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Precise predictions for the QCD axion contribution to dark radiation with full phase-space evolution

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Abstract

We compute the QCD axion contribution to the energy density of dark radiation, parameterized by ∆Neff, by solving Boltzmann equations for the momentum distribution functions including the effects of quantum statistics for all particles involved in the axion production processes. This approach gives precise prediction for ∆Neff independently of whether axions are produced via freeze-out or freeze-in. We focus on axions produced via flavor-conserving and flavor-violating interactions with leptons. Our precise predictions for ∆Neff can differ from those assuming thermal shape for the momentum distribution functions, as commonly done in the literature, by more than the experimental precision of future Cosmic Microwave Background (CMB) observations. Current lower limits on the axion couplings from Planck constraints on ∆Neff are also affected by our precise computation which, in particular, results in a strongly relaxed bound on flavor-violating axion couplings to tau lepton and muon or electron.

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Acknowledgments

The authors would like to thank Michał Łukawski and Seokhoon Yun for useful discussions. This work was partially supported by the National Science Centre, Poland, under research grant no. 2020/38/E/ST2/00243.

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  1. Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093, Warsaw, Poland

    Marcin Badziak & Maxim Laletin

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  1. Marcin Badziak
  2. Maxim Laletin

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Correspondence toMaxim Laletin.

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Badziak, M., Laletin, M. Precise predictions for the QCD axion contribution to dark radiation with full phase-space evolution.J. High Energ. Phys.2025, 108 (2025). https://doi.org/10.1007/JHEP02(2025)108

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