Abstract
Non-Abelian discrete groups have been adopted for the flavor models of the quarks and leptons. In this chapter, we present some successful flavor models of these discrete symmetries. Examples will illustrate how such models are built. However, before discussing the models themselves, we briefly review the main features of the experimental data regarding neutrino flavor mixing.
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Esteban, I., Gonzalez-Garcia, M.C., Maltoni, M., Schwetz, T., Zhou, A.: JHEP 09, 178 (2020). arXiv:2007.14792 [hep-ph]
Harrison, P.F., Perkins, D.H., Scott, W.G.: Phys. Lett. B 530, 167 (2002). arXiv:hep-ph/0202074
Harrison, P.F., Scott, W.G.: Phys. Lett. B 535, 163 (2002). arXiv:hep-ph/0203209
Harrison, P.F., Scott, W.G.: Phys. Lett. B 557, 76 (2003). arXiv:hep-ph/0302025
Harrison, P.F., Scott, W.G.: arXiv:hep-ph/0402006
Altarelli, G., Feruglio, F.: Rev. Mod. Phys. 82, 2701–2729 (2010). arXiv:1002.0211 [hep-ph]
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]
Zyla, P.A. et al.: [Particle Data Group], PTEP 2020(8), 083C01 (2020)
Weinberg, S.: Phys. Rev. Lett. 43, 1566 (1979)
Minkowski, P.: Phys. Lett. B 67, 421 (1977)
Yanagida, T.: In: Proceedings of the Workshop on Unified Theory and Baryon Number in the Universe, KEK (1979)
Gell-Mann, M., Ramond, P., Slansky, R.: Supergravity. Stony Brook (1979)
Glashow, S.L.: In: Cargèse, Lévy, M., et al. (eds.) Quarks and Leptons, p. 707. Plenum, New York (1980)
Mohapatra, R.N., Senjanovic, G.: Phys. Rev. Lett. 44, 912 (1980)
Ma, E., Rajasekaran, G.: Phys. Rev. D 64, 113012 (2001). arXiv:hep-ph/0106291
Lin, Y.: Nucl. Phys. B 824, 95 (2010). arXiv:0905.3534 [hep-ph]
Altarelli, G., Feruglio, F.: Nucl. Phys. B 720, 64 (2005). arXiv:hep-ph/0504165
Altarelli, G., Feruglio, F.: Nucl. Phys. B 741, 215 (2006). arXiv:hep-ph/0512103
Honda, M., Tanimoto, M.: Prog. Theor. Phys. 119, 583 (2008). arXiv:0801.0181 [hep-ph]
Hayakawa, A., Ishimori, H., Shimizu, Y., Tanimoto, M.: Phys. Lett. B 680, 334 (2009). arXiv:0904.3820 [hep-ph]
Brahmachari, B., Choubey, S., Mitra, M.: Phys. Rev. D 77, 073008 (2008) [Erratum-ibid. D 77, 119901 (2008)]. arXiv:0801.3554 [hep-ph]
Babu, K.S., Kobayashi, T., Kubo, J.: Phys. Rev. D 67, 075018 (2003). arXiv:hep-ph/0212350
Ishimori, H., Kobayashi, T., Omura, Y., Tanimoto, M.: JHEP 0812, 082 (2008). arXiv:0807.4625 [hep-ph]
Babu, K.S., Enkhbat, T., Gogoladze, I.: Phys. Lett. B 555, 238 (2003). arXiv:hep-ph/0204246
