Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$

Isken, Tobias; Kubis, Bastian; Schneider, S.; Stoffer, Peter

doi:10.1140/epjc/s10052-017-5024-1

Cited by 49 publications

(50 citation statements)

References 66 publications

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“…7(b) is the prediction for η 0 → ηπ 0 π 0 in Ref. [8] based on the previous BESIII fit result for η 0 → ηπ þ π − [11], which are consistent with the experimental distribution within statistical errors. However, with current statistics, it is difficult to establish the structure (cusp effect) near the π þ π − mass threshold.…”

Section: Comparison Betweensupporting

confidence: 83%

“…The size of this effect is predicted to be about 6% [14] (8% in original work [6]) within the framework of nonrelativistic effective field theory (NREFT), which is confirmed in a dispersive analysis [8]. An analogous cusp has been observed in the K þ → π þ π 0 π 0 [15] decay and allows us to determine the ππ S-wave scattering lengths [16][17][18][19].…”

Section: Introductionmentioning

confidence: 72%

“…However, with current statistics, it is difficult to establish the structure (cusp effect) near the π þ π − mass threshold. central value in Ref [8] fit uncertainty in Ref [8] phase uncertainty in Ref [8] (b) Both the general and the linear representations are used to determine the Dalitz plot parameters, and the corresponding results are summarized in Table II including the systematic uncertainties. The Dalitz plot parameters for both decays are in reasonable agreement and more precise than the previous measurements [9][10][11][12].…”

Section: Comparison Betweenmentioning

confidence: 99%

“…The two dominant hadronic decays, η 0 → ηπ þ π − and η 0 → ηπ 0 π 0 (called charged decay mode and neutral decay mode throughout the text, respectively), are believed to be an ideal place to study ππ and ηπ scattering [2,3], which may lead to a variation in the density of the Dalitz plot. Several extensions of the ChPT framework [4][5][6][7] and dispersive analysis based on the fundamental principles of analyticity and unitarity [8] have been applied to investigate the matrix element of η 0 → ηππ. In experimental analyses, the Dalitz plot for the charged decay mode is usually described by the following two variables:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Measurement of the matrix elements for the decays η′→ηπ+π− an

Ablikim¹,

Ачасов²,

Ahmed³

et al. 2018

Phys. Rev. D

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Based on a sample of 1.31 × 10 9 J=ψ events collected with the BESIII detector, the matrix elements for the decays η 0 → ηπ þ π − and η 0 → ηπ 0 π 0 are determined using 351,016 η 0 → ðη → γγÞπ þ π − and 56,249 η 0 → ðη → γγÞπ 0 π 0 events with background levels less than 1%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between η 0 → ηπ þ π − and η 0 → ηπ 0 π 0 is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in η 0 → ηπ 0 π 0 is observed.

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Section: Comparison Betweensupporting

confidence: 83%

Section: Introductionmentioning

confidence: 72%

Section: Comparison Betweenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Measurement of the matrix elements for the decays η′→ηπ+π− an

Ablikim¹,

Ачасов²,

Ahmed³

et al. 2018

Phys. Rev. D

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“…According to Ref. [18], such an assumption is too strong, but there should still be a nonnegligible contribution from ηπ → ππ rescattering, which can, e.g., be described through dispersion relations [19].…”

Section: Introductionmentioning

confidence: 99%

Measurement of the decay η′→π0π0η at MAMI

Adlarson¹,

Afzal²,

Ahmed³

et al. 2018

Phys. Rev. D

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An experimental study of the η 0 → π 0 π 0 η → 6γ decay has been conducted with the best up-to-date statistical accuracy, by measuring η 0 mesons produced in the γp → η 0 p reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The results obtained for the standard parametrization of the η 0 → π 0 π 0 η matrix element are consistent with the most recent results for η 0 → ππη decays, but have smaller uncertainties. The available statistics and experimental resolution allowed, for the first time, an observation of a structure below the π þ π − mass threshold, the magnitude and sign of which, checked within the framework of the nonrelativistic effective-field theory, demonstrated good agreement with the cusp that was predicted based on the ππ scattering length combination, a 0 − a 2 , extracted from K → 3π decays.

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Two-pion contribution to hadronic vacuum polarization

Colangelo

Hoferichter

Stoffer

2019

J. High Energ. Phys.

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438

286

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We present a detailed analysis of e + e − → π + π − data up to √ s = 1 GeV in the framework of dispersion relations. Starting from a family of ππ P -wave phase shifts, as derived from a previous Roy-equation analysis of ππ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the ω meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time-and space-like data sets we find a ππ µ | ≤1 GeV = 495.0(1.5)(2.1) × 10 −10 and a ππ µ | ≤0.63 GeV = 132.8(0.4)(1.0) × 10 −10 . While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the ππ P -wave, valuable input for future global analyses of low-energy ππ scattering, as well as a determination of the pion charge radius, r 2 π = 0.429(1)(4) fm 2 .

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Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$

Cited by 49 publications

References 66 publications

Measurement of the matrix elements for the decays η′→ηπ+π− an

Measurement of the matrix elements for the decays η′→ηπ+π− an

Measurement of the decay η′→π0π0η at MAMI

Two-pion contribution to hadronic vacuum polarization

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