In the most of parameterizations for Cabibbo-Kobayashi-Masjawa (CKM) matrix,the mixing angles and CP violating phase chosen are not direct measurable quantities and depend on parametrizations. Using the measurable quantities to
study the CKM matrix would be interesting. In this thesis, we propose to use experimentally measurable CP violating quantities, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parameterizations. Approximate Wolfenstein-like expressions are also suggested. Since β is the most accurately measured among these three phase angles, we therefore consider the β parameterization the best one to use. Moreover, it is fascinating to research the connection between quark and lepton mixing. We also study the Quark-Lepton Complementarity (QLC) between mixing angles, the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4. Experimentally in the CK parameterization, two such relations exist approximately. However, these QLC relations are accidental which only manifest themselves in the CK parameterization. We propose reparameterization invariant expressions for the complementarity relations
in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |Vus/Vud|+|Ve2/Ve1|+|Vus/Vud||Ve2/Ve1| = 1
and |Vcb/Vtb| + |Vμ3/Vτ3| + |Vcb/Vtb||Vμ3/Vτ3| = 1. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.

1 Introduction 1
2 The Standard Model and Unitary Matrix 3
2.1 The Standard Model Lagrangian and Higgs Mechanism . . . . . . . . 3
2.2 The CP Violation and CKM Matrix . . . . . . . . . . . . . . . . . . . 7
2.2.1 The Elements of CKM Matrix . . . . . . . . . . . . . . . . . . 8
2.2.2 The Parametrizations of CKM Matrix . . . . . . . . . . . . . 9
2.2.3 The Phases of CKM Matrix . . . . . . . . . . . . . . . . . . . 13
2.3 The Neutrino Oscillation and PMNS Matrix . . . . . . . . . . . . . . 15
2.3.1 The Three Mixing Angles of PMNS Matrix . . . . . . . . . . . 17
2.3.2 The Global Fitting Results of PMNS Matrix . . . . . . . . . . 20
3 The α, β and γ Parametrizations of CKM Matrix 24
3.1 The α, β and γ Parametrizations . . . . . . . . . . . . . . . . . . . . 25
3.2 Relations Between Different Parametrizations . . . . . . . . . . . . . 29
3.3 Wolfenstein-like Expansions . . . . . . . . . . . . . . . . . . . . . . . 30
4 The Quark-Lepton Complementarity 33
4.1 The Quark-Lepton Complementarity Relations . . . . . . . . . . . . . 33
4.2 Reparametrization Invariance of QLC Relations . . . . . . . . . . . . 34
4.3 A Confliction Between QLC and Tribimaximal Mixing Matrix. . . . . 35
4.4 Deviations of QLC relations . . . . . . . . . . . . . . . . . . . . . . . 37
5 Conclusion 39
References 40

[1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).
[2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
[3] L.L. Chau and W.Y. Keung, Phys. Rev. Lett. 53, 1802 (1984).
[4] L. Wolfenstein, Phys. Rev. Lett. 51, 1945(1983).
[5] J. Beringer et al. [Particle Data Group], Phys. Rev. D86, 010001 (2012).
[6] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716, 1 (2012)
[arXiv:1207.7214 [hep-ex]].
[7] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716, 30 (2012)
[arXiv:1207.7235 [hep-ex]].
[8] M. Bonna et al., http://www.utfit.org.
[9] C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985); Z. Phys. C29, 491 (1985).
[10] J. C. Hardy and I. S. Towner, Phys. Rev. C 79, 055502 (2009) [arXiv:0812.1202
[nucl-ex]].
[11] D. Pocanic, E. Frlez, V. A. Baranov, W. H. Bertl, C. .Bronnimann, M. Bychkov,
J. F. Crawford and M. Daum et al., Phys. Rev. Lett. 93, 181803 (2004) [hepex/
0312030].
[12] M. Antonelli et al. [FlaviaNet Working Group on Kaon Decays Collaboration],
arXiv:0801.1817 [hep-ph].
[13] B. Aubert et al. [BaBar Collaboration], Phys. Rev. Lett. 105, 051602 (2010)
[arXiv:0912.0242 [hep-ex]].
[14] F. Ambrosino et al. [KLOE Collaboration], Phys. Lett. B 632, 76 (2006) [hepex/
0509045].
