- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

New bounds on heavy QCD axions from big bang nucleosynthesis

Tae Hyun Jung1,*, Takemichi Okui2,3,†, Kohsaku Tobioka2,3,‡, and Jiabao Wang2,§

  • *Contact author: thjung0720@gmail.com
  • †Contact author: tokui@fsu.edu
  • ‡Contact author: ktobioka@fsu.edu
  • §Contact author: jwang21@fsu.edu
PDF

Phys. Rev. D 113, 055002 – Published 2 March, 2026

DOI: https://doi.org/10.1103/l2m1-h1cp

Abstract

We study big bang nucleosynthesis (BBN) constraints on heavy QCD axions. BBN offers a powerful probe of new physics that modifies the neutron-to-proton ratio during the process, thanks to the precisely measured primordial Helium-4 abundance. A heavy QCD axion provides an attractive target for this probe, because not only is it a well-motivated hypothetical particle by the strong CP problem, but also it dominantly decays to hadrons if kinematically allowed. A range of its lifetime is thus excluded where the hadronic decays would significantly alter the neutron-to-proton ratio. We compute axion-induced modification of the neutron-to-proton ratio, and obtain robust upper bounds on the axion lifetimes, as low as 0.017 s for the axion mass higher than 300 MeV. Remarkably, this is stronger than projected future cosmic microwave background bounds via Neff. Our bounds are largely insensitive to uncertainties in hadronic cross sections and the axion’s branching fractions into various hadrons, as well as to the precise value of the initial axion abundance. We also incorporate, for the first time, several key improvements, such as scattering processes by energetic KL and secondary hadrons, that can also be important for studying general hadronic injections during BBN, not limited to those from axion decays.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (139)

