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An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists

Part of the book series: Lecture Notes in Physics ((LNP,volume 858))

Abstract

These lecture notes aim to provide a phedagical review of non-Abelian discrete groups and show some applications to physical issues. We exhibit group-theoretical aspects of many concrete groups explicitly, for example, representations and their tensor products. For application to particle physics, we exaplain explicitly breaking patterns of discrete groups and anomalies of Abelian and non-Abelian symmetries. We also show some models, where non-Abelian discrete symmetries are applied to derive experimental values of quark and lepton masses and their mixing angles.

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References

  1. Pontecorvo, B.: Sov. Phys. JETP 6, 429 (1957) [Zh. Eksp. Teor. Fiz. 33, 549 (1957)]

    ADS  Google Scholar 

  2. Maki, Z., Nakagawa, M., Sakata, S.: Prog. Theor. Phys. 28, 870 (1962)

    Article  ADS  Google Scholar 

  3. Schwetz, T., Tortola, M.A., Valle, J.W.F.: New J. Phys. 10, 113011 (2008). arXiv:0808.2016 [hep-ph]

    Article  ADS  Google Scholar 

  4. Fogli, G.L., Lisi, E., Marrone, A., Palazzo, A., Rotunno, A.M.: Phys. Rev. Lett. 101, 141801 (2008). arXiv:0806.2649 [hep-ph]

    Article  ADS  Google Scholar 

  5. Fogli, G.L., Lisi, E., Marrone, A., Palazzo, A., Rotunno, A.M.: Nucl. Phys. Proc. Suppl. 188, 27 (2009)

    Article  ADS  Google Scholar 

  6. Gonzalez-Garcia, M.C., Maltoni, M., Salvado, J.: arXiv:1001.4524 [hep-ph]

  7. Schwetz, T., Tortola, M., Valle, J.W.F.: New J. Phys. 13, 063004 (2011). arXiv:1103.0734 [hep-ph]

    Article  ADS  Google Scholar 

  8. Abe, K., et al. (T2K Collaboration): Phys. Rev. Lett. 107, 041801 (2011). arXiv:1106.2822 [hep-ex]

    Article  ADS  Google Scholar 

  9. Abe, Y., et al. (Double Chooz Collaboration): arXiv:1112.6353 [hep-ex]

  10. Harrison, P.F., Perkins, D.H., Scott, W.G.: Phys. Lett. B 530, 167 (2002). arXiv:hep-ph/0202074

    Article  ADS  Google Scholar 

  11. Harrison, P.F., Scott, W.G.: Phys. Lett. B 535, 163 (2002). arXiv:hep-ph/0203209

    Article  ADS  Google Scholar 

  12. Harrison, P.F., Scott, W.G.: Phys. Lett. B 557, 76 (2003). arXiv:hep-ph/0302025

    Article  ADS  MathSciNet  Google Scholar 

  13. Harrison, P.F., Scott, W.G.: arXiv:hep-ph/0402006

  14. Altarelli, G., Feruglio, F.: arXiv:1002.0211 [hep-ph]

  15. Ishimori, H., Kobayashi, T., Ohki, H., Shimizu, Y., Okada, H., Tanimoto, M.: Prog. Theor. Phys. Suppl. 183, 1–163 (2010). arXiv:1003.3552 [hep-th]

    Article  ADS  Google Scholar 

  16. Altarelli, G., Feruglio, F., Lin, Y.: Nucl. Phys. B 775, 31 (2007). arXiv:hep-ph/0610165

    Article  ADS  Google Scholar 

  17. Adulpravitchai, A., Blum, A., Lindner, M.: J. High Energy Phys. 0907, 053 (2009). arXiv:0906.0468 [hep-ph]

    Article  ADS  Google Scholar 

  18. Abe, H., Choi, K.-S., Kobayashi, T., Ohki, H., Sakai, M.: Int. J. Mod. Phys. A 26, 4067–4082 (2011). arXiv:1009.5284 [hep-th]

    Article  ADS  Google Scholar 

  19. Kobayashi, T., Raby, S., Zhang, R.J.: Nucl. Phys. B 704, 3 (2005). arXiv:hep-ph/0409098

    Article  ADS  Google Scholar 

  20. Kobayashi, T., Nilles, H.P., Ploger, F., Raby, S., Ratz, M.: Nucl. Phys. B 768, 135 (2007). arXiv:hep-ph/0611020

    Article  ADS  Google Scholar 

  21. Ko, P., Kobayashi, T., Park, J.H., Raby, S.: Phys. Rev. D 76, 035005 (2007) [Erratum ibid. D 76, 059901 (2007)]. arXiv:0704.2807 [hep-ph]

    Article  ADS  Google Scholar 

  22. Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: Nucl. Phys. B 820, 317 (2009). arXiv:0904.2631 [hep-ph]

    Article  ADS  Google Scholar 

  23. Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: Phys. Rev. D 80, 126006 (2009). arXiv:0907.5274 [hep-th]

    Article  ADS  Google Scholar 

  24. Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: arXiv:1001.1788 [hep-th]

  25. de Medeiros Varzielas, I., King, S.F., Ross, G.G.: Phys. Lett. B 644, 153 (2007). arXiv:hep-ph/0512313

    Article  ADS  Google Scholar 

  26. Adulpravitchai, A., Blum, A., Lindner, M.: J. High Energy Phys. 0909, 018 (2009). arXiv:0907.2332 [hep-ph]

    Article  ADS  Google Scholar 

  27. Frampton, P.H., Kephart, T.W., Rohm, R.M.: Phys. Lett. B 679, 478 (2009). arXiv:0904.0420 [hep-ph]

    Article  ADS  Google Scholar 

  28. Ramond, P.: Group Theory: A Physicist’s Survey. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  29. Miller, G.A., Dickson, H.F., Blichfeldt, L.E.: Theory and Applications of Finite Groups. Wiley, New York (1916)

    MATH  Google Scholar 

  30. Hamermesh, M.: Group Theory and Its Application to Physical Problems. Addison-Wesley, Reading (1962)

    Book  MATH  Google Scholar 

  31. Fairbairn, W.M., Fulton, T., Klink, W.H.: J. Math. Phys. 5, 1038 (1964)

    Article  ADS  Google Scholar 

  32. Georgi, H.: Front. Phys. 54, 1 (1982)

    Google Scholar 

  33. Frampton, P.H., Kephart, T.W.: Int. J. Mod. Phys. A 10, 4689 (1995). arXiv:hep-ph/9409330

    Article  ADS  Google Scholar 

  34. Ludl, P.O.: arXiv:0907.5587 [hep-ph]

  35. Pakvasa, S., Sugawara, H.: Phys. Lett. B 73, 61 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  36. Tanimoto, M.: Phys. Rev. D 41, 1586 (1990)

    Article  ADS  Google Scholar 

  37. Lee, C.E., Lin, C.L., Yang, Y.W.: The minimal extension of the standard model with S(3) symmetry. Prepared for 2nd International Spring School on Medium and High-Energy Nuclear Physics, Taipei, Taiwan, 8–12 May 1990