[15] E. Follana et al. [HPQCD and UKQCD Collaborations], Phys. Rev. Lett. 100,
062002 (2008) [arXiv:0706.1726 [hep-lat]].
[16] K. Maltman, AIP Conf. Proc. 1182, 398 (2009) [arXiv:0906.5008 [hep-ph]];
K. Maltman, C. E. Wolfe, S. Banerjee, I. M. Nugent and J. M. Roney, Nucl.
Phys. Proc. Suppl. 189, 175 (2009) [arXiv:0906.1386 [hep-ph]]; E. Gamiz,
M. Jamin, A. Pich, J. Prades and F. Schwab, PoS KAON , 008 (2008)
[arXiv:0709.0282 [hep-ph]].
[17] B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 105, 051602 (2010)
[arXiv:0912.0242 [hep-ex]].
[18] C. Aubin et al. [Fermilab Lattice and MILC and HPQCD Collaborations], Phys.
Rev. Lett. 94, 011601 (2005) [hep-ph/0408306].
[19] D. Besson et al. [CLEO Collaboration], Phys. Rev. D 80, 032005 (2009)
[arXiv:0906.2983 [hep-ex]].
[20] A. O. Bazarko et al. [CCFR Collaboration], Z. Phys. C 65, 189 (1995) [hepex/
9406007].
[21] T. Bolton, hep-ex/9708014.
[22] W branching fraction results from LEP, LEPEWWG/ XSEC/2005-01,
http://lepewwg.web.cern.ch/LEPEWWG/lepww/4f/Winter05/.
[23] P. Abreu et al. [DELPHI Collaboration], Phys. Lett. B 439, 209 (1998).
[24] L. Widhalm et al. [Belle Collaboration], Phys. Rev. Lett. 100, 241801 (2008)
[arXiv:0709.1340 [hep-ex]].
[25] J. P. Alexander et al. [CLEO Collaboration], Phys. Rev. D 79, 052001 (2009)
[arXiv:0901.1216 [hep-ex]]; P. U. E. Onyisi et al. [CLEO Collaboration], Phys.
Rev. D 79, 052002 (2009) [arXiv:0901.1147 [hep-ex]]; P. Naik et al. [CLEO
Collaboration], Phys. Rev. D 80, 112004 (2009) [arXiv:0910.3602 [hep-ex]].
[26] P. del Amo Sanchez et al. [BaBar Collaboration], Phys. Rev. D 82, 091103
(2010) [arXiv:1008.4080 [hep-ex]].
[27] J. Laiho, E. Lunghi and R. S. Van de Water, Phys. Rev. D 81, 034503 (2010)
[arXiv:0910.2928 [hep-ph]].
[28] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 76, 052005 (2007)
[arXiv:0704.0020 [hep-ex]].
[29] I. I. Y. Bigi, M. A. Shifman, N. G. Uraltsev and A. I. Vainshtein, Phys. Rev.
Lett. 71, 496 (1993) [hep-ph/9304225]; A. V. Manohar and M. B. Wise, Phys.
Rev. D 49, 1310 (1994) [hep-ph/9308246].
[30] N. Isgur and M. B. Wise, Phys. Lett. B 237, 527 (1990); N. Isgur and
M. B. Wise, Phys. Lett. B 232, 113 (1989).
[31] A. Bornheim et al. [CLEO Collaboration], Phys. Rev. Lett. 88, 231803 (2002)
[hep-ex/0202019].
[32] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 73, 012006 (2006) [hepex/
0509040].
[33] A. Limosani et al. [Belle Collaboration], Phys. Lett. B 621, 28 (2005) [hepex/
0504046].
[34] E. Dalgic, A. Gray, M. Wingate, C. T. H. Davies, G. P. Lepage and
J. Shigemitsu, Phys. Rev. D 73, 074502 (2006) [Erratum-ibid. D 75, 119906
(2007)] [hep-lat/0601021].
[35] J. A. Bailey, C. Bernard, C. E. DeTar, M. Di Pierro, A. X. El-Khadra,
R. T. Evans, E. D. Freeland and E. Gamiz et al., Phys. Rev. D 79, 054507
(2009) [arXiv:0811.3640 [hep-lat]].
