Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering

Kolesár, Marián; Novotný, Jiří

doi:10.1140/epjc/s10052-018-5668-5

Cited by 7 publications

(4 citation statements)

References 42 publications

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“…The application of this method to K → 3π turned out to be very successful [37][38][39][40]. These developments have triggered renewed interest in theoretical studies of η → 3π [41][42][43][44][45][46][47][48][49][50][51][52][53]. We briefly summarize the main properties of the transition amplitude at low energies.…”

Section: Branch Cuts Discontinuitiesmentioning

confidence: 99%

“…In Refs. [50][51][52][53] Kolesár and Novotný take a very different point of view from the one adopted here -namely that the reason for the bad convergence of χ PT for this decay is understood and has to do with large final-state rescattering effects -and try to identify the reasons for the bad convergence within the framework of the so-called resummed Chiral Perturbation Theory (rChPT) [120,121]. In this approach, vacuum fluctuations ofss pairs are treated in a special way and their effect resummed.…”

Section: Dispersive Approachesmentioning

confidence: 99%

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Dispersive analysis of $$\eta \rightarrow 3 \pi $$

et al. 2018

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The dispersive analysis of the decay η → 3π is reviewed and thoroughly updated with the aim of determining the quark mass ratio Q 2 = (m 2 s − m 2 ud)/(m 2 d − m 2 u). With the number of subtractions we are using, the effects generated by the final state interaction are dominated by low energy ππ scattering. Since the corresponding phase shifts are now accurately known, causality and unitarity determine the decay amplitude within small uncertainties-except for the values of the subtraction constants. Our determination of these constants relies on the Dalitz plot distribution of the charged channel, which is now measured with good accuracy. The theoretical constraints that follow from the fact that the particles involved in the transition represent Nambu-Goldstone bosons of a hidden approximate symmetry play an equally important role. The ensuing predictions for the Dalitz plot distribution of the neutral channel and for the branching ratio Γ η→3π 0 /Γ η→π + π − π 0 are in very good agreement with experiment. Relying on a known low-energy theorem that relates the meson masses to the masses of the three lightest quarks, our analysis leads to Q = 22.1(7), where the error covers all of the uncertainties encountered in the course of the calculation: experimental uncertainties in decay rates and Dalitz plot distributions, noise in the input used for the phase shifts, as well as theoretical uncertainties in the constraints imposed by chiral symmetry and in the evaluation of isospin breaking effects. Our result indicates that the current algebra formulae for the meson masses only receive small corrections from higher orders of the chiral expansion, but not all of the recent lattice results are consistent with this conclusion.

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Section: Branch Cuts Discontinuitiesmentioning

confidence: 99%

Section: Dispersive Approachesmentioning

confidence: 99%

Dispersive analysis of $$\eta \rightarrow 3 \pi $$

et al. 2018

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“…We have attempted to extract constraints on the three-flavour order parameters from experimental data on the → 3 decays, details can be found in [15]. We employed a Bayesian statistical approach within resummed PT, an approach first used in [16] in the case of scattering.…”

Section: Results: → 3 and Scatteringmentioning

confidence: 99%

Three-flavour order parameters of chiral symmetry in low-energy QCD

Kolesár¹,

Novotný²

2020

Preprint

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The current state of knowledge of the order parameters of the spontaneously broken chiral symmetry, the quark condensate and the pseudoscalar decay constant in the chiral limit, is briefly reviewed, based on available phenomenological fits and lattice QCD calculations. We argue that while the theory is pretty well understood in the two-flavour case, there is still a gap in the knowledge of the characteristics of the QCD vacuum in the three-flavour one. Our constraints for the three-flavour parameters obtained by a Bayesian statistical analysis of the decays of eta to three pions are presented. Possible implications of a new analysis of subthreshold parameters of pion-pion scattering is outlined.

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“…Recent studies of some of the aforementioned decays include Refs. [18][19][20][21] for η → 3π , Ref. [22] for η ( ) → 4π , Refs.…”

Section: Introductionmentioning

confidence: 99%

$$\eta ^{\prime }\rightarrow \eta \pi \pi $$ η ′ → η π π decays in unitarized resonance chiral theory

Gonzàlez-Solís

Passemar

2018

Eur. Phys. J. C

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We study the hadronic η → ηππ decays within the framework of U (3) L ⊗ U (3) R Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the N /D method resumming both the important Sand D-wave ππ and the subleading Swave πη final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associated Dalitz-plot slope parameters are found to be a = − 0.072(7) stat (8) syst , b = − 0.052(1) stat (2) syst , d = − 0.051(8) stat (6) syst , which lie in the ballpark of the current experimental and theoretical determinations.

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Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering

Cited by 7 publications

References 42 publications

Dispersive analysis of $$\eta \rightarrow 3 \pi $$

Dispersive analysis of $$\eta \rightarrow 3 \pi $$

Three-flavour order parameters of chiral symmetry in low-energy QCD

$$\eta ^{\prime }\rightarrow \eta \pi \pi $$ η ′ → η π π decays in unitarized resonance chiral theory

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