    Google Scholar 

  38. Kang, K., Kim, J.E., Ko, P.: Z. Phys. C 72, 671 (1996). arXiv:hep-ph/9503436

    Article  ADS  Google Scholar 

  39. Kang, K., Kang, S.K., Kim, J.E., Ko, P.W.: Mod. Phys. Lett. A 12, 1175 (1997). arXiv:hep-ph/9611369

    Article  ADS  Google Scholar 

  40. Fukugita, M., Tanimoto, M., Yanagida, T.: Phys. Rev. D 57, 4429 (1998). arXiv:hep-ph/9709388

    Article  ADS  Google Scholar 

  41. Tanimoto, M., Watari, T., Yanagida, T.: Phys. Lett. B 461, 345 (1999). arXiv:hep-ph/9904338

    Article  ADS  Google Scholar 

  42. Tanimoto, M.: Phys. Lett. B 483, 417 (2000). arXiv:hep-ph/0001306

    Article  ADS  Google Scholar 

  43. Tanimoto, M.: Phys. Rev. D 59, 017304 (1999). arXiv:hep-ph/9807283

    Article  ADS  Google Scholar 

  44. Tanimoto, M., Yanagida, T.: Phys. Lett. B 633, 567 (2006). arXiv:hep-ph/0511336

    Article  ADS  Google Scholar 

  45. Honda, M., Tanimoto, M.: Phys. Rev. D 75, 096005 (2007). arXiv:hep-ph/0701083

    Article  ADS  Google Scholar 

  46. Dong, P.V., Long, H.N., Nam, C.H., Vien, V.V.: arXiv:1111.6360 [hep-ph]

  47. Xing, Z.Z., Yang, D., Zhou, S.: Phys. Lett. B 690, 304–310 (2010). arXiv:1004.4234 [hep-ph]

    Article  ADS  Google Scholar 

  48. Dicus, D.A., Ge, S.-F., Repko, W.W.: Phys. Rev. D 82, 033005 (2010). arXiv:1004.3266 [hep-ph]

    Article  ADS  Google Scholar 

  49. Meloni, D., Morisi, S., Peinado, E.: J. Phys. G 38, 015003 (2011). arXiv:1005.3482 [hep-ph]

    Article  ADS  Google Scholar 

  50. Jora, R., Schechter, J., Shahid, M.N.: Phys. Rev. D 82, 053006 (2010). arXiv:1006.3307 [hep-ph]

    Article  ADS  Google Scholar 

  51. Bhattacharyya, G., Leser, P., Pas, H.: Phys. Rev. D 83, 011701 (2011). arXiv:1006.5597 [hep-ph]

    Article  ADS  Google Scholar 

  52. Watanabe, A., Yoshioka, K.: Prog. Theor. Phys. 125, 129–148 (2011). arXiv:1007.1527 [hep-ph]

    Article  ADS  Google Scholar 

  53. Kaneko, T., Sugawara, H.: Phys. Lett. B 697, 329–332 (2011). arXiv:1011.5748 [hep-ph]

    Article  ADS  Google Scholar 

  54. Adulpravitchai, A., Batell, B., Pradler, J.: Phys. Lett. B 700, 207–216 (2011). arXiv:1103.3053 [hep-ph]

    Article  ADS  Google Scholar 

  55. Teshima, T., Okumura, Y.: Phys. Rev. D 84, 016003 (2011). arXiv:1103.6127 [hep-ph]

    Article  ADS  Google Scholar 

  56. Dev, S., Gupta, S., Gautam, R.R.: Phys. Lett. B 702, 28–33 (2011). arXiv:1106.3873 [hep-ph]

    Article  ADS  Google Scholar 

  57. Zhou, S.: Phys. Lett. B 704, 291–295 (2011). arXiv:1106.4808 [hep-ph]

    Article  ADS  Google Scholar 

  58. Koide, Y.: Phys. Rev. D 60, 077301 (1999). arXiv:hep-ph/9905416

    Article  ADS  Google Scholar 

  59. Chalut, K., Cheng, H., Frampton, P.H., Stowe, K., Yoshikawa, T.: Mod. Phys. Lett. A 17, 1513 (2002). arXiv:hep-ph/0204074

    Article  ADS  Google Scholar 

  60. Kubo, J., Mondragon, A., Mondragon, M., Rodriguez-Jauregui, E.: Prog. Theor. Phys. 109, 795 (2003) [Erratum ibid. 114, 287 (2005)]. arXiv:hep-ph/0302196

    Article  ADS  Google Scholar 

  61. Kobayashi, T., Kubo, J., Terao, H.: Phys. Lett. B 568, 83 (2003). arXiv:hep-ph/0303084

    Article  ADS  Google Scholar 

  62. Kubo, J.: Phys. Lett. B 578, 156 (2004) [Erratum ibid. B 619, 387 (2005)]. arXiv:hep-ph/0309167

    Article  ADS  Google Scholar 

  63. Chen, S.L., Frigerio, M., Ma, E.: Phys. Rev. D 70, 073008 (2004) [Erratum ibid. D 70, 079905 (2004)]. arXiv:hep-ph/0404084

    Article  ADS  Google Scholar 

  64. Choi, K.Y., Kajiyama, Y., Lee, H.M., Kubo, J.: Phys. Rev. D 70, 055004 (2004). arXiv:hep-ph/0402026

    Article  ADS  Google Scholar 

  65. Kubo, J., Okada, H., Sakamaki, F.: Phys. Rev. D 70, 036007 (2004). arXiv:hep-ph/0402089

    Article  ADS  Google Scholar 

  66. Lavoura, L., Ma, E.: Mod. Phys. Lett. A 20, 1217 (2005). arXiv:hep-ph/0502181

    Article  ADS  Google Scholar 

  67. Grimus, W., Lavoura, L.: J. High Energy Phys. 0508, 013 (2005). arXiv:hep-ph/0504153

    Article  ADS  Google Scholar 

  68. Morisi, S., Picariello, M.: Int. J. Theor. Phys. 45, 1267 (2006). arXiv:hep-ph/0505113

    Article  Google Scholar 

  69. Teshima, T.: Phys. Rev. D 73, 045019 (2006). arXiv:hep-ph/0509094

    Article  ADS  Google Scholar 

  70. Koide, Y.: Phys. Rev. D 73, 057901 (2006). arXiv:hep-ph/0509214

    Article  ADS  Google Scholar 

  71. Kimura, T.: Prog. Theor. Phys. 114, 329 (2005)

    Article  ADS  Google Scholar 

  72. Araki, T., Kubo, J., Paschos, E.A.: Eur. Phys. J. C 45, 465 (2006). arXiv:hep-ph/0502164

    Article  ADS  Google Scholar 

  73. Kubo, J., Mondragon, A., Mondragon, M., Rodriguez-Jauregui, E., Felix-Beltran, O., Peinado, E.: J. Phys. Conf. Ser. 18, 380 (2005)

    Article  ADS  Google Scholar 

  74. Haba, N., Yoshioka, K.: Nucl. Phys. B 739, 254 (2006). arXiv:hep-ph/0511108

    Article  ADS  Google Scholar 

  75. Kim, J.E., Park, J.C.: J. High Energy Phys. 0605, 017 (2006). arXiv:hep-ph/0512130

    Article  ADS  Google Scholar 

  76. Kaneko, S., Sawanaka, H., Shingai, T., Tanimoto, M., Yoshioka, K.: Prog. Theor. Phys. 117, 161 (2007). arXiv:hep-ph/0609220

    Article  ADS  Google Scholar 

  77. Mohapatra, R.N., Nasri, S., Yu, H.B.: Phys. Lett. B 639, 318 (2006). arXiv:hep-ph/0605020

    Article  ADS  Google Scholar 

  78. Picariello, M.: Int. J. Mod. Phys. A 23, 4435 (2008). arXiv:hep-ph/0611189

    Article  ADS  Google Scholar 

  79. Koide, Y.: Eur. Phys. J. C 50, 809 (2007). arXiv:hep-ph/0612058

    Article  ADS  Google Scholar 

  80. Haba, N., Watanabe, A., Yoshioka, K.: Phys. Rev. Lett. 97, 041601 (2006). arXiv:hep-ph/0603116

    Article  ADS  Google Scholar 

  81. Morisi, S.: Int. J. Mod. Phys. A 22, 2921 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  82. Chen, C.Y., Wolfenstein, L.: Phys. Rev. D 77, 093009 (2008). arXiv:0709.3767 [hep-ph]