[36] D. Asner et al. [Heavy Flavor Averaging Group Collaboration], arXiv:1010.1589
[hep-ex].
[37] A. Abulencia et al. [CDF Collaboration], Phys. Rev. Lett. 97, 242003 (2006)
[hep-ex/0609040].
[38] R. Aaij et al. [LHCb Collaboration], Phys. Lett. B 709, 177 (2012)
[arXiv:1112.4311 [hep-ex]].
[39] M. Misiak, H. M. Asatrian, K. Bieri, M. Czakon, A. Czarnecki, T. Ewerth,
A. Ferroglia and P. Gambino et al., Phys. Rev. Lett. 98, 022002 (2007) [hepph/
0609232].
[40] B. Grinstein and D. Pirjol, Phys. Rev. D 62, 093002 (2000) [hep-ph/0002216];
A. Ali, E. Lunghi and A. Y. .Parkhomenko, Phys. Lett. B 595, 323 (2004) [hepph/
0405075]; M. Beneke, T. Feldmann and D. Seidel, Nucl. Phys. B 612, 25
(2001) [hep-ph/0106067]; W. Wang, R. -H. Li and C. -D. Lu, arXiv:0711.0432
[hep-ph].
[41] A. J. Buras, M. Gorbahn, U. Haisch and U. Nierste, Phys. Rev. Lett. 95, 261805
(2005) [hep-ph/0508165].
[42] A. V. Artamonov et al. [E949 Collaboration], Phys. Rev. Lett. 101, 191802
(2008) [arXiv:0808.2459 [hep-ex]]; A. V. Artamonov et al. [BNL-E949 Collaboration],
Phys. Rev. D 79, 092004 (2009) [arXiv:0903.0030 [hep-ex]].
[43] D. Acosta et al. [CDF Collaboration], Phys. Rev. Lett. 95, 102002 (2005) [hepex/
0505091].
[44] V. M. Abazov et al. [D0 Collaboration], Phys. Rev. Lett. 107, 121802 (2011)
[arXiv:1106.5436 [hep-ex]].
[45] CMS-PAS-TOP-11-029(2011)[CMS Collab.].
[46] V. M. Abazov et al. [D0 Collaboration], Phys. Rev. D 84, 112001 (2011)
[arXiv:1108.3091 [hep-ex]].
[47] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D 82, 112005 (2010)
[arXiv:1004.1181 [hep-ex]]; T. Aaltonen et al. [CDF Collaboration], Phys. Rev.
D 81, 072003 (2010) [arXiv:1001.4577 [hep-ex]].
[48] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 107, 091802 (2011)
[arXiv:1106.3052 [hep-ex]].
[49] J. Swain and L. Taylor, Phys. Rev. D 58, 093006 (1998) [hep-ph/9712420].
[50] R. Aaij et al., LHCb-CONF-2012-007.
[51] A. Hocker, H. Lacker, S. Laplace and F. Le Diberder, Eur. Phys. J. C 21, 225
(2001) [hep-ph/0104062].
[52] J. Zhang et al. [BELLE Collaboration], Phys. Rev. Lett. 91, 221801 (2003)
[hep-ex/0306007]; B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett.
97, 261801 (2006) [hep-ex/0607092]; B. Aubert et al. [Babar Collaboration],
Phys. Rev. D 76, 052007 (2007) [arXiv:0705.2157 [hep-ex]].
[53] B. Aubert et al. [BaBar Collaboration], Phys. Rev. D 78, 071104 (2008)
[arXiv:0807.4977 [hep-ex]].
[54] A. Kusaka et al. [Belle Collaboration], Phys. Rev. Lett. 98, 221602 (2007) [hepex/
0701015].
[55] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 76, 012004 (2007) [hepex/
0703008 [HEP-EX]].
[56] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 79, 072009 (2009)
[arXiv:0902.1708 [hep-ex]].
[57] I. Adachi, H. Aihara, D. M. Asner, V. Aulchenko, T. Aushev, T. Aziz, A. M. Bakich
and A. Bay et al., Phys. Rev. Lett. 108, 171802 (2012) [arXiv:1201.4643
[hep-ex]].
