dispersion relation in the pion-mass squared (or, the quark mass) and make a link between the power counting and the analytic properties of chiral expansion. A controversy regarding the determination of the proton's magnetic polarizability from Compton-scattering data is stressed here as well.
We have recently completed the one loop calculation of meson-meson scattering within Chiral Perturbation Theory. Once unitarized, these amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, respecting the chiral symmetry expansion. The position of the poles in these amplitudes is related to the mass and width of the associated resonances that are generated without being explicitly included in the Lagrangian. The spectroscopic nature of these states can then be deduced by studying the behavior of these poles, through t…
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 show the results for the scattering poles associated to the rho, f0, a0, K*, sigma and kappa resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.
We report on our recent progress in the generation of resonant behavior in unitarized meson-meson scattering amplitudes obtained from Chiral Perturbation Theory. These amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, since they respect the chiral symmetry expansion. By studying the position of the poles in these amplitudes it is possible to determine the mass and width of the associated resonances, as well as to get a hint on possible classification schemes, that could be of interest for the spectroscopy of the s…
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. We report on an update of these results examining their possible relevance for meson spectroscopy.
We study the origin of the resonances associated with pole singularities of the scattering amplitude in the chiral unitary approach. We propose a "natural renormalization" scheme using the low-energy interaction and the general principle of the scattering theory. We develop a method to distinguish dynamically generated resonances from genuine quark states [Castillejo-Dalitz-Dyson (CDD) poles] using the natural renormalization scheme and phenomenological fitting. Analyzing physical meson-baryon scatterings, we find that the Lambda(1405) resonance is largely dominated by the meson-baryon molecul…
We study a chirally invariant Higgs-Yukawa model regulated on a space-time lattice. We calculate Higgs boson resonance parameters and mass bounds for various values of the mass of the degenerate fermion doublet. Also, first results on the phase transition temperature are presented. In general, this model may be relevant for BSM scenarios with a heavy fourth generation of quarks.
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 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…
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.
In this paper we document the modifications introduced to the previous version of the Resonance Chiral Lagrangian current ({\it Phys.Rev.} {\bf D86} (2012) 113008) of the $τ^\pm \to π^\pm π^\pm π^\mp ν_τ$ decay which enable the one dimensional distributions measured by the BaBar collaboration to be well modeled. The main change required to model the data is the addition of the $σ$ resonance. Systematic errors, theoretical and experimental ones, limitations due to fits of one dimensional distributions only, and resulting difficulties and statistical/systematic errors for fitted parameters are a…
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.
As the pion mass approaches a critical value $m_π^\star$ from below, an $S$-wave resonance crosses pion-baryon threshold and becomes a bound state with arbitrarily small binding energy, thus driving the scattering length to diverge. I explore the consequences of chiral symmetry for the values of $m_π$ close to $m_π^\star$. It turns out that chiral symmetry is crucial for an $S$-wave resonance to be able to stand very near threshold and in the meantime to remain narrow, provided that the mass splitting is reasonably small. The effective range of pion-baryon scattering is unexpectedly large, pro…
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…
The hadronization structure of $τ^- \to ηπ^- π^0 ν_τ$ decays is analyzed using Chiral Perturbation Theory with resonances, considering only the contribution of the lightest meson resonances at leading order in the $1/N_C$ expansion. After imposing the asymptotic behavior of vector spectral functions ruled by QCD, unknown effective couplings are determined by fitting the $τ^- \to ηπ^- π^0 ν_τ$ branching ratio and decay spectrum to recent data. Predictions for the partner decay $τ^- \to η^\prime π^- π^0 ν_τ$ and the low-energy behavior of the cross section $σ(e^+e^-\to ηπ^+π^-)$ are also discuss…
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 construct pi-pi amplitudes that fulfill exact elastic unitarity, account for one loop Chiral Perturbation Theory contributions and include all 1/Nc leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such scheme, the Nc dependence of sigma and rho masses and widths is discussed. Robust conclusions are drawn in the case of the rho resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, Nc. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of data…
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…
Based on the recent phenomenological analysis done by M. Mojzis, Eur. Phys. Jour. {\bf C2} (1998) 182, of $πN $ scattering within the framework of Heavy Baryon Chiral Perturbation Theory we predict, after a suitable unitarization of the amplitude, the $Δ$ resonance at $\sqrt{s} = M_Δ= 1238 \er{22}{18}{\rm MeV} $ and with a width of $ Γ_Δ= 150 \er{43}{31} {\rm MeV} $ in excellent agreement with the experimental numbers. The error bars reflect only the uncertainties in the low energy parameters as determined from an extrapolation to threshold of experimental data. We also describe satisfactorily…
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…
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.
