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

Neutrino mass variables in three active and two sterile neutrino scenario

Srubabati Goswami1,*, Hemanth M.2,†, Debashis Pachhar1,‡, and N. Rajeev1,3,§

  • *Contact author: sruba@prl.res.in
  • †Contact author: hemanth.m@ug.cusat.ac.in
  • ‡Contact author: debashispachhar@prl.res.in
  • §Contact author: rajeevneutrino@gmail.com

Phys. Rev. D 113, 115050 – Published 22 June, 2026

DOI: https://doi.org/10.1103/3lb9-29zh

Abstract

The three-flavor framework of neutrino oscillations successfully explains most experimental results, but persistent anomalies at short- and long-baseline experiments hint at the existence of additional light sterile states. In particular, eV-scale sterile neutrinos are motivated by LSND and MiniBooNE results, while sub-eV sterile states with mass-squared differences at the 10−2 and 10−5  eV2 scales have been proposed to address the T2K–NOνA tension and the absence of the expected upturn in the solar neutrino energy spectrum, respectively. Such sterile states are singlets under the Standard Model gauge group and mix only through their admixture with active neutrinos. In this work, we investigate the phenomenology of the 3+2 scenario, incorporating one eV-scale sterile neutrino together with a sub-eV state, and analyze their impact on absolute-mass related observables; the sum of neutrino masses Σ constrained by cosmology, the effective electron neutrino mass mβ from β decay, and the effective Majorana mass mββ probed in neutrinoless double β decay. We demonstrate that the presence of two sterile states can significantly modify the allowed parameter space compared to the three-flavor and 3+1 frameworks, with some mass-ordering schemes already disfavored by current cosmological and laboratory limits. Finally, we assess the implications of upcoming sensitivities from KATRIN, Project 8, and LEGEND-1000, highlighting the complementary role of sub-eV sterile neutrinos in probing physics beyond the minimal three-flavor paradigm.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (83)

