Built on

G.A. Miller, H.F. Blichfeldt, and L.E. Dickson, ‘Theory and applications of finite groups’, John Wiley and Sons, 1916
1916
Earlier work this paper cites.
H.F. Blichfeldt, ‘Finite collineation groups’, University of Chicago Press, 1917
1917
Earlier work this paper cites.
W.M. Fairbairn, T. Fulton, and W.H. Klink, J. Math. Phys. 5, 1038 (1964)
1964
Earlier work this paper cites.
H.S.M. Coxeter and W.O.J. Moser, ‘Generators and Relations for Discrete Groups’, (Springer-Verlag, 1980)
1980
Earlier work this paper cites.
J. McKay, Proc. Symp. Pure Math. 37 (1980) 183
1980
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A. Bovier, M. Lüling, and D. Wyler, J. Math. Phys. 22, 1543 (1981)
1981
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A. Aranda, C.D. Carone, R.F. Lebed, Int. J. Mod. Phys. A16S1C (2001) 896; F. Feruglio, C. Hagedorn, Y. Lin, and L. Merlo, arXiv:hep-ph/0702194; P.H. Frampton and T.W. Kephart, arXiv:0706.1186; M.-C. Chen and K.T. Mahanthappa, arXiv:0710.2118; P.H. Frampton and S. Matsuzaki, arXiv:0710.5928; G.-J. Ding, arXiv:0803.2278
Original
2001
Earlier work this paper cites.

Similar

P.F. Harrison, D.H. Perkins, and W.G. Scott, Phys. Lett. B458, (1999) 79, hep-ph/9904297; Phys. Lett. B530, (2002) 167, hep-ph/0202074
2002
Cited alongside, same era.
S. Pakvasa and H. Sugawara, Phys. Lett. B73 (1978) 61; Y.-P. Yao, arXiv:hep-ph/9507207; L.J. Hall, H. Murayama, Phys. Rev. Lett. 75 (1995) 3985; K. Kang, J.E. Kim, and P. Ko, Z. Phys. C72 (1996) 671; C.D. Carone, Nucl. Phys. Proc. Suppl. 52A (1997) 177; S.L. Adler, Phys. Rev. D59 (1998) 015012; Erratum-ibid. D59 (1999) 099902; M. Tanimoto, Phys. Rev. D59 (1999) 017304; Acta Phys. Polon. B30 (1999) 3105; Phys. Lett. B483 (2000) 417; Y. Koide, Phys. Rev. D60 (1999) 077301; E. Ma, Phys. Rev. D61 (2000) 033012; R.N. Mohapatra, A. Pérez-Lorenzana, and C.A. de S. Pires, Phys. Lett. B474 (2000) 355; J.I. Silva-Marcos, JHEP 0307 (2003) 012; P.F. Harrison and W. G. Scott, Phys. Lett. B557 (2003) 76; T. Kobayashi, J. Kubo, and H. Terao, Phys. Lett. B568 (2003) 83; K. Hamaguchi, M. Kakizaki, and M. Yamaguchi, Phys. Rev. D68 (2003) 056007; J. Kubo, A. Mondragon, M. Mondragon, and E. Rodriguez-Jauregui, Prog. Theor. Phys. 109 (2003) 795; Erratum-ibid. 114 (2005) 287; T. Kobayashi, J. Kubo, and H. Terao, Phys. Lett. B568 (2003) 83; J. Kubo, Phys. Lett. B578 (2004) 156; Erratum-ibid. B619 (2005) 387; Phys. Rev. D70 (2004) 036007; S.-L. Chen, M. Frigerio, and E. Ma, Phys. Rev. D70 (2004) 073008; Erratum-ibid. D70 (2004) 079905; W.-l. Guo, Phys. Rev. D70 (2004) 053009; T. Araki, J. Kubo, and E.A. Paschos, Eur. Phys. J. C45 (2006) 465; W. Grimus and L. Lavoura, JHEP 0508 (2005) 013; JHEP 0601 (2006) 018; J. Phys. G34 (2007) 1757; T. Teshima, Phys. Rev. D73 (2006) 045019; Y. Koide, Phys. Rev. D73 (2006) 057901; Eur. Phys. J. C50 (2007) 8009; J.E. Kim and J.-C. Park, JHEP 0605 (2006) 017; N. Haba, A. Watanabe, and K. Yoshioka, Phys. Rev. Lett. 97 (2006) 041601; N. Haba and K. Yoshioka, Nucl. Phys. B739 (2006) 254; H. Morisi, arXiv:hep-ph/0604106; M. Picariello, arXiv:hep-ph/0611189; R.N. Mohapatra, S. Nasri, and H.-B. Yu, Phys. Lett. B639 (2006) 318; R.N. Mohapatra and H.-B. Yu, Phys. Lett. B644 (2007) 346; O. Felix, A. Mondragon, M. Mondragon, and E. Peinado, Rev. Mex. Fis. S52 (2006) 67; A. Mondragon, M. Mondragon, and E. Peinado, Phys. Rev. D76 (2007) 076003; J. Phys. A41 (2008) 304035; K.S. Babu, S.M. Barr, and I. Gogoladze, Phys. Lett. B661 (2008) 124; C.-Y. Chen and L. Wolfenstein, Phys. Rev, D77 (2008) 093009; M. Mitra and S. Choubey, arXiv:0806.3254