[58] P. del Amo Sanchez et al. [BABAR Collaboration], Phys. Rev. D 82, 072004
(2010) [arXiv:1007.0504 [hep-ex]]; B. Aubert et al. [BABAR Collaboration],
Phys. Rev. D 78, 092002 (2008) [arXiv:0807.2408 [hep-ex]]; K. Abe et al.
[BELLE Collaboration], Phys. Rev. D 73, 051106 (2006) [hep-ex/0601032];
Y. Horii et al. [Belle Collaboration], Phys. Rev. Lett. 106, 231803 (2011)
[arXiv:1103.5951 [hep-ex]].
[59] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D 81, 031105 (2010)
[arXiv:0911.0425 [hep-ex]].
[60] R. Aaij et al. [LHCb Collaboration], Phys. Lett. B 712, 203 (2012) [Erratumibid.
B 713, 351 (2012)] [arXiv:1203.3662 [hep-ex]].
[61] M. Gronau and D. London, Phys. Lett. B 253, 483 (1991).
[62] M. Gronau and D. Wyler, Phys. Lett. B 265, 172 (1991).
[63] D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997) [hepph/
9612433]; D. Atwood, I. Dunietz and A. Soni, Phys. Rev. D 63, 036005
(2001) [hep-ph/0008090].
[64] A. Poluektov et al. [Belle Collaboration], Phys. Rev. D 70, 072003 (2004) [hepex/
0406067]; A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D 68,
054018 (2003) [hep-ph/0303187].
[65] A. Poluektov et al. [Belle Collaboration], Phys. Rev. D 81, 112002 (2010)
[arXiv:1003.3360 [hep-ex]].
[66] P. del Amo Sanchez et al. [BABAR Collaboration], Phys. Rev. Lett. 105,
121801 (2010) [arXiv:1005.1096 [hep-ex]].
[67] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 71, 112003 (2005) [hepex/
0504035]; Phys. Rev. D 73, 111101 (2006) [hep-ex/0602049]; S. Bahinipati
et al. [Belle Collaboration], Phys. Rev. D 84, 021101 (2011) [arXiv:1102.0888
[hep-ex]].
[68] B. Pontecorvo, Sov. Phys. JETP 6, 429 (1957).
[69] Z. Maki, M. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28, 870 (1962).
[70] G. Bellini et al. [Borexino Collaboration], Phys. Rev. Lett. 108, 051302
(2012) [arXiv:1110.3230 [hep-ex]]; A. Gando et al. [KamLAND Collaboration],
arXiv:1303.4667 [hep-ex].
[71] Y. Fukuda et al. [Super-Kamiokande Collaboration], Phys. Rev. Lett. 81, 1562
(1998) [hep-ex/9807003].
[72] K. Abe et al. [Super-Kamiokande Collaboration], Phys. Rev. Lett. 97, 171801
(2006) [hep-ex/0607059].
[73] M. H. Ahn et al. [K2K Collaboration], Phys. Rev. D 74, 072003 (2006) [hepex/
0606032].
[74] P. Adamson et al. [MINOS Collaboration], Phys. Rev. Lett. 101, 131802 (2008)
[arXiv:0806.2237 [hep-ex]].
[75] P. Adamson et al. [MINOS Collaboration], Phys. Rev. Lett. 107, 021801
(2011) [arXiv:1104.0344 [hep-ex]]; P. Adamson et al. [MINOS Collaboration],
arXiv:1304.6335 [hep-ex].
[76] S. Yamamoto et al. [K2K Collaboration], Phys. Rev. Lett. 96, 181801 (2006)
[hep-ex/0603004].
[77] K. Abe et al. [T2K Collaboration], Phys. Rev. Lett. 107, 041801 (2011)
[arXiv:1106.2822 [hep-ex]].
[78] P. Adamson et al. [MINOS Collaboration], Phys. Rev. Lett. 107, 181802 (2011)
[arXiv:1108.0015 [hep-ex]].
[79] Y. Abe et al. [DOUBLE-CHOOZ Collaboration], Phys. Rev. Lett. 108, 131801
(2012) [arXiv:1112.6353 [hep-ex]]; Y. Abe et al. [Double Chooz Collaboration],
arXiv:1301.2948 [hep-ex].
