Dispersive analysis of ω→3π and ϕ→3π decays

Niecknig, Franz; Kubis, Bastian; Schneider, S.

doi:10.1140/epjc/s10052-012-2014-1

Cited by 154 publications

(285 citation statements)

References 75 publications

(183 reference statements)

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“…The dispersive method using inhomogeneities as described above has by now been used for a variety of lowenergy processes, such as η → 3π [32,38], ω/φ → 3π [39], K → ππ [40], K l4 [33,34], γγ → ππ [41,42], or γπ → ππ [43,44]. In several of those cases, the inhomogeneities (given in terms of hat functions), which incorporate left-hand-cut structures, and the amplitudes given in terms of Omnès-type solutions with a right-hand cut only are calculated iteratively from each other, until convergence is reached.…”

Section: Omnès Representationmentioning

confidence: 99%

Bl4decays and the extraction of|Vub|

Kubis²,

et al. 2014

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The Cabibbo-Kobayashi-Maskawa matrix element |V ub | is not well determined yet. It can be extracted from both inclusive or exclusive decays, like B → π(ρ)lν l . However, the exclusive determination from B → ρlν l , in particular, suffers from a large model dependence. In this paper, we propose to extract |V ub | from the four-body semileptonic decay B → ππlν l , where the form factors for the pion-pion system are treated in dispersion theory. This is a model-independent approach that takes into account the ππ rescattering effects, as well as the effect of the ρ meson. We demonstrate that both finite-width effects of the ρ meson as well as scalar ππ contributions can be considered completely in this way.

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Section: Omnès Representationmentioning

confidence: 99%

Bl4decays and the extraction of|Vub|

Kubis²,

et al. 2014

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“…The generalization of this representation including the absorptive part of the F -wave can be found in Ref. [20], but in this article Eq. (12) will be sufficient.…”

Section: A Infinite Matching Point and Angular Averagesmentioning

confidence: 99%

“…For the practical purpose of a fit to data, the representations (19) can be significantly simplified, based on the observation that they are completely linear in the subtraction constants C 1 and C (1) 2 , C (2) 2 , respectively [20,28]. We can rewrite…”

Section: A Fitting Dispersive Representations To Datamentioning

confidence: 99%

Extracting the chiral anomaly fromγπ→ππ

Hoferichter

Kubis²,

Sakkas³

2012

Phys. Rev. D

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133

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We derive dispersive representations for the anomalous process γπ → ππ with the ππ P -wave phase shift as input. We investigate how in this framework the chiral anomaly can be extracted from a cross-section measurement using all data up to 1 GeV, and discuss the importance of a precise representation of the γπ → ππ amplitude for the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.

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“…In this framework, we worked out how to define unambiguously and in a model-independent way both the pion-pole and the pion-box contribution. 1 With pion-as well as η-, η -pole contributions determined by their doubly-virtual transition form factors, which by themselves are strongly constrained by unitarity, analyticity, and perturbative QCD in combination with experimental data [38][39][40][41][42][43][44][45][46], we here apply our framework to extend the partial-wave formulation of two-pion rescattering effects for S-waves [28] to arbitrary partial waves. To this end, we identify a special set of (unambiguously defined) scalar functions that fulfill unsubtracted dispersion relations and can be expressed as linear combinations of helicity amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

371

257

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In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g − 2) µ , including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ * γ * → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a π-box µ = −15.9(2)×10 −11 . As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ * γ * → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f 0 (500) to HLbL scattering in (g − 2) µ . We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a π-box µ + a ππ,π-pole LHC µ,J=0 = −24(1) × 10 −11 .

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Dispersive analysis of ω→3π and ϕ→3π decays

Cited by 154 publications

References 75 publications

Bl4decays and the extraction of|Vub|

Bl4decays and the extraction of|Vub|

Extracting the chiral anomaly fromγπ→ππ

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

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