  1. S. L. Glashow, Nucl. Phys. 22, 579 (1961).
  2. S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).
  3. S. Weinberg, Phys. Rev. Lett. 43, 1566 (1979).
  4. Y. Fukuda et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett. 81, 1562 (1998).
  5. Q. R. Ahmad et al. (SNO Collaboration), Phys. Rev. Lett. 89, 011301 (2002).
  6. E. Aliu et al. (K2K Collaboration), Phys. Rev. Lett. 94, 081802 (2005).
  7. P. Adamson et al. (MINOS+ Collaboration), Phys. Rev. Lett. 125, 131802 (2020).
  8. K. Abe et al. (T2K Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 659, 106 (2011).
  9. M. A. Acero et al. (NOvA Collaboration), Phys. Rev. D 106, 032004 (2022).
  10. A. Gando et al. (KamLAND Collaboration), Phys. Rev. D 88, 033001 (2013).
  11. Y. Abe et al. (Double Chooz Collaboration), Phys. Rev. D 86, 052008 (2012).
  12. J. K. Ahn et al. (RENO Collaboration), Phys. Rev. Lett. 108, 191802 (2012).
  13. F. P. An et al. (Daya Bay Collaboration), Phys. Rev. Lett. 112, 061801 (2014).
  14. A. Aguilar et al. (LSND Collaboration), Phys. Rev. D 64, 112007 (2001).
  15. A. A. Aguilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. D 103, 052002 (2021).
  16. W. Hampel et al. (GALLEX Collaboration), Phys. Lett. B 420, 114 (1998).
  17. D. N. Abdurashitov et al., Phys. Rev. Lett. 77, 4708 (1996).
  18. V. V. Barinov et al., Phys. Rev. Lett. 128, 232501 (2022).
  19. S. Goswami, Phys. Rev. D 55, 2931 (1997).
  20. J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996).
  21. A. Tumasyan et al. (CMS Collaboration), Phys. Lett. B 842, 137563 (2023).
  22. C. Giunti and M. Laveder, Phys. Rev. D 84, 073008 (2011).
  23. C. Giunti and M. Laveder, Phys. Rev. D 84, 093006 (2011).
  24. C. Giunti and M. Laveder, Phys. Lett. B 706, 200 (2011).
  25. Y. J. Ko et al. (NEOS Collaboration), Phys. Rev. Lett. 118, 121802 (2017).
  26. I. Alekseev et al., J. Instrum. 11, P11011 (2016).
  27. M. G. Aartsen et al. (IceCube Collaboration), Phys. Rev. Lett. 117, 071801 (2016).
  28. S. Gariazzo, C. Giunti, M. Laveder, and Y. F. Li, J. High Energy Phys. 06 (2017) 135.
  29. C. S. Fong, H. Minakata, and H. Nunokawa, J. High Energy Phys. 02 (2016) 114.
  30. P. B. Denton, Y. Farzan, and I. M. Shoemaker, Phys. Rev. D 99, 035003 (2019).
  31. C. Giunti, Phys. Lett. B 795, 236 (2019).
  32. H. Minakata, arXiv:2503.09280.
  33. A. Albert et al. (ANTARES Collaboration), J. High Energy Phys. 06 (2018) 113.
  34. C. Giunti, Y. F. Li, and Y. Y. Zhang, J. High Energy Phys. 05 (2019) 061.
  35. M. Adams, F. Bezrukov, J. Elvin-Poole, J. J. Evans, P. Guzowski, B. Ó. Fearraigh, and S. Söldner-Rembold, Eur. Phys. J. C 80, 758 (2020).
  36. M. Aker et al. (KATRIN Collaboration), Phys. Rev. Lett. 126, 091803 (2021).
  37. S. Goswami, D. Pachhar, and S. Pan, Phys. Rev. D 110, 015028 (2024).
  38. A. Serebrov, R. Samoilov, and M. Chaikovskii, arXiv:2109.12385.
  39. A. P. Serebrov, R. M. Samoilov, and M. E. Chaikovskii, arXiv:2112.14856.
  40. P. Abratenko et al. (MicroBooNE Collaboration), Nature (London) 648, 64 (2025).
  41. M. Archidiacono, N. Fornengo, C. Giunti, and A. Melchiorri, Phys. Rev. D 86, 065028 (2012).
  42. S. Gariazzo, P. F. de Salas, and S. Pastor, J. Cosmol. Astropart. Phys. 07 (2019) 014.
  43. M. Archidiacono, S. Hannestad, R. S. Hansen, and T. Tram, Phys. Rev. D 91, 065021 (2015).
  44. G. Gelmini, E. Osoba, S. Palomares-Ruiz, and S. Pascoli, J. Cosmol. Astropart. Phys. 10 (2008) 029.
