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Christ N, Feng X, Jin L, Tu C, Zhao Y. Lattice QCD Calculation of π^{0}→e^{+}e^{-} Decay. PHYSICAL REVIEW LETTERS 2023; 130:191901. [PMID: 37243653 DOI: 10.1103/physrevlett.130.191901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 04/11/2023] [Indexed: 05/29/2023]
Abstract
We extend the application of lattice QCD to the two-photon-mediated, order α^{2} rare decay π^{0}→e^{+}e^{-}. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find ReA=18.60(1.19)(1.05) eV, ImA=32.59(1.50)(1.65) eV, a more accurate value for the ratio (ReA/ImA)=0.571(10)(4), and a result for the partial width Γ(π^{0}→γγ)=6.60(0.61)(0.67) eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay K→μ^{+}μ^{-}.
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Affiliation(s)
- Norman Christ
- Physics Department, Columbia University, New York, New York 10027, USA
| | - Xu Feng
- School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China; and Center for High Energy Physics, Peking University, Beijing 100871, China
| | - Luchang Jin
- Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA
| | - Cheng Tu
- Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA
| | - Yidi Zhao
- Physics Department, Columbia University, New York, New York 10027, USA
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Holz S, Hanhart C, Hoferichter M, Kubis B. A dispersive analysis of η ' → π + π - γ and η ' → ℓ + ℓ - γ. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2022; 82:434. [PMID: 35578684 PMCID: PMC9098615 DOI: 10.1140/epjc/s10052-022-10247-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
We present a dispersive representation of the η ' transition form factor that allows one to account, in a consistent way, for the effects of ρ - ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on η ' → π + π - γ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the ρ - ω mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of η ' → ℓ + ℓ - γ , in particular we find the slope parameter b η ' = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the η ' -pole contribution to the anomalous magnetic moment of the muon using experimental input from both η ' decay channels.
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Affiliation(s)
- Simon Holz
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
| | - Christoph Hanhart
- Forschungszentrum Jülich, Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, 52425 Jülich, Germany
| | - Martin Hoferichter
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
- Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 USA
| | - Bastian Kubis
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
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Hoferichter M, Hoid BL, Kubis B, Lüdtke J. Improved Standard-Model Prediction for π^{0}→e^{+}e^{-}. PHYSICAL REVIEW LETTERS 2022; 128:172004. [PMID: 35570465 DOI: 10.1103/physrevlett.128.172004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 08/18/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
We present an improved standard-model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for π^{0}→γ^{*}γ^{*}, for which we employ a dispersive representation that incorporates both spacelike and timelike data as well as short-distance constraints. The resulting SM branching fraction, Br[π^{0}→e^{+}e^{-}]=6.25(3)×10^{-8}, sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.
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Affiliation(s)
- Martin Hoferichter
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
| | - Bai-Long Hoid
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
| | - Bastian Kubis
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
| | - Jan Lüdtke
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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Hoferichter M. Recent progress in hadronic light-by-light scattering. EPJ WEB OF CONFERENCES 2022. [DOI: 10.1051/epjconf/202225806004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In recent years, significant progress in the calculation of the HLbL contribution to the anomalous magnetic moment of the muon has been achieved both with data-driven methods and in lattice QCD. In these proceedings I will discuss current developments aimed at controlling HLbL scattering at the level of 10%, as required for the final precision of the Fermilab E989 experiment.
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Gérardin A. The anomalous magnetic moment of the muon: status of lattice QCD calculations. THE EUROPEAN PHYSICAL JOURNAL. A, HADRONS AND NUCLEI 2021; 57:116. [PMID: 33841046 PMCID: PMC8023536 DOI: 10.1140/epja/s10050-021-00426-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about 3.5 σ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.
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Affiliation(s)
- Antoine Gérardin
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
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Hoid BL, Hoferichter M, Kubis B. Hadronic vacuum polarization and vector-meson resonance parameters from e + e - → π 0 γ. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2020; 80:988. [PMID: 33132752 PMCID: PMC7588363 DOI: 10.1140/epjc/s10052-020-08550-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 10/13/2020] [Indexed: 06/11/2023]
Abstract
We study the reactione + e - → π 0 γ based on a dispersive representation of the underlyingπ 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of theπ 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We finda μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of ω and ϕ . We observe good agreement with thee + e - → 3 π channel, explaining a previous tension in the ω mass betweenπ 0 γ and 3 π by an unphysical phase in the fit function. Combining both channels we findM ¯ ω = 782.736 ( 24 ) MeV andM ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from theK ¯ K channel, demonstrating consistency with 3 π andπ 0 γ . For the ω mass, our result is consistent but more precise, exacerbating tensions with the ω mass extracted via isospin-breaking effects from the 2 π channel.
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Affiliation(s)
- Bai-Long Hoid
- Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
| | - Martin Hoferichter
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
| | - Bastian Kubis
- Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
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Meyer HB. π 0 decay precision-tests the chiral anomaly. Science 2020; 368:469. [PMID: 32355017 DOI: 10.1126/science.aba8063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Harvey B Meyer
- Institute for Nuclear Physics, University of Mainz, 55099 Mainz, Germany.
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