[80] F. P. An et al. [DAYA-BAY Collaboration], Phys. Rev. Lett. 108, 171803 (2012)
[arXiv:1203.1669 [hep-ex]]; F. P. An et al. [Daya Bay Collaboration], Chin.
Phys. C 37, 011001 (2013) [arXiv:1210.6327 [hep-ex]].
[81] J. K. Ahn et al. [RENO Collaboration], Phys. Rev. Lett. 108, 191802 (2012)
[arXiv:1204.0626 [hep-ex]].
[82] http://hitoshi.berkeley.edu/neutrino
[83] G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo and A. M. Rotunno,
Phys. Rev. D 86, 013012 (2012) [arXiv:1205.5254 [hep-ph]].
[84] D. V. Forero, M. Tortola and J. W. F. Valle, Phys. Rev. D 86, 073012 (2012)
[arXiv:1205.4018 [hep-ph]].
[85] H. Fritzsch and Z. -z. Xing, Phys. Rev. D 57, 594(1998); Y. Koide, Phys. Rev.
D73, 073002(2006).
[86] H. -X. Chen, A. Hosaka and S. -L. Zhu, Phys. Rev. D 74, 054001 (2006) [hepph/
0604049].
[87] G. Fogli et al., Phys. Review. D84, 053007(2011).
[88] A.Y. Smirnov, Talk given at 2nd International Workshop on Neutrino Oscillations
in Venice (NO-VE 2003), Venice, Italy, 3-5 Dec 2003. Published in *Venice
2003, Neutrino oscillations* 1-2, arXiv:hep-ph/0402264.
[89] H. Minakata and A.Y. Smirnov, Phys. Rev. D70, 073009 (2004); M. Raidal,
Phys. Rev. Lett. 93, 161801 (2004).
[90] Guan-Nan Li, Hsiu-Hsein Lin and Xiao-Gang He, Phys. Lett. B711,
57-61(2012)[arXiv:1112.2371hep-ph]]; Xinyi Zhang and Bo-Qiang Ma,
arXiv:1202.4258.
[91] N. Li and B. Q. Ma, Phys. Rev. D 71, 097301 (2005) [arXiv:hep-ph/0501226];
N. Li and B. Q. Ma, Eur. Phys. J. C 42, 17 (2005) [arXiv:hep-ph/0504161];
B. C. Chauhan, M. Picariello, J. Pulido and E. Torrente-Lujan, Eur. Phys.
J. C 50, 573 (2007) [arXiv:hep-ph/0605032]; S. W. Li and B. Q. Ma, Phys.
Rev. D 77, 093005 (2008) [arXiv:0806.0670 [hep-ph]]; P. H. Frampton and
S. Matsuzaki, Mod. Phys. Lett. A 24, 429 (2009) [arXiv:0807.4785 [hep-ph]];
Z. z. Xing, Phys. Lett. B 679, 111 (2009) [arXiv:0904.3172 [hep-ph]]; Y. H. Ahn,
H. Y. Cheng and S. Oh, Phys. Rev. D 83, 076012 (2011) [arXiv:1102.0879 [hepph]];
S. K. Kang, Phys. Rev. D 83, 097301 (2011) [arXiv:1104.1969 [hep-ph]];
N. Qin and B. Q. Ma, Phys. Lett. B 702, 143 (2011) [arXiv:1106.3284 [hep-ph]].
[92] P.H. Frampton and R.N. Mohapatra, JHEP 0501, 025 (2005); J. Ferrandis
and S. Pakvasa, Phys. Rev. D71, 033004 (2005); S.K. Kang, C.S. Kim and
J. Lee, Phys. Lett. B619, 129 (2005); S. Antusch, S.F. King and R.N. Mohapatra,
Phys. Lett. B618, 150 (2005); Z. z. Xing, Phys. Lett. B 618, 141
(2005)[arXiv:hep-ph/0503200]; M.A. Schmidt and A.Y. Smirnov, Phys. Rev.
D74, 113003 (2006); F. Plentinger, G. Seidl and W. Winter, Phys. Rev. D76,
113003 (2007); W. Winter, AIP Conf. Proc. 981, 199 (2008) [arXiv:0710.5660
[hep-ph]]; K. M. Patel, Phys. Lett. B 695, 225 (2011) [arXiv:1008.5061 [hepph]].
