We study the light quark mass dependence of the f 0 ð600Þ, ð800Þ, ð770Þ, and K Ã ð892Þ 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 nonstrange 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 ð770Þ and K Ã ð892Þ present a similar and smooth quark mass dependence. In contrast, both scalars present a similar nonanalyticity at high quark masses. Nevertheless, the f 0 ð600Þ dependence on the nonstrange quark mass is stronger than for the ð800Þ 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. As a consequence, vector widths are very well approximated by the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and their masses are shown to scale like their corresponding meson decay constants.

The quark mass dependences of light-element binding energies and nuclear scattering lengths are derived using chiral perturbation theory in combination with nonperturbative methods. In particular, we present new, improved values for the quark mass dependence of meson resonances that enter the nuclear force. A detailed analysis of the theoretical uncertainties arising in this determination is presented. As an application, we derive from a comparison of observed and calculated primordial deuterium and helium abundances a stringent limit on the variation of the light quark mass, m q =m q ¼ 0:02 AE 0:04. Inclusion of the neutron lifetime modification, under the assumption of a variation of the Higgs vacuum expectation value that translates into changing quark, electron, and weak gauge boson masses, leads to a stronger limit, jm q =m q j < 0:009.

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...

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