    Article  ADS  Google Scholar 

  83. Mitra, M., Choubey, S.: Phys. Rev. D 78, 115014 (2008). arXiv:0806.3254 [hep-ph]

    Article  ADS  Google Scholar 

  84. Feruglio, F., Lin, Y.: Nucl. Phys. B 800, 77 (2008). arXiv:0712.1528 [hep-ph]

    Article  ADS  Google Scholar 

  85. Jora, R., Schechter, J., Naeem Shahid, M.: Phys. Rev. D 80, 093007 (2009). arXiv:0909.4414 [hep-ph]

    Article  ADS  Google Scholar 

  86. Beltran, O.F., Mondragon, M., Rodriguez-Jauregui, E.: J. Phys. Conf. Ser. 171, 012028 (2009)

    Article  Google Scholar 

  87. Yamanaka, Y., Sugawara, H., Pakvasa, S.: Phys. Rev. D 25, 1895 (1982) [Erratum ibid. D 29, 2135 (1984)]

    Article  ADS  Google Scholar 

  88. Brown, T., Pakvasa, S., Sugawara, H., Yamanaka, Y.: Phys. Rev. D 30, 255 (1984)

    Article  ADS  Google Scholar 

  89. Brown, T., Deshpande, N., Pakvasa, S., Sugawara, H.: Phys. Lett. B 141, 95 (1984)

    Article  ADS  Google Scholar 

  90. Ma, E.: Phys. Lett. B 632, 352 (2006). arXiv:hep-ph/0508231

    Article  ADS  Google Scholar 

  91. Zhang, H.: Phys. Lett. B 655, 132 (2007). arXiv:hep-ph/0612214

    Article  ADS  Google Scholar 

  92. Hagedorn, C., Lindner, M., Mohapatra, R.N.: J. High Energy Phys. 0606, 042 (2006). arXiv:hep-ph/0602244

    Article  ADS  Google Scholar 

  93. Cai, Y., Yu, H.B.: Phys. Rev. D 74, 115005 (2006). arXiv:hep-ph/0608022

    Article  ADS  Google Scholar 

  94. Caravaglios, F., Morisi, S.: Int. J. Mod. Phys. A 22, 2469 (2007). arXiv:hep-ph/0611078

    Article  ADS  Google Scholar 

  95. Koide, Y.: J. High Energy Phys. 0708, 086 (2007). arXiv:0705.2275 [hep-ph]

    Article  ADS  MathSciNet  Google Scholar 

  96. Parida, M.K.: Phys. Rev. D 78, 053004 (2008). arXiv:0804.4571 [hep-ph]

    Article  ADS  Google Scholar 

  97. Lam, C.S.: Phys. Rev. D 78, 073015 (2008). arXiv:0809.1185 [hep-ph]

    Article  ADS  Google Scholar 

  98. Bazzocchi, F., Morisi, S.: Phys. Rev. D 80, 096005 (2009). arXiv:0811.0345 [hep-ph]

    Article  ADS  Google Scholar 

  99. Ishimori, H., Shimizu, Y., Tanimoto, M.: Prog. Theor. Phys. 121, 769 (2009). arXiv:0812.5031 [hep-ph]

    Article  ADS  Google Scholar 

  100. Bazzocchi, F., Merlo, L., Morisi, S.: Nucl. Phys. B 816, 204 (2009). arXiv:0901.2086 [hep-ph]

    Article  ADS  Google Scholar 

  101. Bazzocchi, F., Merlo, L., Morisi, S.: Phys. Rev. D 80, 053003 (2009). arXiv:0902.2849 [hep-ph]

    Article  ADS  Google Scholar 

  102. Altarelli, G., Feruglio, F., Merlo, L.: J. High Energy Phys. 0905, 020 (2009). arXiv:0903.1940 [hep-ph]

    Article  ADS  Google Scholar 

  103. Grimus, W., Lavoura, L., Ludl, P.O.: J. Phys. G 36, 115007 (2009). arXiv:0906.2689 [hep-ph]

    Article  ADS  Google Scholar 

  104. Ding, G.J.: Nucl. Phys. B 827, 82 (2010). arXiv:0909.2210 [hep-ph]

    Article  ADS  Google Scholar 

  105. Merlo, L.: arXiv:0909.2760 [hep-ph]

  106. Daikoku, Y., Okada, H.: arXiv:0910.3370 [hep-ph]

  107. Meloni, D.: arXiv:0911.3591 [hep-ph]

  108. Morisi, S., Peinado, E.: arXiv:1001.2265 [hep-ph]

  109. de Adelhart Toorop, R., Bazzocchi, F., Merlo, L.: J. High Energy Phys. 1008, 001 (2010). arXiv:1003.4502 [hep-ph]