  1. M. H. Reno and D. Seckel, Primordial nucleosynthesis: The effects of injecting hadrons, Phys. Rev. D 37, 3441 (1988).
  2. K. Kohri, Primordial nucleosynthesis and hadronic decay of a massive particle with a relatively short lifetime, Phys. Rev. D 64, 043515 (2001).
  3. K. Kohri and J. Yokoyama, Primordial black holes and primordial nucleosynthesis. 1. Effects of hadron injection from low mass holes, Phys. Rev. D 61, 023501 (2000).
  4. M. Kawasaki, K. Kohri, and N. Sugiyama, MeV scale reheating temperature and thermalization of neutrino background, Phys. Rev. D 62, 023506 (2000).
  5. K. Jedamzik, Did something decay, evaporate, or annihilate during big bang nucleosynthesis?, Phys. Rev. D 70, 063524 (2004).
  6. M. Kawasaki, K. Kohri, and T. Moroi, Hadronic decay of late—decaying particles and big-bang nucleosynthesis, Phys. Lett. B 625, 7 (2005).
  7. M. Kawasaki, K. Kohri, and T. Moroi, Big-Bang nucleosynthesis and hadronic decay of long-lived massive particles, Phys. Rev. D 71, 083502 (2005).
  8. K. Kohri, T. Moroi, and A. Yotsuyanagi, Big-bang nucleosynthesis with unstable gravitino and upper bound on the reheating temperature, Phys. Rev. D 73, 123511 (2006).
  9. K. Jedamzik, Big bang nucleosynthesis constraints on hadronically and electromagnetically decaying relic neutral particles, Phys. Rev. D 74, 103509 (2006).
  10. M. Kawasaki, K. Kohri, T. Moroi, and A. Yotsuyanagi, Big-Bang nucleosynthesis and gravitino, Phys. Rev. D 78, 065011 (2008).
  11. R. H. Cyburt, J. Ellis, B. D. Fields, F. Luo, K. A. Olive, and V. C. Spanos, Nucleosynthesis constraints on a massive gravitino in neutralino dark matter scenarios, J. Cosmol. Astropart. Phys. 10 (2009) 021.
  12. R. H. Cyburt, J. Ellis, B. D. Fields, F. Luo, K. A. Olive, and V. C. Spanos, Nuclear reaction uncertainties, massive gravitino decays and the cosmological lithium problem, J. Cosmol. Astropart. Phys. 10 (2010) 032.
  13. R. H. Cyburt, J. Ellis, B. D. Fields, F. Luo, K. A. Olive, and V. C. Spanos, Gravitino decays and the cosmological lithium problem in light of the LHC Higgs and supersymmetry searches, J. Cosmol. Astropart. Phys. 05 (2013) 014.
  14. M. Kawasaki, K. Kohri, T. Moroi, and Y. Takaesu, Revisiting big-bang nucleosynthesis constraints on long-lived decaying particles, Phys. Rev. D 97, 023502 (2018).
  15. T. Hasegawa, N. Hiroshima, K. Kohri, R. S. L. Hansen, T. Tram, and S. Hannestad, MeV-scale reheating temperature and thermalization of oscillating neutrinos by radiative and hadronic decays of massive particles, J. Cosmol. Astropart. Phys. 12 (2019) 012.
  16. L. Angel, G. Arcadi, M. M. A. Paixão, and F. S. Queiroz, Updated BBN bounds on hadronic injection in the early universe: The gravitino problem, arXiv:2501.09120.
  17. A. Fradette and M. Pospelov, BBN for the LHC: Constraints on lifetimes of the Higgs portal scalars, Phys. Rev. D 96, 075033 (2017).
  18. A. Fradette, M. Pospelov, J. Pradler, and A. Ritz, Cosmological constraints on very dark photons, Phys. Rev. D 90, 035022 (2014).
  19. J. Berger, K. Jedamzik, and D. G. E. Walker, Cosmological constraints on decoupled dark photons and dark Higgs, J. Cosmol. Astropart. Phys. 11 (2016) 032.
  20. A. Boyarsky, M. Ovchynnikov, O. Ruchayskiy, and V. Syvolap, Improved big bang nucleosynthesis constraints on heavy neutral leptons, Phys. Rev. D 104, 023517 (2021).
  21. Y.-M. Chen and Y. Zhang, BBN constraint on heavy neutrino production and decay, Phys. Rev. D 111, 123024 (2025).
  22. K. Jedamzik and M. Pospelov, Big bang nucleosynthesis and particle dark matter, New J. Phys. 11, 105028 (2009).
  23. B. Henning and H. Murayama, Constraints on light dark matter from big bang nucleosynthesis, arXiv:1205.6479.
  24. A. Omar and A. Ritz, BBN constraints on the hadronic annihilation of sub-GeV dark matter, arXiv:2510.11791.
  25. M. Pospelov and J. Pradler, Metastable GeV-scale particles as a solution to the cosmological lithium problem, Phys. Rev. D 82, 103514 (2010).