Babu, K.S., Ma, E., Valle, J.W.F.: Phys. Lett. B 552, 207 (2003). arXiv:hep-ph/0206292
Ma, E.: Mod. Phys. Lett. A 17, 2361 (2002). arXiv:hep-ph/0211393
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
Ma, E.: Phys. Rev. D 70, 031901 (2004). arXiv:hep-ph/0404199
Chen, S.L., Frigerio, M., Ma, E.: Nucl. Phys. B 724, 423 (2005). arXiv:hep-ph/0504181
Zee, A.: Phys. Lett. B 630, 58 (2005). arXiv:hep-ph/0508278
Ma, E.: Mod. Phys. Lett. A 20, 2601 (2005). arXiv:hep-ph/0508099
Ma, E.: Phys. Lett. B 632, 352 (2006). arXiv:hep-ph/0508231
Ma, E.: Phys. Rev. D 73, 057304 (2006). arXiv:hep-ph/0511133
He, X.G., Keum, Y.Y., Volkas, R.R.: JHEP 0604, 039 (2006). arXiv:hep-ph/0601001
Adhikary, B., Brahmachari, B., Ghosal, A., Ma, E., Parida, M.K.: Phys. Lett. B 638, 345 (2006). arXiv:hep-ph/0603059
Ma, E., Sawanaka, H., Tanimoto, M.: Phys. Lett. B 641, 301 (2006) arXiv:hep-ph/0606103
Valle, J.W.F.: J. Phys. Conf. Ser. 53, 473 (2006). arXiv:hep-ph/0608101
Adhikary, B., Ghosal, A: Phys. Rev. D 75, 073020 (2007). arXiv:hep-ph/0609193
Lavoura, L., Kuhbock, H.: Mod. Phys. Lett. A 22, 181 (2007). arXiv:hep-ph/0610050
King S.F., Malinsky, M.: Phys. Lett. B 645, 351 (2007). arXiv:hep-ph/0610250
Hirsch, M., Joshipura, A.S., Kaneko, S., Valle, J.W.F.: Phys. Rev. Lett. 99, 151802 (2007). arXiv:hep-ph/0703046
Bazzocchi, F., Kaneko, S., Morisi, S.: JHEP 0803, 063 (2008). arXiv:0707.3032 [hep-ph]
Grimus, W., Kuhbock, H.: Phys. Rev. D 77, 055008 (2008). arXiv:0710.1585 [hep-ph]
Adhikary, B., Ghosal, A.: Phys. Rev. D 78, 073007 (2008). arXiv:0803.3582 [hep-ph]
Fukuyama, T.: arXiv:0804.2107 [hep-ph]
Lin, Y.: Nucl. Phys. B 813, 91 (2009). arXiv:0804.2867 [hep-ph]
Frampton, P.H., Matsuzaki, S.: arXiv:0806.4592 [hep-ph]
Feruglio, F., Hagedorn, C., Lin, Y., Merlo, L.: Nucl. Phys. B 809, 218 (2009). arXiv:0807.3160 [hep-ph]
Morisi, S.: Nuovo Cim. 123B, 886 (2008). arXiv:0807.4013 [hep-ph]
Ma, E.: Phys. Lett. B 671, 366 (2009). arXiv:0808.1729 [hep-ph]
Bazzocchi, F., Frigerio, M., Morisi, S.: Phys. Rev. D 78, 116018 (2008). arXiv:0809.3573 [hep-ph]
Hirsch, M., Morisi, S., Valle, J.W.F.: Phys. Rev. D 79, 016001 (2009). arXiv:0810.0121 [hep-ph]
Merlo, L.: arXiv:0811.3512 [hep-ph]
Baek, S., Oh, M.C.: arXiv:0812.2704 [hep-ph]
Morisi, S.: Phys. Rev. D 79, 033008 (2009). arXiv:0901.1080 [hep-ph]
Ciafaloni, P., Picariello, M., Torrente-Lujan, E., Urbano, A.: Phys. Rev. D 79, 116010 (2009). arXiv:0901.2236 [hep-ph]
Merlo, L.: J. Phys. Conf. Ser. 171, 012083 (2009). arXiv:0902.3067 [hep-ph]