    Article  Google Scholar 

  110. Hagedorn, C., King, S.F., Luhn, C.: J. High Energy Phys. 1006, 048 (2010). arXiv:1003.4249 [hep-ph]

    Article  ADS  Google Scholar 

  111. Ishimori, H., Saga, K., Shimizu, Y., Tanimoto, M.: Phys. Rev. D 81, 115009 (2010). arXiv:1004.5004 [hep-ph]

    Article  ADS  Google Scholar 

  112. Ahn, Y.H., Kang, S.K., Kim, C.S., Nguyen, T.P.: Phys. Rev. D 82, 093005 (2010). arXiv:1004.3469 [hep-ph]

    Article  ADS  Google Scholar 

  113. Ding, G.-J.: Nucl. Phys. B 846, 394–428 (2011). arXiv:1006.4800 [hep-ph]

    Article  ADS  Google Scholar 

  114. Daikoku, Y., Okada, H.: arXiv:1008.0914 [hep-ph]

  115. Dong, P.V., Long, H.N., Soa, D.V., Vien, V.V.: Eur. Phys. J. C 71, 1544 (2011). arXiv:1009.2328 [hep-ph]

    Article  ADS  Google Scholar 

  116. Ishimori, H., Shimizu, Y., Tanimoto, M., Watanabe, A.: Phys. Rev. D 83, 033004 (2011). arXiv:1010.3805 [hep-ph]

    Article  ADS  Google Scholar 

  117. Parida, M.K., Sahu, P.K., Bora, K.: Phys. Rev. D 83, 093004 (2011). arXiv:1011.4577 [hep-ph]

    Article  ADS  Google Scholar 

  118. Daikoku, Y., Okada, H., Toma, T.: arXiv:1010.4963 [hep-ph]

  119. Ding, G.-J., Pan, D.-M.: Eur. Phys. J. C 71, 1716 (2011). arXiv:1011.5306 [hep-ph]

    Article  ADS  Google Scholar 

  120. Ishimori, H., Tanimoto, M.: Prog. Theor. Phys. 125, 653–675 (2011). arXiv:1012.2232 [hep-ph]

    Article  ADS  Google Scholar 

  121. Stech, B.: arXiv:1012.6028 [hep-ph]

  122. Park, N.W., Nam, K.H., Siyeon, K.: Phys. Rev. D 83, 056013 (2011). arXiv:1101.4134 [hep-ph]

    Article  ADS  Google Scholar 

  123. Ishimori, H., Kajiyama, Y., Shimizu, Y., Tanimoto, M.: arXiv:1103.5705 [hep-ph]

  124. Yang, R.-Z., Zhang, H.: Phys. Lett. B 700, 316–321 (2011). arXiv:1104.0380 [hep-ph]

    Article  ADS  Google Scholar 

  125. Morisi, S., Peinado, E.: Phys. Lett. B 701, 451–457 (2011). arXiv:1104.4961 [hep-ph]

    Article  ADS  Google Scholar 

  126. Zhao, Z.-h.: Phys. Lett. B 701, 609–613 (2011). arXiv:1106.2715 [hep-ph]

    Article  ADS  Google Scholar 

  127. Ishimori, H., Kobayashi, T.: arXiv:1106.3604 [hep-ph]

  128. Hagedorn, C., Serone, M.: arXiv:1106.4021 [hep-ph]

  129. Daikoku, Y., Okada, H., Toma, T.: arXiv:1106.4717 [hep-ph]

  130. Meloni, D.: arXiv:1107.0221 [hep-ph]

  131. Morisi, S., Patel, K.M., Peinado, E.: arXiv:1107.0696 [hep-ph]

  132. Bhupal Dev, P.S., Mohapatra, R.N., Severson, M.: arXiv:1107.2378 [hep-ph]

  133. Ma, E., Rajasekaran, G.: Phys. Rev. D 64, 113012 (2001). arXiv:hep-ph/0106291

    Article  ADS  Google Scholar 

  134. Babu, K.S., Enkhbat, T., Gogoladze, I.: Phys. Lett. B 555, 238 (2003). arXiv:hep-ph/0204246

    Article  ADS  Google Scholar 

  135. Babu, K.S., Ma, E., Valle, J.W.F.: Phys. Lett. B 552, 207 (2003). arXiv:hep-ph/0206292

    Article  ADS  Google Scholar 

  136. Ma, E.: Mod. Phys. Lett. A 17, 2361 (2002). arXiv:hep-ph/0211393

    Article  ADS  Google Scholar 

  137. Babu, K.S., Kobayashi, T., Kubo, J.: Phys. Rev. D 67, 075018 (2003). arXiv:hep-ph/0212350

    Article  ADS  Google Scholar 

  138. Hirsch, M., Romao, J.C., Skadhauge, S., Valle, J.W.F., Villanova del Moral, A.: Phys. Rev. D 69, 093006 (2004). arXiv:hep-ph/0312265

    Article  ADS  Google Scholar 

  139. Ma, E.: Phys. Rev. D 70, 031901 (2004). arXiv:hep-ph/0404199

    Article  ADS  Google Scholar 

  140. Altarelli, G., Feruglio, F.: Nucl. Phys. B 720, 64 (2005). arXiv:hep-ph/0504165

    Article  ADS  Google Scholar 

  141. Chen, S.L., Frigerio, M., Ma, E.: Nucl. Phys. B 724, 423 (2005). arXiv:hep-ph/0504181

    Article  ADS  Google Scholar 

  142. Zee, A.: Phys. Lett. B 630, 58 (2005). arXiv:hep-ph/0508278

    Article  ADS  Google Scholar 

  143. Ma, E.: Mod. Phys. Lett. A 20, 2601 (2005). arXiv:hep-ph/0508099

    Article  ADS  Google Scholar 

  144. Ma, E.: Phys. Lett. B 632, 352 (2006). arXiv:hep-ph/0508231

    Article  ADS  Google Scholar 

  145. Ma, E.: Phys. Rev. D 73, 057304 (2006). arXiv:hep-ph/0511133

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  147. He, X.G., Keum, Y.Y., Volkas, R.R.: J. High Energy Phys. 0604, 039 (2006). arXiv:hep-ph/0601001

    Article  ADS  Google Scholar 

  148. Adhikary, B., Brahmachari, B., Ghosal, A., Ma, E., Parida, M.K.: Phys. Lett. B 638, 345 (2006). arXiv:hep-ph/0603059

    Article  ADS  Google Scholar 

  149. Ma, E., Sawanaka, H., Tanimoto, M.: Phys. Lett. B 641, 301 (2006). arXiv:hep-ph/0606103

    Article  ADS  Google Scholar 

  150. Valle, J.W.F.: J. Phys. Conf. Ser. 53, 473 (2006). arXiv:hep-ph/0608101

    Article  ADS  Google Scholar 

  151. Adhikary, B., Ghosal, A.: Phys. Rev. D 75, 073020 (2007). arXiv:hep-ph/0609193

    Article  ADS  Google Scholar 

  152. Lavoura, L., Kuhbock, H.: Mod. Phys. Lett. A 22, 181 (2007). arXiv:hep-ph/0610050

    Article  ADS  Google Scholar 

  153. King, S.F., Malinsky, M.: Phys. Lett. B 645, 351 (2007). arXiv:hep-ph/0610250

    Article  ADS  Google Scholar 

  154. Hirsch, M., Joshipura, A.S., Kaneko, S., Valle, J.W.F.: Phys. Rev. Lett. 99, 151802 (2007). arXiv:hep-ph/0703046

    Article  ADS  Google Scholar 

  155. Bazzocchi, F., Kaneko, S., Morisi, S.: J. High Energy Phys. 0803, 063 (2008). arXiv:0707.3032 [hep-ph]

    Article  ADS  Google Scholar 

  156. Grimus, W., Kuhbock, H.: Phys. Rev. D 77, 055008 (2008). arXiv:0710.1585 [hep-ph]

    Article  ADS  Google Scholar 

  157. Honda, M., Tanimoto, M.: Prog. Theor. Phys. 119, 583 (2008). arXiv:0801.0181 [hep-ph]

    Article  ADS  Google Scholar 

  158. Brahmachari, B., Choubey, S., Mitra, M.: Phys. Rev. D 77, 073008 (2008) [Erratum ibid. D 77, 119901 (2008)]. arXiv:0801.3554 [hep-ph]

    Article  ADS  Google Scholar 

  159. Adhikary, B., Ghosal, A.: Phys. Rev. D 78, 073007 (2008). arXiv:0803.3582 [hep-ph]

    Article  ADS  Google Scholar 

  160. Fukuyama, T.: arXiv:0804.2107 [hep-ph]

  161. Lin, Y.: Nucl. Phys. B 813, 91 (2009). arXiv:0804.2867 [hep-ph]

    Article  ADS  Google Scholar 

  162. Frampton, P.H., Matsuzaki, S.: arXiv:0806.4592 [hep-ph]

  163. Feruglio, F., Hagedorn, C., Lin, Y., Merlo, L.: Nucl. Phys. B 809, 218 (2009). arXiv:0807.3160 [hep-ph]

    Article  ADS  Google Scholar 

  164. Morisi, S.: Nuovo Cimento B 123, 886 (2008). arXiv:0807.4013 [hep-ph]

    ADS  Google Scholar 

  165. Ishimori, H., Kobayashi, T., Omura, Y., Tanimoto, M.: J. High Energy Phys. 0812, 082 (2008). arXiv:0807.4625 [hep-ph]

    Article  ADS  Google Scholar 

  166. Ma, E.: Phys. Lett. B 671, 366 (2009). arXiv:0808.1729 [hep-ph]

    Article  ADS  Google Scholar 

  167. Bazzocchi, F., Frigerio, M., Morisi, S.: Phys. Rev. D 78, 116018 (2008). arXiv:0809.3573 [hep-ph]

    Article  ADS  Google Scholar 

  168. Hirsch, M., Morisi, S., Valle, J.W.F.: Phys. Rev. D 79, 016001 (2009). arXiv:0810.0121 [hep-ph]

    Article  ADS  Google Scholar 

  169. Merlo, L.: arXiv:0811.3512 [hep-ph]

  170. Baek, S., Oh, M.C.: arXiv:0812.2704 [hep-ph]

  171. Morisi, S.: Phys. Rev. D 79, 033008 (2009). arXiv:0901.1080 [hep-ph]

    Article  ADS  Google Scholar 

  172. Ciafaloni, P., Picariello, M., Torrente-Lujan, E., Urbano, A.: Phys. Rev. D 79, 116010 (2009). arXiv:0901.2236 [hep-ph]

    Article  ADS  Google Scholar 

  173. Merlo, L.: J. Phys. Conf. Ser. 171, 012083 (2009). arXiv:0902.3067 [hep-ph]

    Article  Google Scholar 

  174. Chen, M.C., King, S.F.: J. High Energy Phys. 0906, 072 (2009). arXiv:0903.0125 [hep-ph]

    Article  ADS  Google Scholar 

  175. Branco, G.C., Gonzalez Felipe, R., Rebelo, M.N., Serodio, H.: Phys. Rev. D 79, 093008 (2009). arXiv:0904.3076 [hep-ph]

