- 
								[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