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2008

The Unique Horizontal Symmetry of Leptons

Lam, C. S.

Understand

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups.

Applying this connection to the tri-bimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely $S_4$, the permutation group of four objects.

Built on

G.A. Miller, H.F. Blichfeldt, and L.E. Dickson, ‘Theory and applications of finite groups’, John Wiley and Sons, 1916
1916
Earlier work this paper cites.
H.F. Blichfeldt, ‘Finite collineation groups’, University of Chicago Press, 1917
1917
Earlier work this paper cites.
W.M. Fairbairn, T. Fulton, and W.H. Klink, J. Math. Phys. 5, 1038 (1964)
1964
Earlier work this paper cites.
H.S.M. Coxeter and W.O.J. Moser, ‘Generators and Relations for Discrete Groups’, (Springer-Verlag, 1980)
1980
Earlier work this paper cites.
J. McKay, Proc. Symp. Pure Math. 37 (1980) 183
1980
Earlier work this paper cites.
A. Bovier, M. Lüling, and D. Wyler, J. Math. Phys. 22, 1543 (1981)
1981
Earlier work this paper cites.
A. Aranda, C.D. Carone, R.F. Lebed, Int. J. Mod. Phys. A16S1C (2001) 896; F. Feruglio, C. Hagedorn, Y. Lin, and L. Merlo, arXiv:hep-ph/0702194; P.H. Frampton and T.W. Kephart, arXiv:0706.1186; M.-C. Chen and K.T. Mahanthappa, arXiv:0710.2118; P.H. Frampton and S. Matsuzaki, arXiv:0710.5928; G.-J. Ding, arXiv:0803.2278
Original
2001
Earlier work this paper cites.