    Article  ADS  Google Scholar 

  176. Hayakawa, A., Ishimori, H., Shimizu, Y., Tanimoto, M.: Phys. Lett. B 680, 334 (2009). arXiv:0904.3820 [hep-ph]

    Article  ADS  Google Scholar 

  177. Altarelli, G., Meloni, D.: J. Phys. G 36, 085005 (2009). arXiv:0905.0620 [hep-ph]

    Article  ADS  Google Scholar 

  178. Urbano, A.: arXiv:0905.0863 [hep-ph]

  179. Hirsch, M., Morisi, S., Valle, J.W.F.: Phys. Lett. B 679, 454 (2009). arXiv:0905.3056 [hep-ph]

    Article  ADS  Google Scholar 

  180. Lin, Y.: Nucl. Phys. B 824, 95 (2010). arXiv:0905.3534 [hep-ph]

    Article  ADS  Google Scholar 

  181. Hirsch, M.: Pramana 72, 183 (2009)

    Article  ADS  Google Scholar 

  182. Hagedorn, C., Molinaro, E., Petcov, S.T.: J. High Energy Phys. 0909, 115 (2009). arXiv:0908.0240 [hep-ph]

    Article  ADS  Google Scholar 

  183. Tamii, A., et al.: Mod. Phys. Lett. A 24, 867 (2009)

    Article  ADS  Google Scholar 

  184. Ma, E.: arXiv:0908.3165 [hep-ph]

  185. Burrows, T.J., King, S.F.: arXiv:0909.1433 [hep-ph]

  186. Albaid, A.: Phys. Rev. D 80, 093002 (2009). arXiv:0909.1762 [hep-ph]

    Article  ADS  Google Scholar 

  187. Merlo, L.: Nucl. Phys. Proc. Suppl. 188, 345 (2009)

    Article  ADS  Google Scholar 

  188. Ciafaloni, P., Picariello, M., Torrente-Lujan, E., Urbano, A.: arXiv:0909.2553 [hep-ph]

  189. Feruglio, F., Hagedorn, C., Merlo, L.: arXiv:0910.4058 [hep-ph]

  190. Morisi, S., Peinado, E.: arXiv:0910.4389 [hep-ph]

  191. Berger, J., Grossman, Y.: arXiv:0910.4392 [hep-ph]

  192. Hagedorn, C., Molinaro, E., Petcov, S.T.: arXiv:0911.3605 [hep-ph]

  193. Feruglio, F., Hagedorn, C., Lin, Y., Merlo, L.: arXiv:0911.3874 [hep-ph]

  194. Ding, G.J., Liu, J.F.: arXiv:0911.4799 [hep-ph]

  195. Barry, J., Rodejohann, W.: arXiv:1003.2385 [hep-ph]

  196. Cooper, I.K., King, S.F., Luhn, C.: Phys. Lett. B 690, 396–402 (2010). arXiv:1004.3243 [hep-ph]

    Article  ADS  Google Scholar 

  197. Albright, C.H., Dueck, A., Rodejohann, W.: Eur. Phys. J. C 70, 1099–1110 (2010). arXiv:1004.2798 [hep-ph]

    Article  ADS  Google Scholar 

  198. Riva, F.: Phys. Lett. B 690, 443–450 (2010). arXiv:1004.1177 [hep-ph]

    Article  ADS  Google Scholar 

  199. Kadosh, A., Pallante, E.: J. High Energy Phys. 1008, 115 (2010). arXiv:1004.0321 [hep-ph]

    Article  ADS  Google Scholar 

  200. Feruglio, F., Paris, A.: Nucl. Phys. B 840, 405–423 (2010). arXiv:1005.5526 [hep-ph]

    Article  ADS  Google Scholar 

  201. Fukuyama, T., Sugiyama, H., Tsumura, K.: Phys. Rev. D 82, 036004 (2010). arXiv:1005.5338 [hep-ph]

    Article  ADS  Google Scholar 

  202. Antusch, S., King, S.F., Spinrath, M.: Phys. Rev. D 83, 013005 (2011). arXiv:1005.0708 [hep-ph]

    Article  ADS  Google Scholar 

  203. Ahn, Y.H.: arXiv:1006.2953 [hep-ph]

  204. Ma, E.: Phys. Rev. D 82, 037301 (2010). arXiv:1006.3524 [hep-ph]

    Article  ADS  Google Scholar 

  205. Hirsch, M., Morisi, S., Peinado, E., Valle, J.W.F.: Phys. Rev. D 82, 116003 (2010). arXiv:1007.0871 [hep-ph]

    Article  ADS  Google Scholar 

  206. Esteves, J.N., Joaquim, F.R., Joshipura, A.S., Romao, J.C., Tortola, M.A., Valle, J.W.F.: Phys. Rev. D 82, 073008 (2010). arXiv:1007.0898 [hep-ph]

    Article  ADS  Google Scholar 

  207. Burrows, T.J., King, S.F.: Nucl. Phys. B 842, 107–121 (2011). arXiv:1007.2310 [hep-ph]

    Article  ADS  Google Scholar 

  208. Haba, N., Kajiyama, Y., Matsumoto, S., Okada, H., Yoshioka, K.: Phys. Lett. B 695, 476–481 (2011). arXiv:1008.4777 [hep-ph]

    Article  ADS  Google Scholar 

  209. Araki, T., Mei, J., Xing, Z.-Z.: Phys. Lett. B 695, 165–168 (2011). arXiv:1010.3065 [hep-ph]

    Article  ADS  Google Scholar 

  210. Meloni, D., Morisi, S., Peinado, E.: Phys. Lett. B 697, 339–342 (2011). arXiv:1011.1371 [hep-ph]

    Article  ADS  Google Scholar 

  211. Machado, A.C.B., Montero, J.C., Pleitez, V.: Phys. Lett. B 697, 318–322 (2011). arXiv:1011.5855 [hep-ph]

    Article  ADS  Google Scholar 

  212. Carone, C.D., Lebed, R.F.: Phys. Lett. B 696, 454–458 (2011). arXiv:1011.6379 [hep-ph]

    Article  ADS  Google Scholar 

  213. de Medeiros Varzielas, I., Merlo, L.: J. High Energy Phys. 1102, 062 (2011). arXiv:1011.6662 [hep-ph]

    Article  Google Scholar 

  214. de Adelhart Toorop, R., Bazzocchi, F., Merlo, L., Paris, A.: J. High Energy Phys. 1103, 035 (2011). arXiv:1012.1791 [hep-ph]

    Article  Google Scholar 

  215. de Adelhart Toorop, R., Bazzocchi, F., Merlo, L., Paris, A.: J. High Energy Phys. 1103, 040 (2011). arXiv:1012.2091 [hep-ph]

    Article  ADS  Google Scholar 

  216. Fukuyama, T., Sugiyama, H., Tsumura, K.: Phys. Rev. D 83, 056016 (2011). arXiv:1012.4886 [hep-ph]

    Article  ADS  Google Scholar 

  217. de Medeiros Varzielas, I., Gonzalez Felipe, R., Serodio, H.: Phys. Rev. D 83, 033007 (2011). arXiv:1101.0602 [hep-ph]

    Article  ADS  Google Scholar 

  218. Boucenna, M.S., Hirsch, M., Morisi, S., Peinado, E., Taoso, M., Valle, J.W.F.: J. High Energy Phys. 1105, 037 (2011). arXiv:1101.2874 [hep-ph]

