Dispersive analysis of the pion transition form factor

Hoferichter, Martin; Kubis, Bastian; Leupold, Stefan; Niecknig, Franz; Schneider, S.

doi:10.1140/epjc/s10052-014-3180-0

Cited by 142 publications

(189 citation statements)

References 127 publications

(238 reference statements)

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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.

385

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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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.

385

257

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“…We expect this description to be reliable in a similar range of |q 2 | as the timelike momenta that enter the description of the spectral function, −q 2 1 GeV 2 ; compare the related discussion of the π 0 transition form factor for spacelike arguments in Ref. [11].…”

Section: Towards a Description Of The Doubly-virtual η (′) Transitionmentioning

confidence: 69%

“…the corresponding discussion in Ref. [11]). Fortunately, the vector-isoscalar spectral function at low energies is strongly dominated by the narrow ω and φ resonances, see Fig.…”

Section: Definition Intermediate Statesmentioning

confidence: 77%

See 1 more Smart Citation

Towards a dispersive determination of the η and η′ transition form factors

Kubis¹

2018

EPJ Web Conf.

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Abstract.We discuss status and prospects of a dispersive analysis of the η and η ′ transition form factors. Particular focus is put on the various pieces of experimental information that serve as input to such a calculation. These can help improve on the precision of an evaluation of the η and η ′ pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. Hadronic light-by-light scattering and the anomalous magnetic moment of the muonThere is a by now long-standing discrepancy between the experimental determination of the anomalous magnetic moment of the muon as measured by the BNL E821 experiment [1], and its calculation within the Standard Model [2], with both experiment and theory affected by a comparable uncertainty. With two different proposals to further improve on the accuracy of the measurement well under way [3,4], it is of utmost importance to also improve the accuracy of the theoretical Standard-Model prediction before a persistent discrepancy of potentially increased significance can be interpreted in terms of physics beyond the Standard Model. The Standard-Model uncertainty is entirely dominated by hadronic contributions. While the dominant hadronic vacuum polarization can be expressed, via a dispersion relation, in terms of measurable e + e − → hadrons total cross sections, which therefore can be further improved upon by a strong experimental effort to determine many of the exclusive channels contributing therein with yet improved precision [5], the situation for the α QED -suppressed hadronic light-by-light scattering is less straightforward, relying until recently to a much larger extent on modeling [6], with badly controlled errors.This presentation is part of an effort to analyze also the hadronic light-by-light scattering tensor using dispersion theory [7,8]. Dispersion theory makes maximal use of analyticity and unitarity, two fundamental consequences of relativistic quantum field theories that mathematically incorporate the principles of causality and probability conservation. The various (in principle infinitely many different) contributions to hadronic light-by-light scattering are organized in terms of their analytic structure, according to the cuts and poles in the different energy variables that are dictated by the above principles. This has the advantage that all contributions will be given in terms of on-shell form factors and scattering amplitudes, hence observables that can to a large extent again be related to experimentally accessible quantities [9]. An ordering principle will be to consider intermediate

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“…The TFF enters in the predictions of observable quantities like the rate of π 0 → e + e − decay and the anomalous magnetic moment of the muon. It has been extensively studied theoretically [3][4][5][6][7][8] and the slope parameter has been measured experimentally in the time-like [9][10][11][12] as well as in the space-like domain [13][14][15][16].…”

Section: Measurement Of the π 0 Transition Form Factormentioning

confidence: 99%

Recent results and prospects from NA62

Bizzeti

2016

EPJ Web Conf.

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Abstract. A large sample of charged kaon decays in 2007 has been collected by the NA62 experiment at CERN SPS using the experimental setup of the former NA48 experiment. Its intense kaon beam provides an abundant source of tagged neutral pions in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion from 1.05 × 10 6 fully reconstructed π 0 Dalitz decays is presented. The obtained preliminary value a = (3.70 ± 0.53 stat ± 0.36 syst ) × 10 −2 is the first 5.8σ observation of a non-zero slope in the time-like region of momentum transfer.

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Dispersive analysis of the pion transition form factor

Cited by 142 publications

References 127 publications

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

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

Towards a dispersive determination of the η and η′ transition form factors

Recent results and prospects from NA62

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