  26. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  27. R. D. Peccei and H. R. Quinn, Constraints imposed by CP conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
  28. S. Weinberg, A new light boson?, Phys. Rev. Lett. 40, 223 (1978).
  29. F. Wilczek, Problem of strong P and T invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
  30. J. E. Kim, Weak interaction singlet and strong CP invariance, Phys. Rev. Lett. 43, 103 (1979).
  31. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural CP invariance of strong interactions?, Nucl. Phys. B166, 493 (1980).
  32. M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong CP problem with a harmless axion, Phys. Lett. 104B, 199 (1981).
  33. A. R. Zhitnitsky, On possible suppression of the axion hadron interactions. (In Russian), Sov. J. Nucl. Phys. 31, 260 (1980).
  34. E. Goudzovski et al., New physics searches at kaon and hyperon factories, Rep. Prog. Phys. 86, 016201 (2023).
  35. S. Dimopoulos, A solution of the strong CP problem in models with scalars, Phys. Lett. 84B, 435 (1979).
  36. S. H. H. Tye, A superstrong force with a heavy axion, Phys. Rev. Lett. 47, 1035 (1981).
  37. P. Agrawal and K. Howe, Factoring the strong CP problem, J. High Energy Phys. 12 (2018) 029.
  38. V. A. Rubakov, Grand unification and heavy axion, JETP Lett. 65, 621 (1997).
  39. A. Valenti, L. Vecchi, and L.-X. Xu, Grand color axion, J. High Energy Phys. 10 (2022) 025.
  40. B. Holdom and M. E. Peskin, Raising the axion mass, Nucl. Phys. B208, 397 (1982).
  41. B. Holdom, Strong QCD at high-energies and a heavy axion, Phys. Lett. 154B, 316 (1985); 156B, 452(E) (1985).
  42. M. Dine and N. Seiberg, String theory and the strong CP problem, Nucl. Phys. B273, 109 (1986).
  43. J. M. Flynn and L. Randall, A computation of the small instanton contribution to the axion potential, Nucl. Phys. B293, 731 (1987).
  44. K. Choi, C. W. Kim, and W. K. Sze, Mass renormalization by instantons and the strong CP problem, Phys. Rev. Lett. 61, 794 (1988).
  45. K. Choi and H. D. Kim, Small instanton contribution to the axion potential in supersymmetric models, Phys. Rev. D 59, 072001 (1999).
  46. T. Gherghetta, V. V. Khoze, A. Pomarol, and Y. Shirman, The axion mass from 5D small instantons, J. High Energy Phys. 03 (2020) 063.
  47. Z. Berezhiani, L. Gianfagna, and M. Giannotti, Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited, Phys. Lett. B 500, 286 (2001).
  48. H. Fukuda, K. Harigaya, M. Ibe, and T. T. Yanagida, Model of visible QCD axion, Phys. Rev. D 92, 015021 (2015).
  49. A. Hook, S. Kumar, Z. Liu, and R. Sundrum, High quality QCD axion and the LHC, Phys. Rev. Lett. 124, 221801 (2020).
  50. K. J. Kelly, S. Kumar, and Z. Liu, Heavy axion opportunities at the DUNE near detector, Phys. Rev. D 103, 095002 (2021).
  51. J. H. Chang, R. Essig, and S. D. McDermott, Supernova 1987A constraints on Sub-GeV dark sectors, millicharged particles, the QCD axion, and an axion-like particle, J. High Energy Phys. 09 (2018) 051.
  52. F. Ertas and F. Kahlhoefer, On the interplay between astrophysical and laboratory probes of MeV-scale axion-like particles, J. High Energy Phys. 07 (2020) 050.
  53. R. Aaij et al. (LHCb Collaboration), Search for hidden-sector bosons in B0→K*0μ+μ− decays, Phys. Rev. Lett. 115, 161802 (2015).
  54. R. Aaij et al. (LHCb Collaboration), Search for long-lived scalar particles in B+→K+χ(μ+μ−) decays, Phys. Rev. D 95, 071101 (2017).
  55. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, Flavor probes of axion-like particles, J. High Energy Phys. 09 (2022) 056.
  56. G. Aad et al. (ATLAS Collaboration), Search for boosted diphoton resonances in the 10 to 70 GeV mass range using 138  fb−1 of 13 TeV pp collisions with the ATLAS detector, J. High Energy Phys. 07 (2023) 155.
  57. A. M. Sirunyan et al. (CMS Collaboration), Search for low mass vector resonances decaying into quark-antiquark pairs in proton-proton collisions at s=13  TeV, J. High Energy Phys. 01 (2018) 097.
  58. X. Cid Vidal, A. Mariotti, D. Redigolo, F. Sala, and K. Tobioka, New axion searches at flavor factories, J. High Energy Phys. 01 (2019) 113.
