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Chiral anomaly in the $η^{(')} \to π^{+} π^{-} γ$ and $η^{(')} \to π^{+} π^{-} l^{+} l^{-}$ decays

M. K. Volkov ^1,*, A. A. Osipov ^1,†, K. Nurlan ^1,2,‡, and A. A. Pivovarov^1,§

¹Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow region, Russia
²The Institute of Nuclear Physics, Almaty, 050032, Kazakhstan

^*Contact author: volkov@theor.jinr.ru
^†Contact author: aaosipov@theor.jinr.ru
^‡Contact author: nurlan@theor.jinr.ru
^§Contact author: pivovarov@theor.jinr.ru

Phys. Rev. D 114, 034044 – Published 21 August, 2026

DOI: https://doi.org/10.1103/fvck-n7xd

Abstract

We report the presence of a flavor-violating correction to the $V A A A$ -type anomaly, $δ^{(')}$ , induced by the surface terms of the anomalous quark triangle diagram, previously found in the $η, η^{'} \to π^{+} π^{-} γ$ decay amplitudes, and investigate its impact on the corresponding semileptonic decay modes of $η$ and $η^{'}$ . The magnitude of $δ^{(')}$ can be set from the experimental data on the $η^{(')} \to π^{+} π^{-} γ$ decay width. We then estimate another low-energy constant, the slope parameter $α^{(')}$ . The impact of different schemes for describing $η - η^{'}$ mixing on the value of $δ^{(')}$ and $α^{(')}$ is discussed. The predictions are shown to be in complete agreement with the available experimental data.

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Phys. Rev. D 114, 034044– Published 21 August, 2026

Vol. 114, Iss. 3 — 1 August 2026

Received 5 March 2026
Accepted 29 June 2026

DOI: https://doi.org/10.1103/fvck-n7xd

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Chiral anomaly in the $η^{(')} \to π^{+} π^{-} γ$ and $η^{(')} \to π^{+} π^{-} l^{+} l^{-}$ decays

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Chiral anomaly in the η(′)→π+π− γ and η(′)→π+π−l+l− decays

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Physics Subject Headings (PhySH)

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References (77)

Chiral anomaly in the $η^{(')} \to π^{+} π^{-} γ$ and $η^{(')} \to π^{+} π^{-} l^{+} l^{-}$ decays