We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays $B_s\to π^+π^-\ell^+\ell^-$ and the $τ$ lepton decay $τ\rightarrowπ^{-}π^{0}ν_τ$, in searches for physics beyond the Standard Model.
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 extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
An investigation of the s-wave channels in meson-meson scattering is performed within a U(3) chiral unitary approach. Our calculations are based on a chiral effective Lagrangian which includes the eta' as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. We employ a coupled channel Bethe-Salpeter equation to generate poles from composed states of two pseudoscalar mesons. Our results are compared with experimental phase shifts up to 1.5 GeV and effects of the eta' within this scheme are discussed.
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…
We study the hadronic $η^{\prime}\toηππ$ decays within the framework of $U(3)_{L}\otimes U(3)_{R}$ Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the $N/D$ method resumming both the important $S$-and $D$-wave $ππ$ and the subleading $S$-wave $πη$ final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associ…
We present our recent results for the rho and sigma mesons considered as resonances in pion-pion scattering in a thermal bath. We use chiral perturbation theory to fourth order in p for the low energy behaviour, then extend the analysis via the unitarization method of the Inverse Amplitude into the resonance region. The width of the rho broadens about twice the amount required by phase space considerations alone, its mass staying practically constant up to temperatures of order 150 MeV. The sigma meson behaves in accordance to chiral symmetry restoration expectations.
We present a brief account of the developments in the description of light meson resonances using unitarized extensions of the Chiral Perturbation Theory series, both in energy and temperature. In particular, we describe how these methods have been recently shown to describe simultaneously the low energy and resonance regions of meson-meson scattering. This approach could be of relevance to understand the light scalar mesons since it provides a formalism that respects chiral symmetry and unitarity and is able to generate resonant states without any a priori theoretical bias toward their existe…
In this talk we briefly review how the unitarization of Chiral Perturbation Theory with dispersion relations can successfully describe the meson-meson scattering data and generate light resonances, whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.
We review the large Nc behavior of light scalar and vector resonances generated from unitarized meson-meson scattering amplitudes at one loop in Chiral Perturbation Theory. The vectors nicely follow the behavior expected for qqbar states, whereas scalar mesons do not. This suggests that the main component of light scalars is not qqbar. We also comment on t-channel vector exchange as well as on the large Nc behavior of the mass splittings between the vectors generated from the inverse amplitude method.
We calculate the scattering amplitudes of Goldstone bosons off the pseudoscalar D-mesons in unitarized heavy meson chiral approach. The low energy constants appearing in $\mathcal{O}(p^2)$ chiral Lagrangian are determined by fitting lattice simulations on $S$-wave scattering lengths. $D_{s0}^{*}(2317)$ is obtained as a bound state in $(S,I)=(1,0)$ $DK$ channel. Possible bound states or resonance states in other channels are investigated as well. The quark mass dependence of the mass and binding energy of $D_{s0}^{*}(2317)$ is also investigated, which indicates predominately $DK$ molecular natu…
By means of unitarized Chiral Perturbation Theory it is possible to obtain a remarkable description of meson-meson scattering amplitudes up to 1.2 GeV, and generate poles associated to scalar and vector resonances. Since Chiral Perturbation Theory is the QCD low energy effective theory, it is possible then to study its large Nc limit where qqbar states are easily identified. The vectors thus generated follow closely a qqbar behavior, whereas the light scalar poles follow the large Nc behavior expected for a dominant tetraquark or two-meson structure.
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…
We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.
By means of the Inverse Amplitude Method we unitarize the elastic pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral Perturbation Theory to O(q^3). Within this approach we can enlarge their applicability range and generate the Delta(1232) resonance. We can find a reasonable description of the pion nucleon phase shifts with (q^2) parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits…
An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a relativistically covariant, three-dimensional quasipotential framework for scalar particles, using the spline technique. Then, an illustrative toy model with the same dynamical equations but now one $q\bar{q}$ and one meson-meson channel, coupled to one another through quark exchange describing the $^3P_0$ mechanism, is solved in closed form on a spline basis. Co…
We improve the calculations of the $η\to π^0 γγ$ decay within the context of meson chiral lagrangians. We use a chiral unitary approach for the meson-meson interaction, thus generating the $a_0(980)$ resonance and fixing the longstanding sign ambiguity on its contribution. This also allows us to calculate the loops with one vector meson exchange, thus removing a former source of uncertainty. In addition we ensure the consistency of the approach with other processes. First, by using vector meson dominance couplings normalized to agree with radiative vector meson decays. And, second, by checking…
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.