[93] C. Jarlskog, Phys. Lett. B 625, 63 (2005) [arXiv:hep-ph/0507212]; Y. j. Zheng,
Phys. Rev. D 81, 073009 (2010) [arXiv:1002.0919 [hep-ph]].
[94] P.F. Harrison, D.H. Perkins, and W.G. Scott, Phys. Lett. B458, 79 (1999);
Phys. Lett. B530, 167 (2002); Z.Z. Xing, Phys. Lett. B533, 85 (2002); P.F. Harrison
and W.G. Scott, Phys. Lett. B535, 163 (2002); Phys. Lett. B557, 76
(2003); X.-G. He and A. Zee, Phys. Lett. B560, 87 (2003). See also L. Wolfen-
stein, Phys. Rev. D18, 958 (1978); Y. Yamanaka, H. Sugawara, and S. Pakvasa,
Phys. Rev. D25, 1895(1982); D29, 2135(E)(1984).
[95] X. G. He, Y. Y. Keum and R. R. Volkas, JHEP 0604, 039 (2006) [arXiv:hepph/
0601001]; Xiao-Gang He and A. Zee, Phys. Lett. B645, 427(2007), hepph/
0607163; C. H. Albright and W. Rodejohann, Eur. Phys. J. C 62, 599
(2009) [arXiv:0812.0436 [hep-ph]]; C. H. Albright, A. Dueck, W. Rodejohann,
Eur. Phys. J. C70, 1099-1110 (2010). [arXiv:1004.2798 [hep-ph]]; Xiao-Gang
He and A. Zee, Phys. Rev. D84, 053004(2011)[arXiv:1106.4359 [hep-ph]].
[96] R. Friedberg and T.D. Lee, Chin. Phys. C34, 1547; Erratum-ibid. C34,
1905(20110)[arXiv:1008.0453[hep-ph]].
[97] P. H. Frampton and S. Matsuzaki, Mod. Phys. Lett. A 24, 429 (2009)
[arXiv:0807.4785 [hep-ph]]; X. G. He, S. W. Li and B. Q. Ma, Phys. Rev. D 78,
111301 (2008) [arXiv:0809.1223 [hep-ph]]; X. G. He, S. W. Li and B. Q. Ma,
Phys. Rev. D 79, 073001 (2009) [arXiv:0903.2880 [hep-ph]]; Y. Shimizu and
R. Takahashi, Europhys. Lett. 93, 61001 (2011) [arXiv:1009.5504 [hep-ph]].
[98] J.D. Bjorken, Nucl. Phys. B(Proc. Suppl.)11, 325(1989).
[99] P. Frampton and Xiao-Gang He, Phys. Lett.
B688:67-70(2010)[arXiv:1003.0310 [hep-ph]]; Phys. Rev.
D82:017301(2010)[arXiv:1004.3679 [hep-ph]]; S. -W. Li and B. -Q. Ma,
Phys. Lett. B 691, 37 (2010) [arXiv:1003.5854 [hep-ph]].
[100] T. N. Pham, arXiv:1110.6050 [hep-ph].
[101] Y. Koide, Phys. Lett. B607: 123-130(2005)[arXiv:hep-ph/0411280].
[102] N. Li and B. -Q. Ma, Phys. Rev. D 71, 097301 (2005) [hep-ph/0501226];
X. -G. He, S. -W. Li and B. -Q. Ma, Phys. Rev. D 78, 111301 (2008)
[arXiv:0809.1223 [hep-ph]]; Phys. Rev. D 79, 073001 (2009) [arXiv:0903.2880
[hep-ph]]; Y. H. Ahn, H. -Y. Cheng and S. Oh, Phys. Lett. B 703, 571 (2011)
[arXiv:1106.0935 [hep-ph]].
[103] N. Qin and B. -Q. Ma, Phys. Lett. B 695, 194 (2011) [arXiv:1011.6412 [hepph]];
N. Qin and B. -Q. Ma, Phys. Rev. D 83, 033006 (2011) [arXiv:1101.4729
[hep-ph]]; Y. H. Ahn, H. -Y. Cheng and S. Oh, Phys. Lett. B 701, 614 (2011)
[arXiv:1105.0450 [hep-ph]].