• [1]

    B. T. Cleveland, T. Daily, R. Davis, J r., J. R. Distel, K. Lande, C. K. Lee, et al., Astrophys. J. 496, 505 (1998)

  • [2]

    Super-Kamiokande collaboration, Y. Fukuda, et al., Phys. Rev. Lett. 81, 1562 (1998), arXiv: hep-ex/9807003

  • [3]

    SNO collaboration, Q. R. Ahmad, et al., Phys. Rev. Lett. 89, 011301 (2002), arXiv: nucl-ex/0204008

  • [4]

    SNO collaboration, S. N. Ahmed, et al., Phys. Rev. Lett. 92, 181301 (2004), arXiv: nucl-ex/0309004

  • [5]

    KamLAND collaboration, K. Eguchi, et al., Phys. Rev. Lett. 90, 021802 (2003), arXiv: hep-ex/0212021

  • [6]

    K2K collaboration, M. H. Ahn, et al., Phys. Rev. D 74, 072003 (2006), arXiv: hep-ex/0606032

  • [7]

    Daya Bay collaboration, F. P. An, et al., Phys. Rev. Lett. 108, 171803 (2012), arXiv: 1203.1669

  • [8]

    R. H. Bernstein and P. S. Cooper, Phys. Rept. 532, 27 (2013), arXiv: 1307.5787

  • [9]

    M. Lindner, M. Platscher and F. S. Queiroz, Phys. Rept. 731, 1 (2018), arXiv: 1610.06587

  • [10]

    L. Calibbi and G. Signorelli, Riv. Nuovo Cim. 41, 71 (2018), arXiv: 1709.00294

  • [11]

    M. Ardu and G. Pezzullo, Universe 8, 299 (2022), arXiv: 2204.08220

  • [12]

    G. Frau and C. Langenbruch, Symmetry 16, 359 (2024)

  • [13]

    P. Minkowski, Phys. Lett. B 67, 421 (1977)

  • [14]

    T. Yanagida, Conf. Proc. C 7902131, 95 (1979)

  • [15]

    M. Gell-Mann, P. Ramond and R. Slansky, Conf. Proc. C 790927, 315 (1979), arXiv: 1306.4669

  • [16]

    M. Magg and C. Wetterich, Phys. Lett. B 94, 61 (1980)

  • [17]

    T. P. Cheng and L.-F. Li, Phys. Rev. D 22, 2860 (1980)

  • [18]

    G. Lazarides, Q. Shafi and C. Wetterich, Nucl. Phys. B 181, 287 (1981)

  • [19]

    J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980)

  • [20]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981)

  • [21]

    R. Foot, H. Lew, X. G. He and G. C. Joshi, Z. Phys. C 44, 441 (1989)

  • [22]

    M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986)

  • [23]

    C. H. Albright and S. M. Barr, Phys. Rev. D 69, 073010 (2004), arXiv: hep-ph/0312224

  • [24]

    G. F. Giudice, A. Notari, M. Raidal, A. Riotto and A. Strumia, Nucl. Phys. B 685, 89 (2004), arXiv: hep-ph/0310123

  • [25]

    E. Ma and U. Sarkar, Phys. Rev. Lett. 80, 5716 (1998), arXiv: hep-ph/9802445

  • [26]

    T. Hambye, M. Raidal and A. Strumia, Phys. Lett. B 632, 667 (2006), arXiv: hep-ph/0510008

  • [27]

    N. D. Barrie, C. Han and H. Murayama, Phys. Rev. Lett. 128, 141801 (2022), arXiv: 2106.03381

  • [28]

    N. D. Barrie, C. Han and H. Murayama, JHEP 05, 160 (2022), arXiv: 2204.08202

  • [29]

    A. Melfo, M. Nemevsek, F. Nesti, G. Senjanovic and Y. Zhang, Phys. Rev. D 85, 055018 (2012), arXiv: 1108.4416

  • [30]

    Y. Du, A. Dunbrack, M. J. Ramsey-Musolf and J.-H. Yu, JHEP 01, 101 (2019), arXiv: 1810.09450

  • [31]

    S. Antusch, O. Fischer, A. Hammad and C. Scherb, JHEP 02, 157 (2019), arXiv: 1811.03476

  • [32]

    P. S. Bhupal Dev and Y. Zhang, JHEP 10, 199 (2018), arXiv: 1808.00943

  • [33]

    S. Ashanujjaman and K. Ghosh, JHEP 03, 195 (2022), arXiv: 2108.10952

  • [34]

    E. J. Chun, S. Khan, S. Mandal, M. Mitra and S. Shil, Phys. Rev. D 101, 075008 (2020), arXiv: 1911.00971

  • [35]

    S. Mandal, O. G. Miranda, G. S. Garcia, J. W. F. Valle and X.-J. Xu, Phys. Lett. B 829, 137110 (2022), arXiv: 2202.04502

  • [36]

    C. Han, Z. Lei and W. Liao, Chin. Phys. C 47, 093104 (2023), arXiv: 2303.15709

  • [37]

    E. J. Chun, K. Y. Lee and S. C. Park, Phys. Lett. B 566, 142 (2003), arXiv: hep-ph/0304069

  • [38]

    M. Kakizaki, Y. Ogura and F. Shima, Phys. Lett. B 566, 210 (2003), arXiv: hep-ph/0304254

  • [39]

    A. G. Akeroyd, M. Aoki and H. Sugiyama, Phys. Rev. D 79, 113010 (2009), arXiv: 0904.3640

  • [40]

    D. N. Dinh, A. Ibarra, E. Molinaro and S. T. Petcov, JHEP 08, 125 (2012), arXiv: 1205.4671

  • [41]

    C. Han, D. Huang, J. Tang and Y. Zhang, Phys. Rev. D 103, 055023 (2021), arXiv: 2102.00758

  • [42]

    M. M. Ferreira, T. B. de Melo, S. Kovalenko, P. R. D. Pinheiro and F. S. Queiroz, Eur. Phys. J. C 79, 955 (2019), arXiv: 1903.07634

  • [43]

    N. D. Barrie and S. T. Petcov, JHEP 01, 001 (2023), arXiv: 2210.02110

  • [44]

    L. Calibbi and X. Gao, Phys. Rev. D 106, 095036 (2022), arXiv: 2206.10682

  • [45]

    M. Ardu, S. Davidson and S. Lavignac, JHEP 11, 101 (2023), arXiv: 2308.16897

  • [46]

    M. Ardu, S. Davidson and S. Lavignac, Eur. Phys. J. C 84, 458 (2024), arXiv: 2401.06214

  • [47]

    J. Adam, et al., Eur. Phys. J. C 73, 2365 (2013), arXiv: 1303.2348

  • [48]

    SINDRUM collaboration, U. Bellgardt, et al., Nucl. Phys. B 299, 1 (1988)

  • [49]

    SINDRUM Ⅱ collaboration, C. Dohmen, et al., Phys. Lett. B 317, 631 (1993)

  • [50]

    SINDRUM Ⅱ collaboration, W. H. Bertl, et al., Eur. Phys. J. C 47, 337 (2006)

  • [51]

    MEG Ⅱ collaboration, A. M. Baldini, et al., Eur. Phys. J. C 78, 380 (2018), arXiv: 1801.04688

  • [52]

    Mu3e collaboration, K. Arndt, et al., Nucl. Instrum. Meth. A 1014, 165679 (2021), arXiv: 2009.11690

  • [53]

    Mu2e collaboration, L. Bartoszek et al., 1501.05241.

  • [54]

    COMET collaboration, R. Abramishvili, et al., PTEP 2020, 033C (2020), arXiv: 1812.09018

  • [55]

    C. Group collaboration, M. Aoki et al., in 3, 2022, 2203.08278.

  • [56]

    ATLAS collaboration, M. Aaboud, et al., Eur. Phys. J. C 78, 199 (2018), arXiv: 1710.09748

  • [57]

    I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz and A. Zhou, JHEP 09, 178 (2020), arXiv: 2007.14792

  • [58]

    Planck collaboration, N. Aghanim, et al., Astron. Astrophys. 641, A6 (2020), arXiv: 1807.06209

  • [59]

    S. Mandal, O. G. Miranda, G. Sanchez Garcia, J. W. F. Valle and X.-J. Xu, Phys. Rev. D 105, 095020 (2022), arXiv: 2203.06362

  • [60]

    A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, M. C. Peyranere, L. Rahili, et al., Phys. Rev. D 84, 095005 (2011), arXiv: 1105.1925

  • [61]

    C. Bonilla, R. M. Fonseca and J. W. F. Valle, Phys. Rev. D 92, 075028 (2015), arXiv: 1508.02323

  • [62]

    I. Affleck and M. Dine, Nucl. Phys. B 249, 361 (1985)

  • [63]

    A. A. Starobinsky, Phys. Lett. B 91, 99 (1980)

  • [64]

    F. L. Bezrukov and M. Shaposhnikov, Phys. Lett. B 659, 703 (2008), arXiv: 0710.3755

  • [65]

    J. L. F. Barbon and J. R. Espinosa, Phys. Rev. D 79, 081302 (2009), arXiv: 0903.0355

  • [66]

    F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, JHEP 01, 016 (2011), arXiv: 1008.5157

  • [67]

    M. P. Hertzberg, JHEP 11, 023 (2010), arXiv: 1002.2995

  • [68]

    C. P. Burgess, H. M. Lee and M. Trott, JHEP 07, 007 (2010), arXiv: 1002.2730

  • [69]

    G. F. Giudice and H. M. Lee, Phys. Lett. B 694, 294 (2011), arXiv: 1010.1417

  • [70]

    O. Lebedev and H. M. Lee, Eur. Phys. J. C 71, 1821 (2011), arXiv: 1105.2284

  • [71]

    C. Han, S. Huang and Z. Lei, Phys. Rev. D 107, 015021 (2023), arXiv: 2208.11336

  • [72]

    V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 155, 36 (1985)

  • [73]

    J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990)

  • [74]

    F. R. Klinkhamer and N. S. Manton, Phys. Rev. D 30, 2212 (1984)

  • [75]

    M. Trodden, Rev. Mod. Phys. 71, 1463 (1999), arXiv: hep-ph/9803479

  • [76]

    R. Kitano, M. Koike and Y. Okada, Phys. Rev. D 66, 096002 (2002), arXiv: hep-ph/0203110