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 show how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the $Δ$ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six $S$ and $P$ wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis.
We study how the scalar mesons below 1 GeV are generated through the Oller-Oset-Pelaez version of the multichannel inverse amplitude method applied to the chiral perturbation theory. We find out that the f0(980) state is certainly generated as a bound state resonance below the K-Kbar threshold, while the a0(980) state, generated through the channel coupling between the pi-eta and K-Kbar channels, appears as a cusp at the K-Kbar threshold. The so-called sigma(500) and kappa(900) need not be interpreted as the conventional resonances.
A unitarized nonrelativistic meson model which is successful for the description of the heavy and light vector and pseudoscalar mesons yields, in its extension to the scalar mesons but for the same model parameters, a complete nonet below 1 GeV. In the unitarization scheme, real and virtual meson-meson decay channels are coupled to the quark-antiquark confinement channels. The flavor-dependent harmonic-oscillator confining potential itself has bound states epsilon(1.3 GeV), S(1.5 GeV), delta(1.3 GeV), kappa(1.4 GeV), similar to the results of other bound-state qqbar models. However, the full c…
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.
By using unitarized two-loop Chiral Perturbation Theory partial waves to describe pion-pion scattering we find that the dominant component of the lightest scalar meson does not follow the q-qbar dependence on the number of colors that, in contrast, is obeyed by the lightest vectors. The method suggests that a subdominant q-qbar component of the f_0(600) possibly originates around 1 GeV.
We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the Inverse Amplitude Method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also prov…
The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.
One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f_0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as is expected for a q-qbar meson, the sigma becomes broader, and its contribution to the total cross section is less and less important. On the other hand, local duality requires a cancellation between the sigma and rho amplitudes, but if there is a different Nc behaviour for them, there is a possible contradiction between the Inverse Amplitude Method (IAM) and local duality for large Nc. However, nex…
The $s-$wave meson-baryon scattering is analyzed for the strangeness S=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $πN$, $ηN$, $K Λ$, $K Σ$. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism and low energy constants are fitted to the elastic $πN $ phase-shifts and the $π^- p \to ηn$ and $π^- p \to K^0 Λ$ cross section data. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and …
We discuss the Padé approximation to the $ππ$ scattering amplitudes in 1--loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produce spurious poles on the complex $s$ plane and therefore plagues its predictions on physical quantities at quantitative level. However we find that one virtual state in the IJ=20 channel may have physical relevance.
We review recent studies of light scalar meson properties by means of unitarization techniques, obtained from dispersion theory, and applied to the Chiral Perturbation Theory expansion. In particular, light scalars do not follow the N_c dependence of $\bar q q$ states although a subdominant quark-antiquark component may be observed to arise for the f_0(600) around 1 GeV, where another quark-antiquark multiplet is believed to exist. Finally, we present our preliminary results on the quark mass dependence of the f_0(600) and rho(770) resonances.
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.
