Enhanced non-quark-antiquark and non-glueballNcbehavior of light scalar mesons

Abstract

We show that the latest and very precise dispersive data analyses require a large and very unnatural fine-tuning of the 1/Nc expansion at Nc = 3 if the f0(600) and K(800) light scalar mesons are to be considered predominantlyqq states, which is not needed for light vector mesons. For this, we use scattering observables whose 1/Nc corrections are suppressed further than one power of 1/Nc forqq or glueball states, thus enhancing contributions of other nature. This is achieved without using unitarized ChPT, but if it is used we can also show that it is not just that the coefficients of the 1/Nc expansion are unnatural, but that the expansion itself does not even follow the expected 1/Nc scaling of a glueball or aqq meson.PACS numbers: 12.39. Mk,12.39.Fe,11.15.Pg,13.75.Lb,14.40.Cs Light scalar resonances play a relevant role for several fields of Physics: For the nucleon-nucleon interaction, because they are largely responsible for the attractive part [1] (with cosmological and anthropic implications). for the QCD non-abelian nature, because some of these resonances have the quantum numbers of the lightest glueball, also common to the vacuum and hence of relevance for the spontaneous chiral symmetry breaking. Moreover, they are also of interest for the saturation [2] of the low energy constants of Chiral Perturbation Theory (ChPT) [3]. However, the precise properties of these mesons, their nature, spectroscopic classification, and even their existence-as for the K(800) or κ-are still the object of an intense debate. In particular, different models [4] suggest that they may not be ordinary quark-antiquark mesons, but tetraquarks, meson molecules, glueballs, or a complicated mixture of all these. The problem, of course, is that we do not know how to solve QCD at low energies.However, since the QCD 1/N c expansion is applicable at all energies, and the mass and width N c dependence ofqq mesons and glueballs is well known [5], the N c scaling of resonances becomes a powerful tool to classify them and understand their nature. In [6,7] some of us studied the mass and width behavior of light resonances using ChPT-which is the QCD low energy effective Lagrangian-and unitarization with a dispersion relation. It was found that the poles of the ρ(770) and K * (982) vectors behave predominantly as expected for qq states whereas those of the f 0 (600), also called σ, and K(800) scalars do not [6]. Still, a possible subdominant qq component for the f 0 (600) may arise naturally at two loops [7] within ChPT (less so at one loop), but with a mass around 1 GeV or more.Of course, all these conclusions rely on unitarized ChPT and the assumption that corrections, suppressed just by 1/N c , are of natural size. Since N c =3 in real life, this may not seem as a large suppression, even more when the meaning of "natural size" may not be clear for dimensional parameters. For that reason, unitarized ChPT was useful to change N c , and reveal the 1/N c scaling, no matter how unnatural the coefficients may appear.Here we will provide adimen...

Determination of Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

“…We have reported a work [9] on the determination the low energy constants of SU(2) Chiral Perturbation Theory (ChPT) at one and two loops by fitting to the threshold parameters obtained from sum rules using a recent and precise dispersive analysis of data [10], together with six additional observables that we have studied here.…”

“…We propose to take the weighted average of the two previous fits, including a systematic uncertainty to cover the LECs values of both fits. In Table IV of the original reference [9], we compare the resulting threshold parameters obtained using this averaged set with the experimental values. Thanks to the larger uncertainty, the threshold parameters obtained are compatible within errors with the experimental values, except for b S0 and b P , which differ by more than three and two standard deviations respectively.…”

“…As a consequence, the fits in terms ofl i and r i are much more unstable, and can even lead to spurious solutions. For this reason we focus on the fits in terms ofb i , and refer to the appendix [9] for a study of thel i , r i fits.…”

“…Here we report our work [9] on the determination of the LECs that appear in the ππ scattering amplitude. We obtain these LECs from fits to the coefficients of the momentum expansion of the amplitude around threshold, known as threshold parameters, which can be calculated within ChPT and expressed in terms of the LECs.…”

New resonance scale and fingerprint identification in minimal composite Higgs models

“…However, above the mass of the rho meson, the unitarity is rescued by the contribution of the diagram of the rho meson mediation. In this case, a sizable phase shift would be induced in partial wave amplitudes of the pion-pion scatterings around the rho meson mass [11,12].…”