    Article  ADS  Google Scholar 

  219. Kadosh, A., Pallante, E.: J. High Energy Phys. 1106, 121 (2011). arXiv:1101.5420 [hep-ph]

    Article  ADS  Google Scholar 

  220. Ahn, Y.H., Cheng, H.-Y., Oh, S.: Phys. Rev. D 83, 076012 (2011). arXiv:1102.0879 [hep-ph]

    Article  ADS  Google Scholar 

  221. Ahn, Y.H., Kim, C.S., Oh, S.: arXiv:1103.0657 [hep-ph]

  222. Morisi, S., Peinado, E., Shimizu, Y., Valle, J.W.F.: Phys. Rev. D 84, 036003 (2011). arXiv:1104.1633 [hep-ph]

    Article  ADS  Google Scholar 

  223. Toorop, R.d.A., Bazzocchi, F., Morisi, S.: arXiv:1104.5676 [hep-ph]

  224. Shimizu, Y., Tanimoto, M., Watanabe, A.: Prog. Theor. Phys. 126, 81–90 (2011). arXiv:1105.2929 [hep-ph]

    Article  ADS  Google Scholar 

  225. Barry, J., Rodejohann, W., Zhang, H.: J. High Energy Phys. 1107, 091 (2011). arXiv:1105.3911 [hep-ph]

    Article  ADS  Google Scholar 

  226. Ma, E., Wegman, D.: Phys. Rev. Lett. 107, 061803 (2011). arXiv:1106.4269 [hep-ph]

    Article  ADS  Google Scholar 

  227. Albaid, A.: arXiv:1106.4070 [hep-ph]

  228. Adulpravitchai, A., Takahashi, R.: arXiv:1107.3829 [hep-ph]

  229. King, S.F., Luhn, C.: J. High Energy Phys. 1109, 042 (2011). arXiv:1107.5332 [hep-ph]

    Article  ADS  Google Scholar 

  230. Machado, A.C.B., Montero, J.C., Pleitez, V.: arXiv:1108.1767 [hep-ph]

  231. Ding, G.-J., Meloni, D.: arXiv:1108.2733 [hep-ph]

  232. Aristizabal Sierra, D., Bazzocchi, F.: arXiv:1110.3781 [hep-ph]

  233. Cooper, I.K., King, S.F., Luhn, C.: arXiv:1110.5676 [hep-ph]

  234. Barry, J., Rodejohann, W., Zhang, H.: arXiv:1110.6382 [hep-ph]

  235. Ferreira, P.M., Lavoura, L.: arXiv:1111.5859 [hep-ph]

  236. King, S.F., Luhn, C.: arXiv:1112.1959 [hep-ph]

  237. Ding, G.-J., Everett, L.L., Stuart, A.J.: arXiv:1110.1688 [hep-ph]

  238. Chen, C.-S., Kephart, T.W., Yuan, T.-C.: J. High Energy Phys. 1104, 015 (2011). arXiv:1011.3199 [hep-ph]

    Article  ADS  Google Scholar 

  239. Feruglio, F., Paris, A.: J. High Energy Phys. 1103, 101 (2011). arXiv:1101.0393 [hep-ph]

    Article  ADS  Google Scholar 

  240. Shirai, K.: J. Phys. Soc. Jpn. 61, 2735 (1992)

    Article  ADS  Google Scholar 

  241. Luhn, C., Nasri, S., Ramond, P.: J. Math. Phys. 48, 123519 (2007). arXiv:0709.1447 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  242. Luhn, C., Ramond, P.: J. Math. Phys. 49, 053525 (2008). arXiv:0803.0526 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  243. Everett, L.L., Stuart, A.J.: Phys. Rev. D 79, 085005 (2009). arXiv:0812.1057 [hep-ph]

    Article  ADS  Google Scholar 

  244. Aranda, A., Carone, C.D., Lebed, R.F.: Phys. Lett. B 474, 170 (2000). arXiv:hep-ph/9910392

    Article  ADS  Google Scholar 

  245. Aranda, A., Carone, C.D., Lebed, R.F.: Phys. Rev. D 62, 016009 (2000). arXiv:hep-ph/0002044

    Article  ADS  Google Scholar 

  246. Carr, P.D., Frampton, P.H.: arXiv:hep-ph/0701034

  247. Feruglio, F., Hagedorn, C., Lin, Y., Merlo, L.: Nucl. Phys. B 775, 120 (2007). arXiv:hep-ph/0702194

    Article  ADS  Google Scholar 

  248. Chen, M.C., Mahanthappa, K.T.: Phys. Lett. B 652, 34 (2007). arXiv:0705.0714 [hep-ph]

    Article  ADS  Google Scholar 

  249. Frampton, P.H., Kephart, T.W.: J. High Energy Phys. 0709, 110 (2007). arXiv:0706.1186 [hep-ph]

    Article  ADS  Google Scholar 

  250. Aranda, A.: Phys. Rev. D 76, 111301 (2007). arXiv:0707.3661 [hep-ph]

    Article  ADS  Google Scholar 

  251. Ding, G.J.: Phys. Rev. D 78, 036011 (2008). arXiv:0803.2278 [hep-ph]

    Article  ADS  Google Scholar 

  252. Frampton, P.H., Kephart, T.W., Matsuzaki, S.: Phys. Rev. D 78, 073004 (2008). arXiv:0807.4713 [hep-ph]

    Article  ADS  Google Scholar 

  253. Eby, D.A., Frampton, P.H., Matsuzaki, S.: Phys. Lett. B 671, 386 (2009). arXiv:0810.4899 [hep-ph]

    Article  ADS  Google Scholar 

  254. Frampton, P.H., Matsuzaki, S.: Phys. Lett. B 679, 347 (2009). arXiv:0902.1140 [hep-ph]

    Article  ADS  Google Scholar 

  255. Chen, M.C., Mahanthappa, K.T., Yu, F.: arXiv:0909.5472 [hep-ph]

  256. Frampton, P.H., Ho, C.M., Kephart, T.W., Matsuzaki, S.: Phys. Rev. D 82, 113007 (2010). arXiv:1009.0307 [hep-ph]

    Article  ADS  Google Scholar 

  257. Aranda, A., Bonilla, C., Ramos, R., Rojas, A.D.: arXiv:1011.6470 [hep-ph]

  258. BenTov, Y., Zee, A.: arXiv:1101.1987 [hep-ph]

  259. Eby, D.A., Frampton, P.H., He, X.-G., Kephart, T.W.: Phys. Rev. D 84, 037302 (2011). arXiv:1103.5737 [hep-ph]

    Article  ADS  Google Scholar 

  260. Chen, M.-C., Mahanthappa, K.T.: arXiv:1107.3856 [hep-ph]

  261. Merlo, L., Rigolin, S., Zaldivar, B.: arXiv:1108.1795 [hep-ph]

  262. Chen, M.-C., Mahanthappa, K.T., Meroni, A., Petcov, S.T.: arXiv:1109.0731 [hep-ph]

  263. Eby, D.A., Frampton, P.H.: arXiv:1112.2675 [hep-ph]

  264. Bergshoeff, E., Janssen, B., Ortin, T.: Class. Quantum Gravity 13, 321 (1996). arXiv:hep-th/9506156

    Article  ADS  Google Scholar 

  265. Frampton, P.H., Kephart, T.W.: Phys. Rev. D 64, 086007 (2001). arXiv:hep-th/0011186

    Article  ADS  MathSciNet  Google Scholar 

  266. Grimus, W., Lavoura, L.: Phys. Lett. B 572, 189 (2003). arXiv:hep-ph/0305046

    Article  ADS  Google Scholar 

  267. Grimus, W., Joshipura, A.S., Kaneko, S., Lavoura, L., Tanimoto, M.: J. High Energy Phys. 0407, 078 (2004). arXiv:hep-ph/0407112

    Article  ADS  Google Scholar 

  268. Grimus, W., Joshipura, A.S., Kaneko, S., Lavoura, L., Sawanaka, H., Tanimoto, M.: Nucl. Phys. B 713, 151 (2005). arXiv:hep-ph/0408123

    Article  ADS  Google Scholar 

  269. Blum, A., Mohapatra, R.N., Rodejohann, W.: Phys. Rev. D 76, 053003 (2007). arXiv:0706.3801 [hep-ph]

    Article  ADS  Google Scholar 

  270. Ishimori, H., Kobayashi, T., Ohki, H., Omura, Y., Takahashi, R., Tanimoto, M.: Phys. Lett. B 662, 178 (2008). arXiv:0802.2310 [hep-ph]

