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*(892) present a similar and smooth quark mass dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. Nevertheless the f_0(600) dependence on both quark masses is stronger than for the kappa(800) and the vectors. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, in contrast, is violated for scalars.
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.
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.
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 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 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…
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.
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…
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 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.
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…
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…
Simulating the kappa(800) on the lattice is a challenging task that starts to become feasible due to the rapid progress in recent-years lattice QCD calculations. As the resonance is broad, special attention to finite-volume effects has to be paid, because no sharp resonance signal as from avoided level crossing can be expected. In the present article, we investigate the finite volume effects in the framework of unitarized chiral perturbation theory using next-to-leading order terms. After a fit to meson-meson partial wave data, lattice levels for piK scattering are predicted. In addition, leve…
We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach. The one-loop pion-pion scattering amplitude in Chiral Perturbation Theory at finite temperature is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the rho and sigma widths. The masses decrease slightly for high T, while the rho-pion-pion coupling increases. The rho behavior seems to be favored by experimental results. In the sigma case, it signals chiral symmetry restoration.
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.
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
Using the largest data set available, we determine the best values that the data at t=0 (total cross sections and real parts of the hadronic amplitudes) give for the intercepts and couplings of the soft pomeron and of the rho/omega and a/f trajectories. We show that these data cannot discriminate between a simple-pole fit and asymptotic log square s and log s fits, and hence are not sufficient to reveal the ultimate nature of the pomeron. However, we evaluate the existing evidence (factorization, universality, quark counting) favouring the simple-pole hypothesis. We also examine the range of v…
Pole trajectories connecting light and heavy scalar mesons, both broad resonances and quasi-bound states, are computed employing a simple coupled-channel model. Instead of varying the coupling constant as in previous work, quark and meson masses are continuously changed, so as to have one scalar meson evolve smoothly into another with different flavor(s). In particular, it is shown, among several other cases, how the still controversial K0*(800) turns into the established chi_c0, via the disputed D_s(2317). Moreover, a chi'_c0(3946) is predicted, which may correspond to the recently observed Y…
Aiming at the calculation of the properties of rho-mesons, non-perturbative QCD-based methods are discussed concerning their potentials as well as their short-comings. The latter are overcome by combining these techniques. The utilized methods are (i) the chiral constituent quark model deduced from the instanton vacuum model and large-N_c arguments, (ii) chiral perturbation theory unitarized by the inverse amplitude method and (iii) QCD sum rules. Advantages of the combination of these methods are especially the absence of un-physical quark-production thresholds and parameter-free results. Alr…
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)…
One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as expected for a qqbar meson, the f0(600) contribution to the total cross section below 1 GeV becomes less and less important. Here we review our recent work where we have shown, by means of finite energy sum rules, that a different Nc behaviour for these resonances may lead to a conflict with semi-local duality for large Nc, since local duality requires a cancellation between the f0(600) and rho(770) …
By scaling the parameters of meson-meson unitarized Chiral Perturbation Theory amplitudes according to the QCD large N_c rules, one can study the spectroscopic nature of light meson resonances. The scalars sigma, kappa f_0(980) and, possibly, the a_0(980) do not seem to behave as q-qbar states, in contrast to the vectors rho(770) and K*(892). The behavior shown by the scalars is naturally explained in terms of diagrams with intermediate $\bar q\bar q qq$-like states. Here we review our recent study and show how the results do not depend on the different fits to data.
I review the large Nc behavior of light resonances generated from unitarized one-loop Chiral Perturbation Theory. In contrast with the rho or K*, the scalar behavior is at odds with a qqbar "dominant component". In fact, in the light scalar region, meson-meson amplitudes vanish as Nc increases. Also, the scalar widths, obtained from their associated poles, behave as O(Nc^{1/2})<Gamma<O(Nc). We also clarify on the physical relevance of considering large Nc not too far from real life, Nc=3, and the interpretation of the mathematical Nc=infinity limit.
I discuss how masses and widths of hadron resonances are extracted from lattice QCD. Recent lattice results on the light, strange and charm meson resonances are reviewed. Their properties are revealed by simulating the corresponding scattering channels pi-pi, K-pi and D-pi on the lattice and extracting the scattering phase shifts. In particular we address the resonances rho, D0*(2400), D1(2430), K*, kappa and K0*(1430).
A non-perturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe the meson-meson interaction up to about 1.2 GeV. The approach uses the O(p^2) and O(p^4) chiral Lagrangians. The seven free parameters of the O(p^4) Lagrangian are fitted to the data. The results are in good agreement with a vast amount of experimental analyses. The amplitudes develop poles in the complex plane corresponding to the f0, a0, rho, K*, phi, sigma and kappa resonances; the latter two, very broad. The total and partial decay widths of the resonances ar…
Resonances and enhancements in meson-meson scattering can be divided into two classes distinguished by their behavior as the number of colors N_c in QCD becomes large: The first are ordinary mesons that become stable as N_c goes to infinity. This class includes textbook q-bar q mesons as well as glueballs and hybrids. The second class, extraordinary mesons, are enhancements that disappear as N_c goes to infinity; they subside into the hadronic continuum. This class includes indistinct and controversial objects that have been classified as q-bar q-bar q q mesons or meson-meson molecules. Pelaez…
The underlying mixing of quark components of scalar mesons is probed in $πK$ scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As other predictions of the model, in the present work the isospins $I$= 1/2, 3/2 and $J$=0 projection of $πK$ scattering amplitude (as well as phase shifts)…
