Some remarks on the Padé unitarization of low-energy amplitudes

Masjuan, Pere; Sanz-Cillero, Juan José; Virto, Javier

doi:10.1016/j.physletb.2008.07.106

Cited by 25 publications

(33 citation statements)

References 32 publications

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“…This means that the one-loop σ propagator has a complex pole. Being a renormalizable model, the position of this pole can be calculated perturbatively to NLO [54,245]. In the chiral limit one finds:…”

Section: The Linear Sigma Modelmentioning

confidence: 99%

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

2016

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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.

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Section: The Linear Sigma Modelmentioning

confidence: 99%

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

2016

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“…[46,47]. Given a symmetric bivariate function F P γ * γ * (Q 2 1 , Q 2 2 ) = F P γ * γ * (Q 2 2 , Q 2 1 ) with known Taylor expansion 46,48] are rational functions 8 of bivariate polynomials of degree N and M , respectively, which coefficients are defined as to match the low-energy expansion of the original [40,47,49,50,53,54]). This construction allows to describe the TFF with the correct low-energy implementation, which is known to play the main role in these processes, a fact often overlooked (see the discussion in [11]).…”

Section: Canterbury Approximantsmentioning

confidence: 99%

η and η ′ decays into lepton pairs

Masjuan

Sánchez-Puertas

2016

J. High Energ. Phys.

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In this work, we calculate the branching ratios for the η(η ) → decays, where = e, µ. These processes have tiny rates in the Standard Model due to spin flip, loop and electromagnetic suppressions, which could make them sensitive to New Physics effects. In order to provide a reliable input for the Standard Model, we exploit the general analytical properties of the amplitude. For that purpose, we invoke the machinery of Canterbury approximants, which provides a systematic description of the underlying hadronic physics in a data-driven fashion. Given the current experimental discrepancies, we discuss in detail the role of the resonant region and comment on the reliability of χPT calculations. Finally, we discuss the kind of new physics which we think would be relevant to account for them.

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“…The final central result will be then defined as the average of the individual central predictions and the error will be obtained as the quadratic sum of the three independent types of error. This procedure leads to slightly smaller errors than in (27,28), namely M = (457 ± 14 ± 14 ± 10) MeV = (457 ± 22) MeV, Γ/2 = (293 ± 14 ± 14 ± 15) MeV = (293 ± 25) MeV,…”

Section: Pole Determination From Padé Approximantsmentioning

confidence: 85%

“…(27,28) and (29,30) for the extrapolation based on Padé approximants. Our safest estimate, with largest errors, is given by the most conservative approach applied to the P analytic continuation through Padé approximants has a larger spread.…”

Section: Discussionmentioning

confidence: 99%

“…In this case, the rest of the poles inside the disk B δ (s 0 ) are unphysical and may be viewed as artifacts that simulate other, more distant singularities, such as branch points produced by unitarity [28]. The next sequence following the Montessus' theorem would be the approximants with two poles, P N 2 (s).…”

Section: Pole Determination From Padé Approximantsmentioning

confidence: 99%

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Uncertainty estimates of theσ-pole determination by Padé approximants

et al. 2016

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We discuss the determination of the f0(500) (or σ) resonance by analytic continuation through Padé approximants of the ππ-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to analyze the uncertainties of the method, having in view the fact that analytic continuation is an ill-posed problem in the sense of Hadamard. Using as input a class of admissible parameterizations of the scalar-isoscalar ππ partial wave, which satisfy with great accuracy the same set of dispersive constraints, we find that the Roy-type integral representations lead to almost identical pole positions for all of them, while the predictions of the Padé approximants have a larger spread, being sensitive to features of the input parameterization that are not controlled by the dispersive constraints. Our conservative conclusion is that the σ-pole determination by Padé approximants is consistent with the prediction of Roy-type equations, but has an uncertainty almost a factor two larger.

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Some remarks on the Padé unitarization of low-energy amplitudes

Cited by 25 publications

References 32 publications

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

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

η and η ′ decays into lepton pairs

Uncertainty estimates of theσ-pole determination by Padé approximants

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