    Article  ADS  Google Scholar 

  271. Ishimori, H., Kobayashi, T., Ohki, H., Omura, Y., Takahashi, R., Tanimoto, M.: Phys. Rev. D 77, 115005 (2008). arXiv:0803.0796 [hep-ph]

    Article  ADS  Google Scholar 

  272. Adulpravitchai, A., Blum, A., Hagedorn, C.: J. High Energy Phys. 0903, 046 (2009). arXiv:0812.3799 [hep-ph]

    Article  ADS  Google Scholar 

  273. Hagedorn, C., Ziegler, R.: Phys. Rev. D 82, 053011 (2010). arXiv:1007.1888 [hep-ph]

    Article  ADS  Google Scholar 

  274. Meloni, D., Morisi, S., Peinado, E.: Phys. Lett. B 703, 281–287 (2011). arXiv:1104.0178 [hep-ph]

    Article  ADS  Google Scholar 

  275. Hagedorn, C., Lindner, M., Plentinger, F.: Phys. Rev. D 74, 025007 (2006). arXiv:hep-ph/0604265

    Article  ADS  Google Scholar 

  276. Kajiyama, Y., Kubo, J., Okada, H.: Phys. Rev. D 75, 033001 (2007). arXiv:hep-ph/0610072

    Article  ADS  Google Scholar 

  277. Blum, A., Hagedorn, C., Lindner, M.: Phys. Rev. D 77, 076004 (2008). arXiv:0709.3450 [hep-ph]

    Article  ADS  Google Scholar 

  278. Hagedorn, C., Lindner, M., Plentinger, F.: Phys. Rev. D 74, 025007 (2006). arXiv:hep-ph/0604265

    Article  ADS  Google Scholar 

  279. Blum, A., Hagedorn, C., Hohenegger, A.: J. High Energy Phys. 0803, 070 (2008). arXiv:0710.5061 [hep-ph]

    Article  ADS  Google Scholar 

  280. Blum, A., Hagedorn, C.: Nucl. Phys. B 821, 327 (2009). arXiv:0902.4885 [hep-ph]

    Article  ADS  Google Scholar 

  281. Adulpravitchai, A., Blum, A., Rodejohann, W.: New J. Phys. 11, 063026 (2009). arXiv:0903.0531 [hep-ph]

    Article  ADS  Google Scholar 

  282. Kim, J.E., Seo, M.-S.: J. High Energy Phys. 1102, 097 (2011). arXiv:1005.4684 [hep-ph]

    Article  ADS  Google Scholar 

  283. Kajiyama, Y., Okada, H., Toma, T.: Eur. Phys. J. C 71, 1688 (2011). arXiv:1104.0367 [hep-ph]

    Article  ADS  Google Scholar 

  284. Kim, J.E., Seo, M.-S.: arXiv:1106.6117 [hep-ph]

  285. Kajiyama, Y., Okada, H., Toma, T.: arXiv:1109.2722 [hep-ph]

  286. Babu, K.S., Kubo, J.: Phys. Rev. D 71, 056006 (2005). arXiv:hep-ph/0411226

    Article  ADS  Google Scholar 

  287. Kajiyama, Y., Itou, E., Kubo, J.: Nucl. Phys. B 743, 74 (2006). arXiv:hep-ph/0511268

    Article  ADS  Google Scholar 

  288. Itou, E., Kajiyama, Y., Kubo, J.: AIP Conf. Proc. 903, 389 (2007). arXiv:hep-ph/0611052

    Article  ADS  Google Scholar 

  289. Kawashima, K., Kubo, J., Lenz, A.: Phys. Lett. B 681, 60 (2009). arXiv:0907.2302 [hep-ph]

    Article  ADS  Google Scholar 

  290. Volkov, G.: arXiv:1006.5627 [math-ph]

  291. Kubo, J., Lenz, A.: Phys. Rev. D 82, 075001 (2010). arXiv:1007.0680 [hep-ph]

    Article  ADS  Google Scholar 

  292. Hackett, J., Kauffman, L.: arXiv:1010.2979 [math-ph]

  293. Furui, S.: AIP Conf. Proc. 1343, 533–535 (2011). arXiv:1011.3086 [hep-ph]

    Article  ADS  Google Scholar 

  294. Kaburaki, Y., Konya, K., Kubo, J., Lenz, A.: Phys. Rev. D 84, 016007 (2011). arXiv:1012.2435 [hep-ph]

    Article  ADS  Google Scholar 

  295. Babu, K.S., Kawashima, K., Kubo, J.: Phys. Rev. D 83, 095008 (2011). arXiv:1103.1664 [hep-ph]

    Article  ADS  Google Scholar 

  296. Araki, T., Li, Y.F.: arXiv:1112.5819 [hep-ph]

  297. Frigerio, M., Kaneko, S., Ma, E., Tanimoto, M.: Phys. Rev. D 71, 011901 (2005). arXiv:hep-ph/0409187

    Article  ADS  Google Scholar 

  298. Frigerio, M., Ma, E.: Phys. Rev. D 76, 096007 (2007). arXiv:0708.0166 [hep-ph]

    Article  ADS  Google Scholar 

  299. Dev, S., Verma, S.: Mod. Phys. Lett. A 25, 2837–2848 (2010). arXiv:1005.4521 [hep-ph]

    Article  ADS  Google Scholar 

  300. Aranda, A., Bonilla, C., Ramos, R., Rojas, A.D.: Phys. Rev. D 84, 016009 (2011). arXiv:1105.6373 [hep-ph]

    Article  ADS  Google Scholar 

  301. Ma, E.: arXiv:0705.0327 [hep-ph]

  302. Bovier, A., Luling, M., Wyler, D.: J. Math. Phys. 22, 1536 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  303. Bovier, A., Luling, M., Wyler, D.: J. Math. Phys. 22, 1543 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  304. Fairbairn, W.M., Fulton, T.: J. Math. Phys. 23, 1747 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  305. Branco, G.C., Gerard, J.M., Grimus, W.: Phys. Lett. B 136, 383 (1984)

    Article  ADS  Google Scholar 

  306. Ma, E.: Mod. Phys. Lett. A 21, 1917 (2006). arXiv:hep-ph/0607056

    Article  ADS  Google Scholar 

  307. Luhn, C., Nasri, S., Ramond, P.: J. Math. Phys. 48, 073501 (2007). arXiv:hep-th/0701188

    Article  ADS  MathSciNet  Google Scholar 

  308. de Medeiros Varzielas, I., King, S.F., Ross, G.G.: Phys. Lett. B 648, 201 (2007). arXiv:hep-ph/0607045

