Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory

Nebreda, J.; Peláez, J. R.; Ríos, G.

doi:10.1103/physrevd.83.094011

Cited by 42 publications

(37 citation statements)

References 70 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We simply scale f Nc → f N c /3, the one loop constants as l (5) and (6). For the one-loop calculations we use the set of LECs in [18], whereas for the two-loop calculation we use the fit D from [18,19]. We have checked that similar results are obtained when using other sets of LECs in these references or the estimates from resonance saturation [2].…”

mentioning

confidence: 86%

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

2011

Self Cite

View full text Add to dashboard Cite

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...

show abstract

mentioning

confidence: 86%

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

2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, the ρ(770) and σ parameter dependence on the averaged non-strange light quark-massm has been studied within the unitarized SU(2) elastic IAM formalism to NLO in [297] and to NNLO in [235]. In addition, the ππ elastic scattering phases dependence was also studied in [298] with the same methods. Moreover the ρ(700), σ, κ(800) and K * (892) dependence on both the non-strange quark massm and the strange one m s was studied in [256] within the SU(3) NLO IAM formalism.…”

Section: Quark Mass Dependencementioning

confidence: 99%

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

2016

View full text Add to dashboard Cite

The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleonnucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: f 0 (500). We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position √ s σ = 449 +22−16 −i(275±12). In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD 1/N c expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

show abstract

“…In any case, it is not the purpose of this work to provide a very precise fit to experimental data, as in other unitarized or dispersive approaches [50,53] which can even be compared to lattice results by suitable mass extrapolations [54]. After all, this is just a two-parameter fit in the chiral limit.…”

Section: Partial Wave Analysis and Unitaritymentioning

confidence: 99%

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

2016

View full text Add to dashboard Cite

We consider the OðN þ 1Þ=OðNÞ nonlinear sigma model for large N as an effective theory for lowenergy QCD at finite temperature T, in the chiral limit. At T ¼ 0 this formulation provides a good description of scattering data in the scalar channel and dynamically generates the f 0 ð500Þ pole, the pole position lying within experimental determinations. Previous T ¼ 0 results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite T and show that it exactly satisfies thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the T ¼ 0 result, and we show that one can define a proper renormalization scheme with T ¼ 0 counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behavior of the f 0 ð500Þ pole at finite T, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f 0 ð500Þ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.

show abstract

Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory

Cited by 42 publications

References 70 publications

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

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

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

Contact Info

Product

Resources

About