Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations

Kamiński, R.; Peláez, J. R.; Ynduráin, Félix

doi:10.1103/physrevd.77.054015

Cited by 119 publications

(210 citation statements)

References 43 publications

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“…As we did in [3], we will now use the average discrepancies " d 2 i , defined in Eqs. (19) and (20), to obtain these constrained fits, by minimizing…”

Section: A Minimization Proceduresmentioning

confidence: 99%

“…The previous works [3,6] of this series made use of two complementary dispersive approaches, forward dispersion relations and Roy equations, that we briefly review next, before introducing the new set of once-subtracted Roylike equations.…”

Section: Dispersion Relations and Sum Rulesmentioning

confidence: 99%

“…Note that, as explained in [3], the limits above are to be taken for s > 4M 2 . In practice, for the value of a 1 we simply use its Froissart-Gribov representation, and we are left with a sum rule representation for both b ð0Þ 0 and b ð2Þ 0 .…”

Section: A Sum Rules For Threshold Parametersmentioning

confidence: 99%

“…This led to a remarkable improvement in the consistency of the 0 0 FDR. (iii) In KPY08 [3] we also considered Roy equations [9] for our amplitudes below K " K threshold. The UFD fits, where we had previously incorporated [6] the most reliable low energy data from K '4 decays to that date [8], satisfied Roy equations fairly well and the agreement was remarkably good once they were imposed into a new set of CFD.…”

Section: The Unconstrained Fits To Data a Our Previous Workmentioning

confidence: 99%

“…In a series of papers [1][2][3] that we will denote by PY05, KPY06, and KPY08, respectively, we have provided several sets of precise phenomenological fits to scattering data. The interest in a precise and model-independent description of the data available in this process is twofold: On the one hand, it could be used at low energies to extract information about the parameters of chiral perturbation theory (ChPT) [4], quark masses, and the size of the chiral condensate, pionic atom decays, or CP violation in the kaonic system.…”

Section: Introductionmentioning

confidence: 99%

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Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

et al. 2011

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We improve our description of scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K '4 decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

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“…As we did in [3], we will now use the average discrepancies " d 2 i , defined in Eqs. (19) and (20), to obtain these constrained fits, by minimizing…”

Section: A Minimization Proceduresmentioning

confidence: 99%

Section: Dispersion Relations and Sum Rulesmentioning

confidence: 99%

Section: A Sum Rules For Threshold Parametersmentioning

confidence: 99%

Section: The Unconstrained Fits To Data a Our Previous Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

et al. 2011

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Rescattering effects in η → 3π decays

Schneider¹,

Kubis²,

Ditsche³

2011

J. High Energ. Phys.

113

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The isospin-breaking decay η → 3π is an ideal tool to extract information on light quark mass ratios from experiment. For a precise determination, however, a detailed description of the Dalitz plot distribution is necessary. In that respect, in particular the slope parameter α of the neutral decay channel causes some concern, since the one-loop prediction from chiral perturbation theory misses the experimental value substantially. We use the modified non-relativistic effective field-theory, a dedicated framework to analyze final-state interactions beyond one loop including isospin-breaking corrections, to extract charged and neutral Dalitz plot parameters. Matching to chiral perturbation theory at next-to-leading order, we find α = −0.025 ± 0.005, in marginal agreement with experimental findings. We derive a relation between charged and neutral decay parameters that points towards a significant tension between the most recent KLOE measurements of these observables.

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Two-meson form factors in unitarized chiral perturbation theory

Shi

Seng

Guo

et al. 2021

J. High Energ. Phys.

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We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays Bs→ π+π−ℓ+ℓ− and the τ lepton decay τ → π−π0ντ, in searches for physics beyond the Standard Model.

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Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations

Cited by 119 publications

References 43 publications

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

Rescattering effects in η → 3π decays

Two-meson form factors in unitarized chiral perturbation theory

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