For several decades, the $σ/f_0(500)$ and $κ/K_0^*(700)$ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $σ/f_0(500)$ and $κ/K_0^*(700)$. Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective th…
We study the pion mass dependence of the rho(770) and f_0(600) masses and widths from one and two-loop unitarized Chiral Perturbation Theory. We show the consistency of one-loop calculations with lattice results for the M_rho, f_pi and the isospin 2 scattering length a_20.Then, we develop and apply the modified Inverse Amplitude Method formalism for two-loop ChPT. In contrast to the f_0(600), the rho(770) is rather sensitive to the two-loop ChPT parameters --our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M_rho, f_pi, by…
We study the strange and non-strange quark mass dependence of the parameters of the f_0(600), kappa(800), rho(770) and K*(892) resonances generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. We fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 440 MeV. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattice studies. In these amplitudes, the mass and width of the rho(770) and K*(…
The $s-$wave meson-baryon scattering is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $πΣ$, $\bar K N$, $ηΛ$ and $K Ξ$. The required input to solve the Bethe-Salpeter equation is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. There appear undetermined low energy constants, as a consequence of the renormalization of the amplitudes, which are obtained from fits to the $πΣ\toπΣ$ mass-spectrum, to the elastic $\bar K N \to \bar K N$ and $ \b…
The Bethe-Salpeter equation restores exact elastic unitarity in the $s-$ channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken in the two particle irreducible amplitude and the propagators accomplishing exact elastic unitarity at any step. Renormalizability of the amplitudes can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Crossing constraints can be imposed on the parameters to a given order. Within this framework, we calculate the leading and next-t…
We study the dependence of the pion-pion scattering phase shifts on the light quark mass in both standard and unitarized SU(2) Chiral Perturbation Theory (ChPT) to one and two loops. We then use unitarized SU(3) ChPT to study the elastic f_0(600), kappa(800), rho(770) and K*(892) resonances. The quark masses are varied up to values of interest for lattice studies. We find a very soft dependence on the light quark mass of the pion-pion phase shifts at one loop and slightly stronger at two loops and a good agreement with lattice results. The SU(3) analysis shows that the properties of the rho(77…
The properties of mesonic resonances can be calculated in terms of the low-energy coefficients of chiral perturbation theory (chiPT) by extending unitarized chiPT to higher energies. On the other hand these low-energy coefficients can be calculated in two different models, namely (i) by assuming resonance saturation and (ii) within a constituent quark model. By matching the expressions of the two models combined with the results of unitarized chiPT and the Weinberg sum rules the properties of vector and axial-vector mesons can be calculated in the combined large-N_c and chiral limit.
We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi…
We study the light quark mass dependence of the f_0(600), kappa(800), rho(770) and K*(892) resonance parameters generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. First, we show that it is possible to fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 400 MeV, using chiral parameters compatible with existing determinations. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattic…
In this work, a color structure dependent flip-flop potential is developed for the two quarks and two antiquarks system. Then, this potential is applied to a microscopic quark model which, by integrating the internal degrees of freedom, is transformed into a model of mesons with non-local interactions. With this, the T matrix for the system is constructed and meson-meson scattering is studied. Tetraquarks states, interpreted as poles of of the T matrix, both bound states and resonances, are found. Special emphasis is given to the truly exotic $qq\bar{Q}\bar{Q}$ system, but some results for the…
Using ideas underlying the flavour-blind "Nijmegen Unitarised Meson Model" we try to understand on the basis of a system of Schroedinger equations with one meson-meson and one (spinless) quark-antiquark channel coupled by a simple delta-shell transition potential the formation of (e.g. scalar) meson-meson scattering singularities in the complex momentum and energy plane. Surprisingly we are able to describe without direct meson-meson interaction and without any need for glueballs the whole known scalar meson spectrum. "Light" scalar mesons (e.g. f0(600), kappa(800), f0(980), a0(985), D*0(2290)…
Chiral potentials are derived for the interactions between Goldstone bosons and pseudoscalar charmed mesons up to next-to-next-to-leading order in a covariant chiral effective field theory with explicit vector charmed-meson degrees of freedom. Using the extended-on-mass-shell scheme, we demonstrate that the ultraviolet divergences and the so-called power counting breaking terms can be properly absorbed by the low-energy constants of the chiral Lagrangians. We calculate the scattering lengths by unitarizing the one-loop potentials and fit them to the data extracted from lattice QCD. The obtaine…
The three flavor linear sigma model is studied as a ``toy model'' for understanding the role of possible light scalar mesons in the ππ, πK and πηscattering channels. The approach involves computing the tree level partial wave amplitude for each channel and unitarizing by a simple K-matrix prescription which does not introduce any new parameters. If the renormalizable version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain ππscatteirng, it is ``not quite'' right. A reasonable fit can be made if the renormali…
We review our studies on the rho and sigma resonances properties derived from the Inverse Amplitude Method. In particular, we study the leading $1/N_c$ behavior of the resonances masses and widths and their evolution with changing $m_π$. The $1/N_c$ expansion gives a clear definition of $\bar qq$ states, which is neatly satisfied by the $ρ$ but not by the sigma, showing that its dominant component is not $\bar qq$. The $m_π$ dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that th…
We calculate the S-wave scattering lengths for charmed mesons scattering off Goldstone bosons and explore their quark mass dependence using chiral perturbation theory up to next-to-leading order as well as a unitarized version of it. The quark mass dependence of all scattering lengths determined in a recent lattice calculation can be reproduced by the unitarized version. We also discuss signals of possible bound states in these observables.