  59. R. Aaij et al. (LHCb Collaboration), Search for resonances decaying to photon pairs with masses between 4.9 and 19.4 GeV, arXiv:2507.14390.
  60. D. Aloni, Y. Soreq, and M. Williams, Coupling QCD-scale axionlike particles to gluons, Phys. Rev. Lett. 123, 031803 (2019).
  61. S. Chakraborty, M. Kraus, V. Loladze, T. Okui, and K. Tobioka, Heavy QCD axion in b→s transition: Enhanced limits and projections, Phys. Rev. D 104, 055036 (2021).
  62. E. Bertholet, S. Chakraborty, V. Loladze, T. Okui, A. Soffer, and K. Tobioka, Heavy QCD axion at Belle II: Displaced and prompt signals, Phys. Rev. D 105, L071701 (2022).
  63. J. P. Lees et al. (BABAR Collaboration), Search for an axionlike particle in B meson decays, Phys. Rev. Lett. 128, 131802 (2022).
  64. F. Bergsma et al. (CHARM Collaboration), Search for axion like particle production in 400-GeV proton—copper interactions, Phys. Lett. 157B, 458 (1985).
  65. J. Blumlein et al., Limits on neutral light scalar and pseudoscalar particles in a proton beam dump experiment, Z. Phys. C 51, 341 (1991).
  66. R. Acciarri et al. (ArgoNeuT Collaboration), First constraints on heavy QCD axions with a liquid argon time projection chamber using the ArgoNeuT experiment, Phys. Rev. Lett. 130, 221802 (2023).
  67. Y. Afik, B. Döbrich, J. Jerhot, Y. Soreq, and K. Tobioka, Probing long-lived axions at the KOTO experiment, Phys. Rev. D 108, 055007 (2023).
  68. E. Cortina Gil et al. (NA62 Collaboration), Search for hadronic decays of feebly-interacting particles at NA62, Eur. Phys. J. C 85, 571 (2025).
  69. D. I. Dunsky, L. J. Hall, and K. Harigaya, Dark radiation constraints on heavy QCD axions, J. High Energy Phys. 04 (2024) 130.
  70. P. F. Depta, M. Hufnagel, and K. Schmidt-Hoberg, Robust cosmological constraints on axion-like particles, J. Cosmol. Astropart. Phys. 05 (2020) 009.
  71. C. Balázs et al., Cosmological constraints on decaying axion-like particles: A global analysis, J. Cosmol. Astropart. Phys. 12 (2022) 027.
  72. D. Cadamuro and J. Redondo, Cosmological bounds on pseudo Nambu-Goldstone bosons, J. Cosmol. Astropart. Phys. 02 (2012) 032.
  73. M. Millea, L. Knox, and B. Fields, New bounds for axions and axion-like particles with keV-GeV masses, Phys. Rev. D 92, 023010 (2015).
  74. H.-C. Cheng, L. Li, and E. Salvioni, A theory of dark pions, J. High Energy Phys. 01 (2022) 122.
  75. D. Bisht, S. Chakraborty, and A. Samanta, A comprehensive study of ALPs from B-decays, J. High Energy Phys. 07 (2025) 092.
  76. Y. Bai, T.-K. Chen, J. Liu, and X. Ma, Wess-Zumino-Witten interactions of axions: Three-flavor, arXiv:2505.24822.
  77. R. Balkin, T. Coren, Y. Soreq, and M. Williams, A covariant description of the interactions of axion-like particles and hadrons, arXiv:2506.15637.
  78. K. G. Chetyrkin, B. A. Kniehl, M. Steinhauser, and W. A. Bardeen, Effective QCD interactions of CP odd Higgs bosons at three loops, Nucl. Phys. B535, 3 (1998).
  79. C. Bierlich et al., A comprehensive guide to the physics and usage of pythia 8.3, SciPost Phys. Codebases 2022, 8 (2022).
  80. G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Seymour, and B. R. Webber, herwig 6: An event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), J. High Energy Phys. 01 (2001) 010.
  81. M. Bahr et al., herwig++ physics and manual, Eur. Phys. J. C 58, 639 (2008).
  82. J. Bellm et al., herwig 7.0/herwig++ 3.0 release note, Eur. Phys. J. C 76, 196 (2016).
  83. C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Precision big bang nucleosynthesis with improved Helium-4 predictions, Phys. Rep. 754, 1 (2018).
  84. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  85. R. Srianand, N. Gupta, P. Petitjean, P. Noterdaeme, and C. Ledoux, Detection of 21-cm, H2 and deuterium absorption at z>3 along the line-of-sight to J1337+3152, Mon. Not. R. Astron. Soc. 405, 1888 (2010).
  86. M. Valerdi, A. Peimbert, M. Peimbert, and A. Sixtos, Determination of the primordial helium abundance based on NGC 346, an H II region of the small magellanic cloud, Astrophys. J. 876, 98 (2019).