    Article  ADS  Google Scholar 

  309. Ma, E.: Phys. Lett. B 660, 505 (2008). arXiv:0709.0507 [hep-ph]

    Article  ADS  Google Scholar 

  310. Grimus, W., Lavoura, L.: J. High Energy Phys. 0809, 106 (2008). arXiv:0809.0226 [hep-ph]

    Article  ADS  Google Scholar 

  311. Howl, R., King, S.F.: J. High Energy Phys. 0805, 008 (2008). arXiv:0802.1909 [hep-ph]

    Article  ADS  Google Scholar 

  312. King, S.F., Luhn, C.: J. High Energy Phys. 0910, 093 (2009). arXiv:0908.1897 [hep-ph]

    Article  ADS  Google Scholar 

  313. King, S.F.: J. High Energy Phys. 1009, 114 (2010). arXiv:1006.5895 [hep-ph]

    Article  ADS  Google Scholar 

  314. Luhn, C., Nasri, S., Ramond, P.: Phys. Lett. B 652, 27 (2007). arXiv:0706.2341 [hep-ph]

    Article  ADS  Google Scholar 

  315. Hagedorn, C., Schmidt, M.A., Smirnov, A.Y.: Phys. Rev. D 79, 036002 (2009). arXiv:0811.2955 [hep-ph]

    Article  ADS  Google Scholar 

  316. Cao, Q.-H., Khalil, S., Ma, E., Okada, H.: Phys. Rev. Lett. 106, 131801 (2011). arXiv:1009.5415 [hep-ph]

    Article  ADS  Google Scholar 

  317. Ma, E.: Mod. Phys. Lett. A 26, 377–385 (2011). arXiv:1101.4972 [hep-ph]

    Article  ADS  Google Scholar 

  318. Cao, Q.-H., Khalil, S., Ma, E., Okada, H.: arXiv:1108.0570 [hep-ph]

  319. Kajiyama, Y., Okada, H.: Nucl. Phys. B 848, 303–313 (2011). arXiv:1011.5753 [hep-ph]

    Article  ADS  Google Scholar 

  320. Parattu, K.M., Wingerter, A.: Phys. Rev. D 84, 013011 (2011). arXiv:1012.2842 [hep-ph]

    Article  ADS  Google Scholar 

  321. Ding, G.-J.: Nucl. Phys. B 853, 635–662 (2011). arXiv:1105.5879 [hep-ph]

    Article  ADS  Google Scholar 

  322. Hartmann, C., Zee, A.: Nucl. Phys. B 853, 105–124 (2011). arXiv:1106.0333 [hep-ph]

    Article  ADS  Google Scholar 

  323. Hartmann, C.: arXiv:1109.5143 [hep-ph]

  324. Ishimori, H., Kobayashi, T.: arXiv:1201.3429 [hep-ph]

  325. Escobar, J.A., Luhn, C.: J. Math. Phys. 50, 013524 (2009). arXiv:0809.0639 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  326. Ishimori, H., Kobayashi, T., Okada, H., Shimizu, Y., Tanimoto, M.: J. High Energy Phys. 0904, 011 (2009). arXiv:0811.4683 [hep-ph]

    Article  ADS  Google Scholar 

  327. Ishimori, H., Kobayashi, T., Okada, H., Shimizu, Y., Tanimoto, M.: J. High Energy Phys. 0912, 054 (2009). arXiv:0907.2006 [hep-ph]

    Article  ADS  Google Scholar 

  328. Escobar, J.A.: arXiv:1102.1649 [hep-ph]

  329. Varzielas, I.d.M., Emmanuel-Costa, D.: arXiv:1106.5477 [hep-ph]

  330. Toorop, R.d.A., Feruglio, F., Hagedorn, C.: Phys. Lett. B 703, 447–451 (2011). arXiv:1107.3486 [hep-ph]

    Article  ADS  Google Scholar 

  331. Krauss, L.M., Wilczek, F.: Phys. Rev. Lett. 62, 1221 (1989)

    Article  ADS  Google Scholar 

  332. Ibáñez, L.E., Ross, G.G.: Phys. Lett. B 260, 291–295 (1991)

    Article  ADS  Google Scholar 

  333. Banks, T., Dine, M.: Phys. Rev. D 45, 1424–1427 (1992). arXiv:hep-th/9109045

    Article  ADS  MathSciNet  Google Scholar 

  334. Dine, M., Graesser, M.: J. High Energy Phys. 01, 038 (2005). arXiv:hep-th/0409209

    Article  ADS  Google Scholar 

  335. Csaki, C., Murayama, H.: Nucl. Phys. B 515, 114–162 (1998). arXiv:hep-th/9710105

    Article  ADS  Google Scholar 

  336. Ibáñez, L.E., Ross, G.G.: Nucl. Phys. B 368, 3–37 (1992)

    Article  ADS  Google Scholar 

  337. Ibáñez, L.E.: Nucl. Phys. B 398, 301–318 (1993). arXiv:hep-ph/9210211

    Article  ADS  Google Scholar 

  338. Babu, K.S., Gogoladze, I., Wang, K.: Nucl. Phys. B 660, 322–342 (2003). arXiv:hep-ph/0212245

    Article  ADS  Google Scholar 

  339. Dreiner, H.K., Luhn, C., Thormeier, M.: Phys. Rev. D 73, 075007 (2006). arXiv:hep-ph/0512163

    Article  ADS  Google Scholar 

  340. Araki, T.: Prog. Theor. Phys. 117, 1119–1138 (2007). arXiv:hep-ph/0612306

    Article  ADS  Google Scholar 

  341. Araki, T., Choi, K.S., Kobayashi, T., Kubo, J., Ohki, H.: Phys. Rev. D 76, 066006 (2007). arXiv:0705.3075 [hep-ph]

    Article  ADS  MathSciNet  Google Scholar 

  342. Araki, T., Kobayashi, T., Kubo, J., Ramos-Sanchez, S., Ratz, M., Vaudrevange, P.K.S.: Nucl. Phys. B 805, 124 (2008). arXiv:0805.0207 [hep-th]

    Article  ADS  Google Scholar 

  343. Luhn, C., Ramond, P.: J. High Energy Phys. 0807, 085 (2008). arXiv:0805.1736 [hep-ph]

    Article  ADS  Google Scholar 

  344. Luhn, C.: Phys. Lett. B 670, 390 (2009). arXiv:0807.1749 [hep-ph]

    Article  ADS  Google Scholar 

  345. Merle, A., Zwicky, R.: arXiv:1110.4891 [hep-ph]

  346. Grimus, W., Ludl, P.O.: J. Phys. A 43, 445209 (2010). arXiv:1006.0098 [hep-ph]

    Article  ADS  MathSciNet  Google Scholar 

  347. Ludl, P.O.: J. Phys. A 43, 395204 (2010). arXiv:1006.1479 [math-ph]

    Article  MathSciNet  Google Scholar 

  348. Ludl, P.O.: J. Phys. A 44, 255204 (2011). arXiv:1101.2308 [math-ph]

    Article  ADS  MathSciNet  Google Scholar 

  349. Luhn, C.: J. High Energy Phys. 1103, 108 (2011). arXiv:1101.2417 [hep-ph]

    Article  ADS  Google Scholar 

  350. King, S.F., Luhn, C.: Nucl. Phys. B 820, 269 (2009). arXiv:0905.1686 [hep-ph]

    Article  ADS  Google Scholar 

  351. King, S.F., Luhn, C.: Nucl. Phys. B 832, 414 (2010). arXiv:0912.1344 [hep-ph]

    Article  ADS  Google Scholar 

  352. Everett, L.L., Stuart, A.J.: Phys. Lett. B 698, 131–139 (2011). arXiv:1011.4928 [hep-ph]

    Article  ADS  Google Scholar 

  353. Hashimoto, K., Okada, H.: arXiv:1110.3640 [hep-ph]

  354. Chen, C.-S., Kephart, T.W., Yuan, T.-C.: arXiv:1110.6233 [hep-ph]

  355. An, F.P., et al. (Daya Bay Collaboration): Phys. Rev. Lett. 108, 171803 (2012). arXiv:1203.1669 [hep-ex]

    Article  ADS  Google Scholar 

  356. Ahn, J.K., et al. (Reno Collaboration): Phys. Rev. Lett. 108, 191802 (2012). arXiv:1204.0626 [hep-ex]

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMJ), Nagoya University, Nagoya, Japan

    Hajime Ishimori

  2. School of Physics, Korean Institute for Advanced Study, Seoul, Korea

    Tatsuo Kobayashi

  3. Department of Physics, Kyoto University, Kyoto, Japan

    Hiroshi Ohki

  4. Department of Physics, Niigata University, Niigata, Japan

    Hiroshi Okada

  5. Department of Physics, Niigata University, Niigata, Japan

    Yusuke Shimizu

  6. Department of Physics, Niigata University, Niigata, Japan

    Morimitsu Tanimoto

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  1. Hajime Ishimori
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  2. Tatsuo Kobayashi
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  3. Hiroshi Ohki
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  5. Yusuke Shimizu
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  6. Morimitsu Tanimoto
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Ishimori, H., Kobayashi, T., Ohki, H., Okada, H., Shimizu, Y., Tanimoto, M. (2012). Introduction. In: An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists. Lecture Notes in Physics, vol 858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30805-5_1

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