- Open Access
Neutrino mass variables in three active and two sterile neutrino scenario
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 and scales have been proposed to address the T2K– 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 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 constrained by cosmology, the effective electron neutrino mass from decay, and the effective Majorana mass probed in neutrinoless double decay. We demonstrate that the presence of two sterile states can significantly modify the allowed parameter space compared to the three-flavor and 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.
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References (83)
- S. L. Glashow, Nucl. Phys. 22, 579 (1961).
- S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).
- S. Weinberg, Phys. Rev. Lett. 43, 1566 (1979).
- Y. Fukuda et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett. 81, 1562 (1998).
- Q. R. Ahmad et al. (SNO Collaboration), Phys. Rev. Lett. 89, 011301 (2002).
- E. Aliu et al. (K2K Collaboration), Phys. Rev. Lett. 94, 081802 (2005).
- P. Adamson et al. (MINOS+ Collaboration), Phys. Rev. Lett. 125, 131802 (2020).
- K. Abe et al. (T2K Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 659, 106 (2011).
- M. A. Acero et al. (NOvA Collaboration), Phys. Rev. D 106, 032004 (2022).
- A. Gando et al. (KamLAND Collaboration), Phys. Rev. D 88, 033001 (2013).
- Y. Abe et al. (Double Chooz Collaboration), Phys. Rev. D 86, 052008 (2012).
- J. K. Ahn et al. (RENO Collaboration), Phys. Rev. Lett. 108, 191802 (2012).
- F. P. An et al. (Daya Bay Collaboration), Phys. Rev. Lett. 112, 061801 (2014).
- A. Aguilar et al. (LSND Collaboration), Phys. Rev. D 64, 112007 (2001).
- A. A. Aguilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. D 103, 052002 (2021).
- W. Hampel et al. (GALLEX Collaboration), Phys. Lett. B 420, 114 (1998).
- D. N. Abdurashitov et al., Phys. Rev. Lett. 77, 4708 (1996).
- V. V. Barinov et al., Phys. Rev. Lett. 128, 232501 (2022).
- S. Goswami, Phys. Rev. D 55, 2931 (1997).
- J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996).
- A. Tumasyan et al. (CMS Collaboration), Phys. Lett. B 842, 137563 (2023).
- C. Giunti and M. Laveder, Phys. Rev. D 84, 073008 (2011).
- C. Giunti and M. Laveder, Phys. Rev. D 84, 093006 (2011).
- C. Giunti and M. Laveder, Phys. Lett. B 706, 200 (2011).
- Y. J. Ko et al. (NEOS Collaboration), Phys. Rev. Lett. 118, 121802 (2017).
- I. Alekseev et al., J. Instrum. 11, P11011 (2016).
- M. G. Aartsen et al. (IceCube Collaboration), Phys. Rev. Lett. 117, 071801 (2016).
- S. Gariazzo, C. Giunti, M. Laveder, and Y. F. Li, J. High Energy Phys. 06 (2017) 135.
- C. S. Fong, H. Minakata, and H. Nunokawa, J. High Energy Phys. 02 (2016) 114.
- P. B. Denton, Y. Farzan, and I. M. Shoemaker, Phys. Rev. D 99, 035003 (2019).
- C. Giunti, Phys. Lett. B 795, 236 (2019).
- H. Minakata, arXiv:2503.09280.
- A. Albert et al. (ANTARES Collaboration), J. High Energy Phys. 06 (2018) 113.
- C. Giunti, Y. F. Li, and Y. Y. Zhang, J. High Energy Phys. 05 (2019) 061.
- 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).
- M. Aker et al. (KATRIN Collaboration), Phys. Rev. Lett. 126, 091803 (2021).
- S. Goswami, D. Pachhar, and S. Pan, Phys. Rev. D 110, 015028 (2024).
- A. Serebrov, R. Samoilov, and M. Chaikovskii, arXiv:2109.12385.
- A. P. Serebrov, R. M. Samoilov, and M. E. Chaikovskii, arXiv:2112.14856.
- P. Abratenko et al. (MicroBooNE Collaboration), Nature (London) 648, 64 (2025).
- M. Archidiacono, N. Fornengo, C. Giunti, and A. Melchiorri, Phys. Rev. D 86, 065028 (2012).
- S. Gariazzo, P. F. de Salas, and S. Pastor, J. Cosmol. Astropart. Phys. 07 (2019) 014.
- M. Archidiacono, S. Hannestad, R. S. Hansen, and T. Tram, Phys. Rev. D 91, 065021 (2015).