  87. V. Fernández, E. Terlevich, A. I. Díaz, and R. Terlevich, A bayesian direct method implementation to fit emission line spectra: Application to the primordial he abundance determination, Mon. Not. R. Astron. Soc. 487, 3221 (2019).
  88. O. A. Kurichin, P. A. Kislitsyn, V. V. Klimenko, S. A. Balashev, and A. V. Ivanchik, A new determination of the primordial helium abundance using the analyses of H II region spectra from SDSS, Mon. Not. R. Astron. Soc. 502, 3045 (2021).
  89. T. Hsyu, R. J. Cooke, J. X. Prochaska, and M. Bolte, The PHLEK survey: A new determination of the primordial helium abundance, Astrophys. J. 896, 77 (2020).
  90. M. Valerdi, A. Peimbert, and M. Peimbert, Chemical abundances in seven metal-poor HII regions and a determination of the primordial helium abundance, Mon. Not. R. Astron. Soc. 505, 3624 (2021).
  91. E. Aver, D. A. Berg, A. S. Hirschauer, K. A. Olive, R. W. Pogge, N. S. J. Rogers, J. J. Salzer, and E. D. Skillman, A comprehensive chemical abundance analysis of the extremely metal poor Leoncino Dwarf galaxy (AGC 198691), Mon. Not. R. Astron. Soc. 510, 373 (2021).
  92. A. Matsumoto et al., EMPRESS. VIII. A new determination of primordial he abundance with extremely metal-poor galaxies: A suggestion of the lepton asymmetry and implications for the Hubble tension, Astrophys. J. 941, 167 (2022).
  93. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  94. A. Salvio, A. Strumia, and W. Xue, Thermal axion production, J. Cosmol. Astropart. Phys. 01 (2014) 011.
  95. F. D’Eramo, F. Hajkarim, and S. Yun, Thermal axion production at low temperatures: A smooth treatment of the QCD phase transition, Phys. Rev. Lett. 128, 152001 (2022).
  96. F. D’Eramo, F. Hajkarim, and S. Yun, Thermal QCD axions across thresholds, J. High Energy Phys. 10 (2021) 224.
  97. Z. G. Berezhiani, A. S. Sakharov, and M. Y. Khlopov, Primordial background of cosmological axions, Sov. J. Nucl. Phys. 55, 1063 (1992).
  98. S. Chang and K. Choi, Hadronic axion window and the big bang nucleosynthesis, Phys. Lett. B 316, 51 (1993).
  99. S. Hannestad, A. Mirizzi, and G. Raffelt, New cosmological mass limit on thermal relic axions, J. Cosmol. Astropart. Phys. 07 (2005) 002.
  100. F. D’Eramo, L. J. Hall, and D. Pappadopulo, Multiverse dark matter: SUSY or axions, J. High Energy Phys. 11 (2014) 108.
  101. M. Kawasaki, M. Yamada, and T. T. Yanagida, Observable dark radiation from a cosmologically safe QCD axion, Phys. Rev. D 91, 125018 (2015).
  102. R. Z. Ferreira, A. Notari, and F. Rompineve, Dine-Fischler-Srednicki-Zhitnitsky axion in the CMB, Phys. Rev. D 103, 063524 (2021).
  103. L. Di Luzio, G. Martinelli, and G. Piazza, Breakdown of chiral perturbation theory for the axion hot dark matter bound, Phys. Rev. Lett. 126, 241801 (2021).
  104. E. Masso, F. Rota, and G. Zsembinszki, On axion thermalization in the early universe, Phys. Rev. D 66, 023004 (2002).
  105. P. Graf and F. D. Steffen, Thermal axion production in the primordial quark-gluon plasma, Phys. Rev. D 83, 075011 (2011).
  106. R. Z. Ferreira and A. Notari, Observable windows for the QCD axion through the number of relativistic species, Phys. Rev. Lett. 120, 191301 (2018).
  107. F. Arias-Aragón, F. D’eramo, R. Z. Ferreira, L. Merlo, and A. Notari, Cosmic imprints of XENON1T axions, J. Cosmol. Astropart. Phys. 11 (2020) 025.
  108. W. Giarè, E. Di Valentino, A. Melchiorri, and O. Mena, New cosmological bounds on hot relics: Axions and neutrinos, Mon. Not. R. Astron. Soc. 505, 2703 (2021).
  109. A. Notari, F. Rompineve, and G. Villadoro, Improved hot dark matter bound on the QCD axion, Phys. Rev. Lett. 131, 011004 (2023).
  110. F. Bianchini, G. G. di Cortona, and M. Valli, QCD axion: Some like it hot, Phys. Rev. D 110, 123527 (2024).
  111. https://github.com/Kohsaku-Tobioka/axion_BBN
  112. O. Pisanti, A. Cirillo, S. Esposito, F. Iocco, G. Mangano, G. Miele, and P. D. Serpico, PArthENoPE: Public algorithm evaluating the nucleosynthesis of primordial elements, Comput. Phys. Commun. 178, 956 (2008).