Chen, M.C., King, S.F.: JHEP 0906, 072 (2009). arXiv:0903.0125 [hep-ph]
Branco, G.C., Gonzalez Felipe, R., Rebelo, M.N., Serodio, H.: Phys. Rev. D 79, 093008 (2009). arXiv:0904.3076 [hep-ph]
Altarelli, G., Meloni, D.: J. Phys. G 36, 085005 (2009). arXiv:0905.0620 [hep-ph]
Urbano, A.: arXiv:0905.0863 [hep-ph]
Hirsch, M., Morisi, S., Valle, J.W.F.: Phys. Lett. B 679, 454 (2009).arXiv:0905.3056 [hep-ph]
Grimus, W., Lavoura, L.: JHEP 0809, 106 (2008). arXiv:0809.0226 [hep-ph]
Haba, N., Watanabe, A., Yoshioka, K.: Phys. Rev. Lett. 97, 041601 (2006). arXiv:hep-ph/0603116
Ishimori, H., Shimizu, Y., Tanimoto, M., Watanabe, A.: Phys. Rev. D 83, 033004 (2011). arXiv:1010.3805 [hep-ph]
Ishimori, H., Shimizu, Y., Tanimoto, M.: Prog. Theor. Phys. 121, 769 (2009). arXiv:0812.5031 [hep-ph]
Froggatt, C.D., Nielsen, H.B.: Nucl. Phys. B 147, 277 (1979)
Fusaoka, H., Koide, Y.: Phys. Rev. D 57, 3986 (1998). arXiv:hep-ph/9712201
Jarlskog, C.: Phys. Rev. Lett. 55, 1039 (1985)
Kajiyama, Y., Raidal, M., Strumia, A.: Phys. Rev. D 76, 117301 (2007). arXiv:0705.4559 [hep-ph]
Barger, V.D., Pakvasa, S., Weiler, T.J., Whisnant, K.: Phys. Lett. B 437, 107 (1998). arXiv:hep-ph/9806387
Everett, L.L., Stuart, A.J.: Phys. Rev. D 79, 085005 (2009). arXiv:0812.1057 [hep-ph]
Adulpravitchai, A., Blum, A., Rodejohann, W.: New J. Phys. 11, 063026 (2009). arXiv:0903.0531 [hep-ph]
Altarelli, G., Feruglio, F., Merlo, L.: JHEP 0905, 020 (2009). arXiv:0903.1940 [hep-ph]
Minakata, H., Smirnov, A.Y.: Phys. Rev. D 70, 073009 (2004). arXiv:hep-ph/0405088
Merlo, L.: AIP Conf. Proc. 1200(1), 948–951 (2010). arXiv:0909.2760 [hep-ph]
de Adelhart Toorop, R., Feruglio, F., Hagedorn, C.: Nucl. Phys. B 858, 437 (2012) arXiv:1112.1340 [hep-ph]
Feruglio, F.: In: Levy, A., Stefano Forte, S., Ridolfi, G. (eds.) From My Vast Repertoire ...: Guido Altarelli’s Legacy, pp. 227–266 (2019). arXiv:1706.08749 [hep-ph]
Kobayashi, T., Tanaka, K., Tatsuishi, T.H.: Phys. Rev. D 98(1), 016004 (2018). arXiv:1803.10391 [hep-ph]
Penedo, J.T., Petcov, S.T.: Nucl. Phys. B 939, 292 (2019). arXiv:1806.11040 [hep-ph]
Novichkov, P.P., Penedo, J.T., Petcov, S.T., Titov, A.V.: JHEP 1904, 174 (2019). arXiv:1812.02158 [hep-ph]
Kobayashi, T., Omoto, N., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H.: JHEP 11, 196 (2018). arXiv:1808.03012 [hep-ph]
Giusarma, E., Gerbino, M., Mena, O., Vagnozzi, S., Ho, S., Freese, K.: Phys. Rev. D 94(8), 083522 (2016). arXiv:1605.04320 [astro-ph.CO]