- G. Gelmini, E. Osoba, S. Palomares-Ruiz, and S. Pascoli, J. Cosmol. Astropart. Phys. 10 (2008) 029.
- K. Chakraborty, S. Goswami, and B. Karmakar, Phys. Rev. D 100, 035017 (2019).
- S. Jana, L. Puetter, and A. Y. Smirnov, Phys. Rev. D 111, 015011 (2025).
- S. Goswami and W. Rodejohann, Phys. Rev. D 73, 113003 (2006).
- S. Goswami and W. Rodejohann, J. High Energy Phys. 10 (2007) 073.
- P. C. de Holanda and A. Y. Smirnov, Phys. Rev. D 83, 113011 (2011).
- P. C. de Holanda and A. Y. Smirnov, Phys. Rev. D 69, 113002 (2004).
- A. de Gouvêa, G. Jusino Sánchez, and K. J. Kelly, Phys. Rev. D 106, 055025 (2022).
- A. Chatterjee, S. Goswami, and S. Pan, Nucl. Phys. B996, 116370 (2023).
- E. Cabrera, M. Jin, C. A. Argüelles, and A. Esmaili, Phys. Rev. D 113, 075015 (2026).
- E. Cabrera, A. Esmaili, H. Nunokawa, and A. M. G. Trzeciak, Phys. Rev. D 113, 015017 (2026).
- S. Kumar Agarwalla, S. S. Chatterjee, and A. Palazzo, J. High Energy Phys. 12 (2019) 174.
- S. K. Agarwalla, S. S. Chatterjee, and A. Palazzo, J. High Energy Phys. 04 (2018) 091.
- E. Cabrera, A. Esmaili, and A. A. Quiroga, J. Cosmol. Astropart. Phys. 11 (2024) 059.
- N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
- B. Dasgupta and J. Kopp, Phys. Rev. Lett. 112, 031803 (2014).
- S. Hannestad, R. S. Hansen, and T. Tram, Phys. Rev. Lett. 112, 031802 (2014).
- J. M. Cline, Phys. Lett. B 802, 135182 (2020).
- Y. Farzan, Phys. Lett. B 797, 134911 (2019).
- F. Forastieri, M. Lattanzi, G. Mangano, A. Mirizzi, P. Natoli, and N. Saviano, J. Cosmol. Astropart. Phys. 07 (2017) 038.
- C. E. Yaguna, J. High Energy Phys. 06 (2007) 002.
- G. B. Gelmini, P. Lu, and V. Takhistov, J. Cosmol. Astropart. Phys. 12 (2019) 047.
- G. B. Gelmini, P. Lu, and V. Takhistov, Phys. Lett. B 800, 135113 (2020).
- T. Hasegawa, N. Hiroshima, K. Kohri, R. S. L. Hansen, T. Tram, and S. Hannestad, J. Cosmol. Astropart. Phys. 08 (2020) 015.
- 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).
- 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.
- K. Akita and M. Yamaguchi, J. Cosmol. Astropart. Phys. 08 (2020) 012.
- J. Froustey, C. Pitrou, and M. C. Volpe, J. Cosmol. Astropart. Phys. 12 (2020) 015.
- H. Acharya et al. (KATRIN Collaboration), Nature (London) 648, 70 (2025).
- M. Aker et al. (KATRIN Collaboration), Science 388, adq9592 (2025).
- P. Adamson et al. (MINOS+ Collaboration), Phys. Rev. Lett. 122, 091803 (2019).
- M. A. Acero et al., J. Phys. G 51, 120501 (2024).
- I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, J. High Energy Phys. 12 (2024) 216.
- A. Abusleme et al. (JUNO Collaboration), arXiv:2511.14593.
- G. Karagiorgi, Z. Djurcic, J. M. Conrad, M. H. Shaevitz, and M. Sorel, Phys. Rev. D 80, 073001 (2009); 81, 039902(E) (2010).
- A. Donini and D. Meloni, Eur. Phys. J. C 22, 179 (2001).
- S. Abe et al. (KamLAND-Zen Collaboration), Phys. Rev. Lett. 135, 262501 (2025).
- A. A. Esfahani et al. (Project 8 Collaboration), in Snowmass 2021 (2022), arXiv:2203.07349.
- E. Di Valentino, A. Melchiorri, and J. Silk, Phys. Rev. D 92, 121302 (2015).
- H. Shao, J. J. Givans, J. Dunkley, M. Madhavacheril, F. J. Qu, G. Farren, and B. Sherwin, Phys. Rev. D 111, 083535 (2025).