Similar

P.F. Harrison, D.H. Perkins, and W.G. Scott, Phys. Lett. B458, (1999) 79, hep-ph/9904297; Phys. Lett. B530, (2002) 167, hep-ph/0202074
2002
Cited alongside, same era.
S. Pakvasa and H. Sugawara, Phys. Lett. B73 (1978) 61; Y.-P. Yao, arXiv:hep-ph/9507207; L.J. Hall, H. Murayama, Phys. Rev. Lett. 75 (1995) 3985; K. Kang, J.E. Kim, and P. Ko, Z. Phys. C72 (1996) 671; C.D. Carone, Nucl. Phys. Proc. Suppl. 52A (1997) 177; S.L. Adler, Phys. Rev. D59 (1998) 015012; Erratum-ibid. D59 (1999) 099902; M. Tanimoto, Phys. Rev. D59 (1999) 017304; Acta Phys. Polon. B30 (1999) 3105; Phys. Lett. B483 (2000) 417; Y. Koide, Phys. Rev. D60 (1999) 077301; E. Ma, Phys. Rev. D61 (2000) 033012; R.N. Mohapatra, A. Pérez-Lorenzana, and C.A. de S. Pires, Phys. Lett. B474 (2000) 355; J.I. Silva-Marcos, JHEP 0307 (2003) 012; P.F. Harrison and W. G. Scott, Phys. Lett. B557 (2003) 76; T. Kobayashi, J. Kubo, and H. Terao, Phys. Lett. B568 (2003) 83; K. Hamaguchi, M. Kakizaki, and M. Yamaguchi, Phys. Rev. D68 (2003) 056007; J. Kubo, A. Mondragon, M. Mondragon, and E. Rodriguez-Jauregui, Prog. Theor. Phys. 109 (2003) 795; Erratum-ibid. 114 (2005) 287; T. Kobayashi, J. Kubo, and H. Terao, Phys. Lett. B568 (2003) 83; J. Kubo, Phys. Lett. B578 (2004) 156; Erratum-ibid. B619 (2005) 387; Phys. Rev. D70 (2004) 036007; S.-L. Chen, M. Frigerio, and E. Ma, Phys. Rev. D70 (2004) 073008; Erratum-ibid. D70 (2004) 079905; W.-l. Guo, Phys. Rev. D70 (2004) 053009; T. Araki, J. Kubo, and E.A. Paschos, Eur. Phys. J. C45 (2006) 465; W. Grimus and L. Lavoura, JHEP 0508 (2005) 013; JHEP 0601 (2006) 018; J. Phys. G34 (2007) 1757; T. Teshima, Phys. Rev. D73 (2006) 045019; Y. Koide, Phys. Rev. D73 (2006) 057901; Eur. Phys. J. C50 (2007) 8009; J.E. Kim and J.-C. Park, JHEP 0605 (2006) 017; N. Haba, A. Watanabe, and K. Yoshioka, Phys. Rev. Lett. 97 (2006) 041601; N. Haba and K. Yoshioka, Nucl. Phys. B739 (2006) 254; H. Morisi, arXiv:hep-ph/0604106; M. Picariello, arXiv:hep-ph/0611189; R.N. Mohapatra, S. Nasri, and H.-B. Yu, Phys. Lett. B639 (2006) 318; R.N. Mohapatra and H.-B. Yu, Phys. Lett. B644 (2007) 346; O. Felix, A. Mondragon, M. Mondragon, and E. Peinado, Rev. Mex. Fis. S52 (2006) 67; A. Mondragon, M. Mondragon, and E. Peinado, Phys. Rev. D76 (2007) 076003; J. Phys. A41 (2008) 304035; K.S. Babu, S.M. Barr, and I. Gogoladze, Phys. Lett. B661 (2008) 124; C.-Y. Chen and L. Wolfenstein, Phys. Rev, D77 (2008) 093009; M. Mitra and S. Choubey, arXiv:0806.3254

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2005

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2005

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E. Ma, hep-ph/0606039, Pramana 67 (2006) 803

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2006

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Y. Koide, H. Nishiura, K. Matsuda, T. Kikuchi, and T. Fukuyama, Phys. Rev. D66 (2002) 093006; E. Ma, arXiv:hep-ph/0312192; W. Grimus, A.S.Joshipura, S. Kaneko, L. Lavoura, H. Sawanaka, and M. Tanimoto, Nucl. Phys. B713 (2005) 151; B. Hu, F. Wu, Y.-L. Wu, Phys. Rev. D75 (2007) 113003

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C.S. Lam, arxiv:0804.2622, to appear in the Physical Review Letters

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