Vagnozzi, S., Giusarma, E., Mena, O., Freese, K., Gerbino, M., Ho, S., Lattanzi, M.: Phys. Rev. D 96(12), 123503 (2017). arXiv:1701.08172 [astro-ph.CO]
Aghanim, N., et al.: [Planck Collaboration]. arXiv:1807.06209 [astro-ph.CO]
Antusch, S., Maurer, V.: JHEP 1311, 115 (2013). arXiv:1306.6879 [hep-ph]
Björkeroth, F., de Anda, F.J., de Medeiros Varzielas, I., King, S.F.: JHEP 1506, 141 (2015). arXiv:1503.03306 [hep-ph]
Criado, J.C., Feruglio, F.: SciPost Phys. 5(5), 042 (2018). arXiv:1807.01125 [hep-ph]
Ding, G.J., King, S.F., Liu, X.G.: JHEP 1909, 074 (2019). arXiv:1907.11714 [hep-ph]
Zhang, D.: Nucl. Phys. B 952, 114935 (2020). arXiv:1910.07869 [hep-ph]
Novichkov, P.P., Penedo, J.T., Petcov, S.T., Titov, A.V.: JHEP 1904, 005 (2019). arXiv:1811.04933 [hep-ph]
Kobayashi, T., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H.: JHEP 02, 097 (2020). arXiv:1907.09141 [hep-ph]
Wang, X., Zhou, S.: JHEP 05, 017 (2020). arXiv:1910.09473 [hep-ph]
Ding, G.J., King, S.F., Liu, G.: Phys. Rev. D 100(11), 115005 (2019). arXiv:1903.12588 [hep-ph]
Liu, X.G., Ding, G.J.: JHEP 1908, 134 (2019). arXiv:1907.01488 [hep-ph]
Chen, P., Ding, G.J., Lu, J.N., Valle, J.W.F.: Phys. Rev. D 102(9), 095014 (2020). arXiv:2003.02734 [hep-ph]
Novichkov, P.P., Penedo, J.T., Petcov, S.T.: Nucl. Phys. B 963, 115301 (2021). arXiv:2006.03058 [hep-ph]
Liu, X.G., Yao, C.Y., Ding, G.J.: Phys. Rev. D 103(5), 056013 (2021). arXiv:2006.10722 [hep-ph]
Wang, X., Yu, B., Zhou, S.: Phys. Rev. D 103(7), 076005 (2021). arXiv:2010.10159 [hep-ph]
Yao, C.Y., Liu, X.G., Ding, G.J.: arXiv:2011.03501 [hep-ph]
Kobayashi, T., Tamba, S.: Phys. Rev. D 99(4), 046001 (2019). arXiv:1811.11384 [hep-th]
Ding, G.J., King, S.F., Li, C.C., Zhou, Y.L.: JHEP 08, 164 (2020). arXiv:2004.12662 [hep-ph]
Okada, H., Tanimoto, M.: Phys. Lett. B 791, 54 (2019). arXiv:1812.09677 [hep-ph]
Okada, H., Tanimoto, M.: Eur. Phys. J. C 81(1), 52 (2021). arXiv:1905.13421 [hep-ph]
de Anda, F.J., King, S.F., Perdomo, E.: Phys. Rev. D 101(1), 015028 (2020). arXiv:1812.05620 [hep-ph]
Kobayashi, T., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H.: arXiv:1906.10341 [hep-ph]
King, S.F., Zhou, Y.L.: JHEP 04, 291 (2021). arXiv:2103.02633 [hep-ph]
Chen, P., Ding, G.J., King, S.F.: JHEP 04, 239 (2021). arXiv:2101.12724 [hep-ph]
Ding, G.J., King, S.F., Yao, C.Y.: arXiv:2103.16311 [hep-ph]
Asaka, T., Heo, Y., Tatsuishi, T.H., Yoshida, T.: JHEP 2001, 144 (2020). arXiv:1909.06520 [hep-ph]
Okada, H., Shimizu, Y., Tanimoto, M., Yoshida, T.: JHEP 07, 184 (2021). arXiv:2105.14292 [hep-ph]
Qu, B.Y., Liu, X.G., Chen, P.T., Ding, G.J.: arXiv:2106.11659 [hep-ph]
Novichkov, P.P., Petcov, S.T., Tanimoto, M.: Phys. Lett. B 793, 247 (2019). arXiv:1812.11289 [hep-ph]
Ding, G.J., King, S.F., Liu, X.G., Lu, J.N.: JHEP 1912, 030 (2019). arXiv:1910.03460 [hep-ph]
Okada, H., Tanimoto, M.: Phys. Rev. D 103(1), 015005 (2021). arXiv:2009.14242 [hep-ph]
Feruglio, F., Gherardi, V., Romanino, A., Titov, A.: arXiv:2101.08718 [hep-ph]
Novichkov, P.P., Penedo, J.T., Petcov, S.T.: JHEP 04, 206 (2021). arXiv:2102.07488 [hep-ph]
Kobayashi, T., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H., Uchida, H.: Phys. Lett. B 794, 114 (2019). arXiv:1812.11072 [hep-ph]
de Medeiros Varzielas, I., King, S.F., Zhou, Y.L.: Phys. Rev. D 1015, 055033 (2020). arXiv:1906.02208 [hep-ph]
King, S.J.D., King, S.F.: JHEP 09, 043 (2020). arXiv:2002.00969 [hep-ph]
Kuranaga, H., Ohki, H., Uemura, S.: arXiv:2105.06237 [hep-ph]
Criado, J.C., Feruglio, F., King, S.J.D.: JHEP 2002, 001 (2020). arXiv:1908.11867 [hep-ph]
de Medeiros Varzielas, I., Levy, M., Zhou, Y.L.: JHEP 11, 085 (2020). arXiv:2008.05329 [hep-ph]
King, S.F., Zhou, Y.L.: Phys. Rev. D 101(1), 015001 (2020). arXiv:1908.02770 [hep-ph]
Nomura, T., Okada, H., Patra, S.: Nucl. Phys. B 967, 115395 (2021). arXiv:1912.00379 [hep-ph]
Kobayashi, T., Nomura, T., Shimomura, T.: Phys. Rev. D 102(3), 035019 (2020). arXiv:1912.00637 [hep-ph]
Lu, J.N., Liu, X.G., Ding, G.J.: Phys. Rev. D 101(11), 115020 (2020). arXiv:1912.07573 [hep-ph]
Wang, X.: Nucl. Phys. B 957, 115105 (2020). arXiv:1912.13284 [hep-ph]
Abbas, M.: Phys. Rev. D 103(5), 056016 (2021). arXiv:2002.01929 [hep-ph]
Okada, H., Shoji, Y.: Phys. Dark Univ. 31, 100742 (2021). arXiv:2003.11396 [hep-ph]
Okada, H., Shoji, Y.: Nucl. Phys. B 961, 115216 (2020). arXiv:2003.13219 [hep-ph]
Ding, G.J., Feruglio, F.: JHEP 06, 134 (2020). arXiv:2003.13448 [hep-ph]
Nomura, T., Okada, H.: arXiv:2007.04801 [hep-ph]
Nomura, T., Okada, H.: arXiv:2007.15459 [hep-ph]
Asaka, T., Heo, Y., Yoshida, T.: Phys. Lett. B 811, 135956 (2020). arXiv:2009.12120 [hep-ph]
Nomura, T., Okada, H.: Nucl. Phys. B 966, 115372 (2021). arXiv:1906.03927 [hep-ph]
Okada, H., Orikasa, Y.: arXiv:1908.08409 [hep-ph]
Nomura, T., Okada, H., Popov, O.: Phys. Lett. B 803, 135294 (2020). arXiv:1908.07457 [hep-ph]
Okada, H., Tanimoto, M.: arXiv:2005.00775 [hep-ph]
Nagao, K.I., Okada, H.: JCAP 05, 063 (2021). arXiv:2008.13686 [hep-ph]
Nagao, K.I., Okada, H.: arXiv:2010.03348 [hep-ph]
Abbas, M.: Phys. Atom. Nucl. 83(5), 764–769 (2020)
Kobayashi, T., Kubo, J., Terao, H.: Phys. Lett. B 568, 83 (2003). arXiv:hep-ph/0303084
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]
Ishimori, H., Kobayashi, T., Ohki, H., Omura, Y., Takahashi, R., Tanimoto, M.: Phys. Rev. D 77, 115005 (2008). arXiv:0803.0796 [hep-ph]
Ishimori, H., Kobayashi, T., Okada, H., Shimizu, Y., Tanimoto, M.: JHEP 0912, 054 (2009). arXiv:0907.2006 [hep-ph]
Kobayashi, T., Shimomura, T., Tanimoto, M.: Phys. Lett. B 819, 136452 (2021). arXiv:2102.10425 [hep-ph]
Tanimoto, M., Yamamoto, K.: JHEP 10, 183 (2021). arXiv:2106.10919 [hep-ph]
Hirsch, M., Morisi, S., Peinado, E., Valle, J.W.F.: Phys. Rev. D 82, 116003 (2010). arXiv:1007.0871 [hep-ph]
Meloni, D., Morisi, S., Peinado, E.: Phys. Lett. B697, 339–342 (2011). arXiv:1011.1371 [hep-ph]
Boucenna, M.S., Hirsch, M., Morisi, S., Peinado, E., Taoso, M., Valle, J.W.F.: JHEP 1105, 037 (2011). arXiv:1101.2874 [hep-ph]
Meloni, D., Morisi, S., Peinado, E.: Phys. Lett. B 703, 281–287 (2011). arXiv:1104.0178 [hep-ph]
Adriani, O., et al.: [PAMELA], Nature 458, 607–609 (2009). arXiv:0810.4995 [astro-ph]
Adriani, O., et al.: [PAMELA], Phys. Rev. Lett. 111, 081102 (2013). arXiv:1308.0133 [astro-ph.HE]
Abdo, A.A., et al.: [Fermi-LAT], Phys. Rev. Lett. 102, 181101 (2009). arXiv:0905.0025 [astro-ph.HE]
Accardo, L., et al.: AMS. Phys. Rev. Lett. 113, 121101 (2014)
Ambrosi, G., et al.: [DAMPE]. Nature 552, 63–66 (2017). arXiv:1711.10981 [astro-ph.HE]
Adriani, O., et al.: [CALET]. Phys. Rev. Lett. 119(18), 181101 (2017). arXiv:1712.01711 [astro-ph.HE]
Adriani, O., Akaike, Y., Asano, K., Asaoka, Y., Bagliesi, M.G., Berti, E., Bigongiari, G., Binns, W.R., Bonechi, S., Bongi, M., et al.: Phys. Rev. Lett. 120(26), 261102 (2018). arXiv:1806.09728 [astro-ph.HE]
Adriani, O., Barbarino, G.C., Bazilevskaya, G.A., Bellotti, R., Boezio, M., Bogomolov, E.A., Bonechi, L., Bongi, M., Bonvicini, V., Bottai, S., et al.: Phys. Rev. Lett. 102, 051101 (2009). arXiv:0810.4994 [astro-ph]
Aguilar, M., et al.: [AMS]. Phys. Rev. Lett. 117(9), 091103 (2016)
Papucci, M., Strumia, A.: JCAP 1003, 014 (2010). arXiv:0912.0742 [hep-ph]
Haba, N., Kajiyama, Y., Matsumoto, S., Okada, H., Yoshioka, K.: Phys. Lett. B 695, 476–481 (2011). arXiv:1008.4777 [hep-ph]
Kajiyama, Y., Okada, H.: Nucl. Phys. B848, 303–313 (2011). arXiv:1011.5753 [hep-ph]
Daikoku, Y., Okada, H., Toma, T.: arXiv:1106.4717 [hep-ph]
Kajiyama, Y., Okada, H., Toma, T.: arXiv:1109.2722 [hep-ph]
Kajiyama, Y., Okada, H., Toma, T.: Eur. Phys. J. C 71, 1688 (2011). arXiv:1104.0367 [hep-ph]
Nomura, T., Okada, H.: Phys. Lett. B 797, 134799 (2019). arXiv:1904.03937 [hep-ph]
Altarelli, G., Feruglio, F., Lin, Y.: Nucl. Phys. B 775, 31 (2007). arXiv:hep-ph/0610165
Adulpravitchai, A., Blum, A., Lindner, M.: JHEP 0907, 053 (2009). arXiv:0906.0468 [hep-ph]
Abe, H., Choi, K.-S., Kobayashi, T., Ohki, H., Sakai, M.: Int. J. Mod. Phys. A26, 4067–4082 (2011). arXiv:1009.5284 [hep-th]
Kobayashi, T., Raby, S., Zhang, R.J.: Nucl. Phys. B 704, 3 (2005). arXiv:hep-ph/0409098
Kobayashi, T., Nilles, H.P., Ploger, F., Raby, S., Ratz, M.: Nucl. Phys. B 768, 135 (2007). arXiv:hep-ph/0611020
Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: Nucl. Phys. B 820, 317 (2009). arXiv:0904.2631 [hep-ph]
Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: Phys. Rev. D 80, 126006 (2009). arXiv:0907.5274 [hep-th]
Abe, H., Choi, K.S., Kobayashi, T., Ohki, H.: arXiv:1001.1788 [hep-th]
Lauer, J., Mas, J., Nilles, H.P.: Phys. Lett. B 226, 251 (1989)
Lauer, J., Mas, J., Nilles, H.P.: Nucl. Phys. B 351, 353 (1991)
Lerche, W., Lust, D., Warner, N.P.: Phys. Lett. B 231, 417 (1989)
Ferrara, S., Lust, D., Theisen, S.: Phys. Lett. B 233, 147 (1989)
Kikuchi, S., Kobayashi, T., Takada, S., Tatsuishi, T.H., Uchida, H.: Phys. Rev. D 102(10), 105010 (2020). arXiv:2005.12642 [hep-th]
Kobayashi, T., Nagamoto, S.: Phys. Rev. D 96(9), 096011 (2017). arXiv:1709.09784 [hep-th]
Kobayashi, T., Nagamoto, S., Takada, S., Tamba, S., Tatsuishi, T.H.: Phys. Rev. D 97(11), 116002 (2018). arXiv:1804.06644 [hep-th]
Kariyazono, Y., Kobayashi, T., Takada, S., Tamba, S., Uchida, H.: Phys. Rev. D 100(4), 045014 (2019). arXiv:1904.07546 [hep-th]
Ohki, H., Uemura, S., Watanabe, R.: Phys. Rev. D 102(8), 085008 (2020). arXiv:2003.04174 [hep-th]
Kikuchi, S., Kobayashi, T., Otsuka, H., Takada, S., Uchida, H.: JHEP 11, 101 (2020). arXiv:2007.06188 [hep-th]
Kikuchi, S., Kobayashi, T., Uchida, H.: arXiv:2101.00826 [hep-th]
Almumin, Y., Chen, M.C., Knapp-Pérez, V., Ramos-Sánchez, S., Ratz, M., Shukla, S.: JHEP 05, 078 (2021). arXiv:2102.11286 [hep-th]
Tatsuta, Y.: arXiv:2104.03855 [hep-th]
Baur, A., Nilles, H.P., Trautner, A., Vaudrevange, P.K.S.: Phys. Lett. B 795, 7 (2019). arXiv:1901.03251 [hep-th]
Baur, A., Nilles, H.P., Trautner, A., Vaudrevange, P.K.S.: arXiv:1908.00805 [hep-th]
Nilles, H.P., Ramos-Śanchez, S., Vaudrevange, P.K.S.: JHEP 02, 045 (2020). arXiv:2001.01736 [hep-ph]
Nilles, H.P., Ramos-Sánchez, S., Vaudrevange, P.K.S.: Nucl. Phys. B 957, 115098 (2020). arXiv:2004.05200 [hep-ph]
Nilles, H.P., Ramos-Sánchez, S., Vaudrevange, P.K.S.: Phys. Lett. B 808, 135615 (2020). arXiv:2006.03059 [hep-th]
Baur, A., Kade, M., Nilles, H.P., Ramos-Sanchez, S., Vaudrevange, P.K.S.: JHEP 02, 018 (2021). arXiv:2008.07534 [hep-th]
Nilles, H.P., Ramos-Sánchez, S., Vaudrevange, P.K.S.: Nucl. Phys. B 966, 115367 (2021). arXiv:2010.13798 [hep-th]
Ishiguro, K., Kobayashi, T., Otsuka, H.: arXiv:2010.10782 [hep-th]
Baur, A., Kade, M., Nilles, H.P., Ramos-Sanchez, S., Vaudrevange, P.K.S.: Phys. Lett. B 816, 136176 (2021). arXiv:2012.09586 [hep-th]
Ding, G.J., Feruglio, F., Liu, X.G.: JHEP 01, 037 (2021). arXiv:2010.07952 [hep-th]
Ishiguro, K., Kobayashi, T., Otsuka, H.: arXiv:2107.00487 [hep-th]
Kobayashi, T., Omura, Y., Yoshioka, K.: Phys. Rev. D 78, 115006 (2008). arXiv:0809.3064
Seidl, G.: Phys. Rev. D 81, 025004 (2010). arXiv:0811.3775 [hep-ph]
Adulpravitchai, A., Schmidt, M.A.: JHEP 01, 106 (2011). arXiv:1001.3172 [hep-ph]
Kobayashi, T., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H.: Phys. Rev. D 100(11), 115045 (2019) [erratum: Phys. Rev. D 101(3), 039904 (2020)]. arXiv:1909.05139 [hep-ph]
Kobayashi, T., Shimizu, Y., Takagi, K., Tanimoto, M., Tatsuishi, T.H., Uchida, H.: Phys. Rev. D 101(5), 055046 (2020). arXiv:1910.11553 [hep-ph]
Ishiguro, K., Kobayashi, T., Otsuka, H.: JHEP 03, 161 (2021). arXiv:2011.09154 [hep-ph]
Kobayashi, T., Otsuka, H.: Phys. Rev. D 102(2), 026004 (2020). arXiv:2004.04518 [hep-th]
Kobayashi, T., Okada, H., Orikasa, Y.: arXiv:2111.05674 [hep-ph]
Kobayashi, T., Otsuka, H.: arXiv:2108.02700 [hep-ph]
Kobayashi, T., Otsuka, H., Tanimoto, M., Yamamoto, K.: arXiv:2112.00493 [hep-ph]
Kikuchi, S., Kobayashi, T., Otsuka, H., Tanimoto, M., Uchida, H., Yamamoto, K.: arXiv:2201.04505 [hep-ph]
Novichkov, P.P., Penedo, J.T., Petcov, S.T.: arXiv:2201.02020 [hep-ph]
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Kobayashi, T., Ohki, H., Okada, H., Shimizu, Y., Tanimoto, M. (2022). Non-Abelian Discrete Symmetry in Quark/Lepton Flavor Models. In: An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists. Lecture Notes in Physics, vol 995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64679-3_19
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