In this work, we present an updated study about the interactions of quarkonia with surrounding hadronic medium. The meson-meson interactions are described with a chiral effective Lagrangian within the framework of unitarized coupled channel amplitudes. In particular, we extend a previous work performed in the charmonium sector by calculating the cross-sections for $Υ$ scattering by light pseudoscalar mesons ($π, K, η$) and vector mesons ($ρ, K^\ast, ω$). We evaluate the relevant channels and compare the results with existing literature. The analysis is completed by including the finite-tempera…
In this work we interpret the Einstein-Hilbert (EH) Lagrangian of gravitation as the first term of a low-energy effective theory similar to those considered in the chiral Lagrangian approach to low-energy hadron physics or the electroweak chiral Lagragians describing the symmetry breaking sector of the Standard Model (SM). Starting from the one-loop computation of the elastic graviton-graviton scattering amplitude by Dunbar and Norridge, we unitarize the IR regularized partial waves by using the Inverse Amplitude Method (IAM). This method enlarges the regime of applicability of the perturbativ…
We investigate the isospin-violating mixing of the light scalar mesons a0(980) and f0(980) within the unitarized chiral approach. Isospin-violating effects are considered to leading order in the quark mass differences and electromagnetism. In this approach both mesons are generated through meson-meson dynamics. Our results provide a description of the mixing phenomenon within a framework consistent with chiral symmetry and unitarity, where these resonances are not predominantly q q-bar states. Amongst the possible experimental signals, we discuss observable consequences for the reaction J/Psi …
We study the thermal properties of the lowest multiplet of the QCD light-flavor scalar resonances, including the $f_0(500)/σ$, $K_{0}^{*}(700)/κ$, $f_0(980)$ and $a_0(980)$, in the framework of unitarized $U(3)$ chiral perturbation theory. After the successful fits to the meson-meson scattering inputs, such as the phase shifts and inelasticities, we obtain the unknown parameters and further calculate the resonance poles and their residues at zero temperature. By including the finite-temperature effects in the unitarized meson-meson scattering amplitudes, the thermal behaviors of the scalar res…
We examine the role of resonant coupled channel final state interactions (FSI), as well as weak annihilation and exchange contributions in explaining all the two body hadronic $D\rightarrow PP$ decay modes data. In the un-unitarized amplitudes we include modified Wilson coefficients with non-factorizable corrections as parameters. For the hadronic form factors, the z-series expansion method is used to get the $q^2$ dependence. The FSI effects are incorporated via a phenomenological approach with widths of resonances to various channels taken from observations where available, and others as add…
We study the unitarized meson-baryon scattering amplitude at leading order in the strangeness $S=-1$ sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $Λ(1405)$ resonance. We also point out the necessity of including higher-order terms.
We present the complete one-loop calculation of all the two meson scattering amplitudes within the framework of SU(3) Chiral Perturbation Theory, which includes pions, kaons and the eta. In addition, we have unitarized these amplitudes with the coupled channel Inverse Amplitude Method, which ensures simultaneously the good low energy properties of Chiral Perturbation Theory and unitarity. We show how this method provides a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and the generation of seven light resonances, which is consistent with p…
We report on our present work, where by means of the Inverse Amplitude Method we unitarize the elastic pion nucleon scattering amplitudes of Heavy Barion Chiral Perturbation Theory at O(q^3). We reproduce the scattering up to the inelastic thresholds including the Delta(1232) resonance. The fitted chiral constants are rather different from those obtained by fitting the extrapolated threshold parameters for the non-unitarized theory.
We report on our one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. Once the amplitudes are unitarized with the coupled channel Inverse Amplitude Method, they satisfy simultaneously the correct low-energy chiral constraints and unitarity. We obtain a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and seven light resonances.
The generalized linear sigma model for mixing among two- and four-quark components of scalar (and psedudosclar) mesons below and above 1 GeV is applied to the $πη$ channel in which the isovector scalars $a_0(980)$ and $a_0(1450)$ are probed. In the leading order, the model parameters have been previously fixed by various low-energy experimental data, and then applied to $ππ$ and $πK$ channels in which the properties of the light and broad $σ$ and $κ$ mesons are extracted in agreement with estimates reported in the literature. With the same parameters fixed in the leading order, in the present …