  45. K. Chakraborty, S. Goswami, and B. Karmakar, Phys. Rev. D 100, 035017 (2019).
  46. S. Jana, L. Puetter, and A. Y. Smirnov, Phys. Rev. D 111, 015011 (2025).
  47. S. Goswami and W. Rodejohann, Phys. Rev. D 73, 113003 (2006).
  48. S. Goswami and W. Rodejohann, J. High Energy Phys. 10 (2007) 073.
  49. P. C. de Holanda and A. Y. Smirnov, Phys. Rev. D 83, 113011 (2011).
  50. P. C. de Holanda and A. Y. Smirnov, Phys. Rev. D 69, 113002 (2004).
  51. A. de Gouvêa, G. Jusino Sánchez, and K. J. Kelly, Phys. Rev. D 106, 055025 (2022).
  52. A. Chatterjee, S. Goswami, and S. Pan, Nucl. Phys. B996, 116370 (2023).
  53. E. Cabrera, M. Jin, C. A. Argüelles, and A. Esmaili, Phys. Rev. D 113, 075015 (2026).
  54. E. Cabrera, A. Esmaili, H. Nunokawa, and A. M. G. Trzeciak, Phys. Rev. D 113, 015017 (2026).
  55. S. Kumar Agarwalla, S. S. Chatterjee, and A. Palazzo, J. High Energy Phys. 12 (2019) 174.
  56. S. K. Agarwalla, S. S. Chatterjee, and A. Palazzo, J. High Energy Phys. 04 (2018) 091.
  57. E. Cabrera, A. Esmaili, and A. A. Quiroga, J. Cosmol. Astropart. Phys. 11 (2024) 059.
  58. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  59. B. Dasgupta and J. Kopp, Phys. Rev. Lett. 112, 031803 (2014).
  60. S. Hannestad, R. S. Hansen, and T. Tram, Phys. Rev. Lett. 112, 031802 (2014).
  61. J. M. Cline, Phys. Lett. B 802, 135182 (2020).
  62. Y. Farzan, Phys. Lett. B 797, 134911 (2019).
  63. F. Forastieri, M. Lattanzi, G. Mangano, A. Mirizzi, P. Natoli, and N. Saviano, J. Cosmol. Astropart. Phys. 07 (2017) 038.
  64. C. E. Yaguna, J. High Energy Phys. 06 (2007) 002.
  65. G. B. Gelmini, P. Lu, and V. Takhistov, J. Cosmol. Astropart. Phys. 12 (2019) 047.
  66. G. B. Gelmini, P. Lu, and V. Takhistov, Phys. Lett. B 800, 135113 (2020).
  67. T. Hasegawa, N. Hiroshima, K. Kohri, R. S. L. Hansen, T. Tram, and S. Hannestad, J. Cosmol. Astropart. Phys. 08 (2020) 015.
  68. S. Hagstotz, P. F. de Salas, S. Gariazzo, M. Gerbino, M. Lattanzi, S. Vagnozzi, K. Freese, and S. Pastor, Phys. Rev. D 104, 123524 (2021).
  69. J. J. Bennett, G. Buldgen, P. F. De Salas, M. Drewes, S. Gariazzo, S. Pastor, and Y. Y. Y. Wong, J. Cosmol. Astropart. Phys. 04 (2020) 073.
  70. K. Akita and M. Yamaguchi, J. Cosmol. Astropart. Phys. 08 (2020) 012.
  71. J. Froustey, C. Pitrou, and M. C. Volpe, J. Cosmol. Astropart. Phys. 12 (2020) 015.
  72. H. Acharya et al. (KATRIN Collaboration), Nature (London) 648, 70 (2025).
  73. M. Aker et al. (KATRIN Collaboration), Science 388, adq9592 (2025).
  74. P. Adamson et al. (MINOS+ Collaboration), Phys. Rev. Lett. 122, 091803 (2019).
  75. M. A. Acero et al., J. Phys. G 51, 120501 (2024).
  76. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, J. High Energy Phys. 12 (2024) 216.
  77. A. Abusleme et al. (JUNO Collaboration), arXiv:2511.14593.
  78. G. Karagiorgi, Z. Djurcic, J. M. Conrad, M. H. Shaevitz, and M. Sorel, Phys. Rev. D 80, 073001 (2009); 81, 039902(E) (2010).
  79. A. Donini and D. Meloni, Eur. Phys. J. C 22, 179 (2001).
  80. S. Abe et al. (KamLAND-Zen Collaboration), Phys. Rev. Lett. 135, 262501 (2025).
  81. A. A. Esfahani et al. (Project 8 Collaboration), in Snowmass 2021 (2022), arXiv:2203.07349.
  82. E. Di Valentino, A. Melchiorri, and J. Silk, Phys. Rev. D 92, 121302 (2015).
  83. H. Shao, J. J. Givans, J. Dunkley, M. Madhavacheril, F. J. Qu, G. Farren, and B. Sherwin, Phys. Rev. D 111, 083535 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation