• [1]

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

  • [2]

    S NO, Q. R. Ahmad et al., Phys. Rev. Lett. 87, 071301 (2001), arXiv:nucl-ex/0106015

  • [3]

    H. Fritzsch and Z.-z. Xing, Phys. Lett. B 353, 114 (1995), arXiv:hep-ph/9502297

  • [4]

    H. Nishiura, K. Matsuda, and T. Fukuyama, Phys. Rev. D 60, 013006 (1999), arXiv:hepph/9902385

  • [5]

    K. Matsuda, T. Fukuyama, and H. Nishiura, Phys. Rev. D 61, 053001 (2000), arXiv:hepph/9906433

  • [6]

    H. Fritzsch and Z.-z. Xing, Prog. Part. Nucl. Phys. 45, 1 (2000), arXiv:hep-ph/9912358

  • [7]

    H. Fritzsch and Z.-z. Xing, Phys. Lett. B 555, 63 (2003), arXiv:hep-ph/0212195

  • [8]

    Z.-z. Xing and H. Zhang, Phys. Lett. B 569, 30 (2003), arXiv:hep-ph/0304234

  • [9]

    Z.-z. Xing and H. Zhang, J. Phys. G 30, 129 (2004), arXiv:hep-ph/0309112

  • [10]

    M. Bando, S. Kaneko, M. Obara et al., Prog. Theor. Phys. 112, 533 (2004), arXiv:hep-ph/0405071

  • [11]

    K. Matsuda and H. Nishiura, Phys. Rev. D 74, 033014 (2006), arXiv:hep-ph/0606142

  • [12]

    G. Ahuja, S. Kumar, M. Randhawa et al., Phys. Rev. D 76, 013006 (2007), arXiv:hep-ph/0703005

  • [13]

    Z.-z. Xing and Z.-h. Zhao, Nucl. Phys. B 897, 302 (2015), arXiv:1501.06346

  • [14]

    H. Harari, H. Haut, and J. Weyers, Phys. Lett. B 78, 459 (1978

  • [15]

    Y. Koide, Phys. Rev. D 28, 252 (1983

  • [16]

    Y. Koide, Phys. Rev. D 39, 1391 (1989

  • [17]

    M. Tanimoto, Phys. Rev. D 41, 1586 (1990

  • [18]

    H. Fritzsch and J. Plankl, Phys. Lett. B 237, 451 (1990

  • [19]

    H. Lehmann, C. Newton, and T. T. Wu, Phys. Lett. B 384, 249 (1996

  • [20]

    M. Fukugita, M. Tanimoto, and T. Yanagida, Phys. Rev. D 57, 4429 (1998), arXiv:hepph/9709388

  • [21]

    M. Tanimoto, T. Watari, and T. Yanagida, Phys. Lett. B 461, 345 (1999), arXiv:hepph/9904338

  • [22]

    N. Haba, Y. Matsui, N. Okamura et al., Phys. Lett. 489, 184 (2000), arXiv:hepph/0005064

  • [23]

    K. Hamaguchi, M. Kakizaki, and M. Yamaguchi, Phys. Rev. D 68, 056007 (2003), arXiv:hep-ph/0212172

  • [24]

    M. Kakizaki and M. Yamaguchi, Phys. Lett. B 573, 123 (2003), arXiv:hep-ph/0307362

  • [25]

    T. Kobayashi, H. Shirano, and H. Terao, Prog. Theor. Phys. 113, 1077 (2005), arXiv:hepph/0412299

  • [26]

    H. Fritzsch and Z.-z. Xing, Phys. Lett. B 598, 237 (2004), arXiv:hep-ph/0406206

  • [27]

    R. Jora, S. Nasri, and J. Schechter, Int. J. Mod. Phys. A 21, 5875 (2006), arXiv:hepph/0605069

  • [28]

    A. Mondragon, M. Mondragon, and E. Peinado, Phys. Rev. D 76, 076003 (2007), arXiv:0706.0354

  • [29]

    Z.-z. Xing, D. Yang, and S. Zhou, Phys. Lett. B 690, 304 (2010), arXiv:1004.4234

  • [30]

    S. Zhou, Phys. Lett. B 704, 291 (2011), arXiv:1106.4808

  • [31]

    F. Gonzalez Canales, A. Mondragon, and M. Mondragon, Fortsch. Phys. 61, 546 (2013), arXiv:1205.4755

  • [32]

    M. J. S. Yang, Phys. Lett. B 760, 747 (2016), arXiv:1604.07896

  • [33]

    M. J. S. Yang, Phys. Rev. D 95, 055029 (2017), arXiv:1612.09049

  • [34]

    T. Fukuyama and H. Nishiura, (1997), arXiv: hep-ph/9702253

  • [35]

    C. S. Lam, Phys. Lett. B 507, 214 (2001), arXiv:hep-ph/0104116

  • [36]

    E. Ma and M. Raidal, Phys. Rev. Lett. 87, 011802 (2001), arXiv: hep-ph/0102255, [Erratum: Phys. Rev. Lett. 87, 159901(2001)]

  • [37]

    K. R. S. Balaji, W. Grimus, and T. Schwetz, Phys. Lett. B 508, 301 (2001), arXiv:hepph/0104035

  • [38]

    Y. Koide, H. Nishiura, K. Matsuda et al., Phys. Rev. D 66, 093006 (2002), arXiv:hep-ph/0209333

  • [39]

    T. Kitabayashi and M. Yasue, Phys. Rev. D 67, 015006 (2003), arXiv:hep-ph/0209294

  • [40]

    Y. Koide, Phys. Rev. D 69, 093001 (2004), arXiv:hep-ph/0312207

  • [41]

    A. Ghosal, (2003), arXiv: hep-ph/0304090

  • [42]

    I. Aizawa, M. Ishiguro, T. Kitabayashi et al., Phys. Rev. D 70, 015011 (2004), arXiv:hep-ph/0405201

  • [43]

    A. Ghosal, Mod. Phys. Lett. A 19, 2579 (2004

  • [44]

    R. N. Mohapatra and W. Rodejohann, Phys. Rev. D 72, 053001 (2005), arXiv:hepph/0507312

  • [45]

    Y. Koide, Phys. Lett. B 607, 123 (2005), arXiv:hep-ph/0411280

  • [46]

    T. Kitabayashi and M. Yasue, Phys. Lett. B 621, 133 (2005), arXiv:hep-ph/0504212

  • [47]

    N. Haba and W. Rodejohann, Phys. Rev. D 74, 017701 (2006), arXiv:hep-ph/0603206

  • [48]

    Z.-z. Xing, H. Zhang, and S. Zhou, Phys. Lett. B 641, 189 (2006), arXiv:hep-ph/0607091

  • [49]

    Y. H. Ahn, S. K. Kang, C. S. Kim et al., Phys. Rev. D 73, 093005 (2006), arXiv:hepph/0602160

  • [50]

    A. S. Joshipura, Eur. Phys. J. C 53, 77 (2008), arXiv:hep-ph/0512252

  • [51]

    J. C. Gomez-Izquierdo and A. Perez-Lorenzana, Phys. Rev. D 82, 033008 (2010), arXiv:0912.5210

  • [52]

    H.-J. He and F.-R. Yin, Phys. Rev. D 84, 033009 (2011), arXiv:1104.2654

  • [53]

    H.-J. He and X.-J. Xu, Phys. Rev. D 86, 111301 (2012), arXiv:1203.2908

  • [54]

    J. C. Gómez-Izquierdo, Eur. Phys. J. C 77, 551 (2017), arXiv:1701.01747

  • [55]

    T. Fukuyama, PTEP 2017, 033B11 (2017), arXiv:1701.04985

  • [56]

    P. F. Harrison and W. G. Scott, Phys. Lett. B 547, 219 (2002), arXiv:hep-ph/0210197

  • [57]

    W. Grimus and L. Lavoura, Phys. Lett. B 579, 113 (2004), arXiv:hep-ph/0305309

  • [58]

    W. Grimus, S. Kaneko, L. Lavoura et al., JHEP 01, 110 (2006), arXiv:hep-ph/0510326

  • [59]

    Y. Farzan and A. Yu. Smirnov, JHEP 01, 059 (2007), arXiv:hep-ph/0610337

  • [60]

    A. S. Joshipura and B. P. Kodrani, Phys. Lett. B 670, 369 (2009), arXiv:0706.0953

  • [61]

    B. Adhikary, A. Ghosal, and P. Roy, JHEP 10, 040 (2009), arXiv:0908.2686

  • [62]

    A. S. Joshipura, B. P. Kodrani, and K. M. Patel, Phys. Rev. D 79, 115017 (2009), arXiv:0903.2161

  • [63]

    Z.-z. Xing and Y.-L. Zhou, Phys. Lett. B 693, 584 (2010), arXiv:1008.4906

  • [64]

    S.-F. Ge, H.-J. He, and F.-R. Yin, JCAP 1005, 017 (2010), arXiv:1001.0940

  • [65]

    S. Gupta, A. S. Joshipura, and K. M. Patel, Phys. Rev. D 85, 031903 (2012), arXiv:1112.6113

  • [66]

    W. Grimus and L. Lavoura, Fortsch. Phys. 61, 535 (2013), arXiv:1207.1678

  • [67]

    A. S. Joshipura and K. M. Patel, Phys. Lett. B 749, 159 (2015), arXiv:1507.01235

  • [68]

    Z.-z. Xing and Z.-h. Zhao, Rept. Prog. Phys. 79, 076201 (2016), arXiv:1512.04207

  • [69]

    X.-G. He, Chin. J. Phys. 53, 100101 (2015), arXiv:1504.01560

  • [70]

    P. Chen, G.-J. Ding, F. Gonzalez-Canales et al., Phys. Lett. B 753, 644 (2016), arXiv:1512.01551

  • [71]

    H.-J. He, W. Rodejohann, and X.-J. Xu, Phys. Lett. B 751, 586 (2015), arXiv:1507.03541

  • [72]

    R. Samanta, P. Roy, and A. Ghosal, JHEP 06, 085 (2018), arXiv:1712.06555

  • [73]

    Z.-z. Xing and J.-y. Zhu, Chin. Phys. C 41, 123103 (2017), arXiv:1707.03676

  • [74]

    C. C. Nishi, B. L. Sánchez-Vega, and G. Souza Silva, JHEP 09, 042 (2018), arXiv:1806.07412

  • [75]

    N. Nath, Z.-z. Xing, and J. Zhang, Eur. Phys. J. C 78, 289 (2018), arXiv:1801.09931

  • [76]

    R. Sinha, P. Roy, and A. Ghosal, Phys. Rev. D 99, 033009 (2019), arXiv:1809.06615

  • [77]

    Z.-Z. Xing and D. Zhang, JHEP 03, 184 (2019), arXiv:1901.07912

  • [78]

    J. Pan, J. Sun, and X.-G. He, Int. J. Mod. Phys. A 34, 1950235 (2020), arXiv:1910.06688

  • [79]

    M. J. Yang, Phys. Lett. B 806, 135483 (2020), arXiv:2002.09152

  • [80]

    G. Ecker, W. Grimus, and W. Konetschny, Nucl. Phys. B 177, 489 (1981

  • [81]

    G. Ecker, W. Grimus, and H. Neufeld, Nucl. Phys. B 247, 70 (1984

  • [82]

    M. Gronau and R. N. Mohapatra, Phys. Lett. B 168, 248 (1986

  • [83]

    G. Ecker, W. Grimus, and H. Neufeld, J. Phys. A 20, L807 (1987

  • [84]

    H. Neufeld, W. Grimus, and G. Ecker, Int. J. Mod. Phys. A 3, 603 (1988

  • [85]

    P. Ferreira, H. E. Haber, and J. P. Silva, Phys. Rev. D 79, 116004 (2009), arXiv:0902.1537

  • [86]

    F. Feruglio, C. Hagedorn, and R. Ziegler, JHEP 07, 027 (2013), arXiv:1211.5560

  • [87]

    M. Holthausen, M. Lindner, and M. A. Schmidt, JHEP 04, 122 (2013), arXiv:1211.6953

  • [88]

    G.-J. Ding, S. F. King, and A. J. Stuart, JHEP 12, 006 (2013), arXiv:1307.4212

  • [89]

    I. Girardi, A. Meroni, S. Petcov et al., JHEP 02, 050 (2014), arXiv:1312.1966

  • [90]

    C. Nishi, Phys. Rev. D 88, 033010 (2013), arXiv:1306.0877

  • [91]

    G.-J. Ding, S. F. King, C. Luhn et al., JHEP 05, 084 (2013), arXiv:1303.6180

  • [92]

    F. Feruglio, C. Hagedorn, and R. Ziegler, Eur. Phys. J. C 74, 2753 (2014), arXiv:1303.7178

  • [93]

    G.-J. Ding, S. F. King, and T. Neder, JHEP 12, 007 (2014), arXiv:1409.8005

  • [94]

    G.-J. Ding and Y.-L. Zhou, JHEP 06, 023 (2014), arXiv:1404.0592

  • [95]

    M.-C. Chen, M. Fallbacher, K. Mahanthappa et al., Nucl. Phys. B 883, 267 (2014), arXiv:1402.0507

  • [96]

    C.-C. Li and G.-J. Ding, JHEP 05, 100 (2015), arXiv:1503.03711

  • [97]

    J. Turner, Phys. Rev. D 92, 116007 (2015), arXiv:1507.06224

  • [98]

    J. Penedo, S. Petcov, and A. Titov, JHEP 12, 022 (2017), arXiv:1705.00309

  • [99]

    N. Nath, R. Srivastava, and J. W. Valle, Phys. Rev. D 99, 075005 (2019), arXiv:1811.07040

  • [100]

    R. Peccei and H. R. Quinn, Phys.Rev.Lett. 38, 1440 (1977

  • [101]

    J. E. Kim, Phys.Rev.Lett. 43, 103 (1979

  • [102]

    M. A. Shifman, A. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 166, 493 (1980

  • [103]

    A. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980

  • [104]

    M. Dine, W. Fischler, and M. Srednicki, Phys. Lett. B 104, 199 (1981

  • [105]

    A. Davidson and K. C. Wali, Phys. Rev. Lett. 48, 11 (1982

  • [106]

    F. Wilczek, Phys. Rev. Lett. 49, 1549 (1982

  • [107]

    Z. Berezhiani and M. Khlopov, Z. Phys. C 49, 73 (1991

  • [108]

    Y. Ahn, Phys. Rev. D 91, 056005 (2015), arXiv:1410.1634

  • [109]

    Y. Ema, K. Hamaguchi, T. Moroi et al., JHEP 01, 096 (2017), arXiv:1612.05492

  • [110]

    L. Calibbi, F. Goertz, D. Redigolo et al., Phys. Rev. D 95, 095009 (2017), arXiv:1612.08040

  • [111]

    G. ’t Hooft, Phys. Rev. D 14, 3432 (1976

  • [112]

    R. N. Mohapatra and G. Senjanovic, Phys. Lett. B 79, 283 (1978

  • [113]

    M. Beg and H.-S. Tsao, Phys. Rev. Lett. 41, 278 (1978

  • [114]

    A. E. Nelson, Phys. Lett. B 136, 387 (1984

  • [115]

    S. M. Barr, D. Chang, and G. Senjanovic, Phys. Rev. Lett. 67, 2765 (1991

  • [116]

    J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974), [Erratum: Phys. Rev. D 11, 703 (1975)]

  • [117]

    G. Senjanovic and R. N. Mohapatra, Phys. Rev. D 12, 1502 (1975

  • [118]

    R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 566 (1975

  • [119]

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

  • [120]

    T. Yanagida, Conf. Proc. C7902131, 95 (1979

  • [121]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980

  • [122]

    M. Gell-Mann, P. Ramond, and R. Slansky, Conf. Proc. C790927, 315 (1979

  • [123]

    G. Branco, D. Emmanuel-Costa, and R. Gonzalez Felipe, Phys. Lett. B 477, 147 (2000), arXiv:hep-ph/9911418

  • [124]

    G. Branco, D. Emmanuel-Costa, R. Gonzalez Felipe et al., Phys. Lett. B 670, 340 (2009), arXiv:0711.1613

  • [125]

    Z.-z. Xing, J. Phys. G 23, 1563 (1997), arXiv:hep-ph/9609204

  • [126]

    K. Kang and S. K. Kang, Phys. Rev. D 56, 1511 (1997), arXiv:hep-ph/9704253

  • [127]

    A. Mondragon and E. Rodriguez-Jauregui, Phys. Rev. D 59, 093009 (1999), arXiv:hepph/9807214

  • [128]

    J. Barranco, F. Gonzalez Canales, and A. Mondragon, Phys. Rev. D 82, 073010 (2010), arXiv:1004.3781

  • [129]

    M. Shin, Phys. Lett. B 160, 411 (1985

  • [130]

    M. Shin, Phys. Lett. B 154, 205 (1985

  • [131]

    K. Kang and M. Shin, Phys. Rev. D 33, 2688 (1986

  • [132]

    S. L. Glashow and S. Weinberg, Phys. Rev. D 15, 1958 (1977

  • [133]

    G. Altarelli and F. Feruglio, Nucl. Phys. B 741, 215 (2006), arXiv:hep-ph/0512103

  • [134]

    H.-Y. Cheng, Phys. Rept. 158, 1 (1988

  • [135]

    I. Esteban, M. C. Gonzalez-Garcia, A. Hernandez-Cabezudo et al., JHEP 01, 106 (2019), arXiv:1811.05487

  • [136]

    G. C. Branco, L. Lavoura, and M. N. Rebelo, Phys. Lett. B 180, 264 (1986)

  • [137]

    E. E. Jenkins and A. V. Manohar, Nucl. Phys. B 792, 187 (2008), arXiv:0706.4313

  • [138]

    G. C. Branco, R. G. Felipe, and F. R. Joaquim, Rev. Mod. Phys. 84, 515 (2012), arXiv:1111.5332

  • [139]

    H. Georgi and C. Jarlskog, Phys. Lett. B 86, 297 (1979

  • [140]

    Z.-z. Xing, H. Zhang, and S. Zhou, Phys. Rev. D 77, 113016 (2008), arXiv:0712.1419

  • [141]

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

  • [142]

    S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002), arXiv:hep-ph/0202239

  • [143]

    K. Hamaguchi, H. Murayama, and T. Yanagida, Phys. Rev. D 65, 043512 (2002), arXiv:hep-ph/0109030

  • [144]

    O. Vives, Phys. Rev. D 73, 073006 (2006), arXiv:hep-ph/0512160

  • [145]

    Z.-z. Xing, Phys. Rept. 854, 1 (2020), arXiv:1909.09610

  • [146]

    H. Fritzsch and Z.-Z. Xing, Phys. Lett. B 413, 396 (1997), arXiv:hep-ph/9707215