  113. R. Consiglio, P. F. de Salas, G. Mangano, G. Miele, S. Pastor, and O. Pisanti, PArthENoPE reloaded, Comput. Phys. Commun. 233, 237 (2018).
  114. S. Gariazzo, P. F. de Salas, O. Pisanti, and R. Consiglio, PArthENoPE revolutions, Comput. Phys. Commun. 271, 108205 (2022).
  115. K. Saikawa and S. Shirai, Primordial gravitational waves, precisely: The role of thermodynamics in the standard model, J. Cosmol. Astropart. Phys. 05 (2018) 035.
  116. S. Ganguly, T. H. Jung, and S. Yun, Consistent Neff fitting in big bang nucleosynthesis analysis, arXiv:2507.23354.
  117. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972).
  118. A. D. Martin and G. G. Ross, K matrix analysis of the low-energy data for K−p and K20p reactions, Nucl. Phys. B16, 479 (1970).
  119. W. E. Cleland, B. Goz, D. Freytag, T. J. Devlin, R. J. Esterling, and K. G. Vosburgh, Measurement of the KL0−p and KL0−d total cross-sections, Phys. Rev. D 12, 1247 (1975).
  120. G. A. Sayer, E. F. Beall, T. J. Devlin, P. Shepard, and J. Solomon, Measurements of total cross sections for K20 mesons on protons and selected nuclei from 168 to 343 MeV/c and measurement of the K20 mean life, Phys. Rev. 169, 1045 (1968).
  121. M. Ferro-Luzzi, R. D. Tripp, and M. B. Watson, Excited hyperon of mass 1520 MeV, Phys. Rev. Lett. 8, 28 (1962).
  122. S. Adhikari et al. (GlueX Collaboration), Strange hadron spectroscopy with a secondary KL beam at GlueX, arXiv:1707.05284.
  123. P. Capiluppi, G. Giacomelli, G. Mandrioli, A. M. Rossi, P. Serra-Lugaresi, and L. Zitelli, A compilation of K0(L) p cross-sections.
  124. T.-G. Lee and C.-Y. Wong, Nuclear annihilation by antinucleons, Phys. Rev. C 93, 014616 (2016); 95, 029901(E) (2017).
  125. K. Abazajian et al. (CMB-S4 Collaboration), Snowmass 2021 CMB-S4 white paper, arXiv:2203.08024.
  126. P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis, Nucl. Phys. B360, 145 (1991).
  127. E. Fermi, An attempt of a theory of beta radiation. 1., Z. Phys. 88, 161 (1934).
  128. R. L. Workman, R. A. Arndt, W. J. Briscoe, M. W. Paris, and I. I. Strakovsky, Parameterization dependence of T matrix poles and eigenphases from a fit to πN elastic scattering data, Phys. Rev. C 86, 035202 (2012).
  129. R. A. Arndt, I. I. Strakovsky, and R. L. Workman, The SAID PWA program, Int. J. Mod. Phys. A 18, 449 (2003).
  130. The George Washington University, The SAID PWA program, https://gwdac.phys.gwu.edu/ (accessed in 2025).
  131. J. Gasser, V. E. Lyubovitskij, and A. Rusetsky, Hadronic atoms in QCD+QED, Phys. Rep. 456, 167 (2008).
  132. W. K. H. Panofsky, R. L. Aamodt, and J. Hadley, The gamma-ray spectrum resulting from capture of negative π-mesons in hydrogen and deuterium, Phys. Rev. 81, 565 (1951).
  133. J. Spuller, D. Berghofer, M. D. Hasinoff, R. Macdonald, D. F. Measday, M. Salomon, T. Suzuki, J. M. Poutissou, R. Poutissou, and J. K. P. Lee, A remeasurement of the Panofsky ratio, Phys. Lett. B 67, 479 (1977).
  134. T. Flugel, The pion beta decay experiment and a remeasurement of the Panofsky ratio, thesis, Federal Institute of Technology Zurich (ETHZ), 3, 1999.
  135. R. H. Dalitz and S. F. Tuan, The phenomenological description of -K -nucleon reaction processes, Ann. Phys. (N.Y.) 10, 307 (1960).
  136. S. Cassel, Sommerfeld factor for arbitrary partial wave processes, J. Phys. G 37, 105009 (2010).
  137. R. L. Workman et al. (Particle Data Group Collaboration), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  138. R. Yamartino, G. W. Brandenburg, W. B. Johnson, D. W. G. S. Leith, J. S. Loos, G. Luste, J. A. J. Matthews, K. Moriyasu, W. M. Smart, and F. C. Winkelmann, A study of the reactions K¯p0→Λπ+ and K¯p0→Σ0π+ from 1-GeV/c to 12-GeV/c, Phys. Rev. D 10, 9 (1974).
  139. J. C. M. Armitage et al., A study of K0 p charge exchange scattering from 0.6-GeV/c to 1.5-GeV/c, Nucl. Phys. B123, 11 (1977).

Outline

Information

Phys. Rev. D 113, 055002– Published 2 March, 2026
  • Received 3 November 2025
  • Accepted 12 January 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation