Implications of equalities among the elements of CKM and PMNS matrices

Hong-Wei Ke; Song-Xue Zhao; Xue-Qian Li

doi:10.1088/1674-1137/40/5/053101

Chinese Physics C> 2016, Vol. 40> Issue(5) : 053101 DOI: 10.1088/1674-1137/40/5/053101

Implications of equalities among the elements of CKM and PMNS matrices

1.
School of Science, Tianjin University, Tianjin 300072, China
2.
School of Physics, Nankai University, Tianjin 300071, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Investigating the CKM matrix in different parameterization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal i.e. there exist several relations among the CP phases. Using those relations, several approximate equalities among the elements of CKM matrix are established. The case can also be generalized to the PMNS matrix for the lepton sector. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in the literature are obtained. Other authors have derived several mixing textures by using presumed symmetries; amazingly, some, though not all, of their forms are the same as those we obtained. This hints at the existence of a hidden symmetry which is broken in the practical world. Nature makes its own selection of the underlying symmetry and the way to break it, while we just guess what it is.
- CKM ,
- PMNS ,
- symmetry ,
- parameterization scheme

References

[1]	M. Kobayashi and T. Maskawa, Prog. Theor. Phys., 49:652(1973)
[2]	N. Cabibbo, Phys. Rev. Lett., 10:531(1963)
[3]	H. Fritzsch, Nucl. Phys. B, 155:189(1979)
[4]	L. F. Li, Phys. Lett. B, 84:461(1979)
[5]	H. Fritzsch and Z. Z. Xing, Phys. Lett. B, 413:396(1997)[hep-ph/9707215]
[6]	H. W. Ke and X. Q. Li, arXiv:1412.0116[hep-ph]
[7]	C. Jarlskog, Phys. Rev. Lett., 55:1039(1985)
[8]	D. D. Wu, Phys. Rev. D, 33:860(1986)
[9]	O. W. Greenberg, Phys. Rev. D, 32:1841(1985)
[10]	E. E. Jenkins and A. V. Manohar, Nucl. Phys. B, 792:187(2008)
[11]	B. Pontecorvo, Sov. Phys. JETP, 26:984(1968)[Zh. Eksp. Teor. Fiz. 53:1717(1967)]
[12]	Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys., 28:870(1962) PTPKA,28,870;
[13]	C. S. Lam, arXiv:1105.4622[hep-ph]
[14]	C. S. Lam, Phys. Rev. D, 83:113002(2011)
[15]	H. Minakata and A. Y..Smirnov, Phys. Rev. D, 70:073009(2004)
[16]	M. Raidal, Phys. Rev. Lett., 93:161801(2004)
[17]	G. Altarelli, F. Feruglio, and L. Merlo, JHEP, 0905:020(2009)
[18]	G. Altarelli and D. Meloni, J. Phys. G, 36:085005(2009)
[19]	R. de Adelhart Toorop, F. Bazzocchi, and L. Merlo, JHEP, 1008:001(2010)
[20]	G. Altarelli, F. Feruglio, L. Merlo, and E. Stamou, JHEP, 1208:021(2012)
[21]	Y. J. Zheng and B.-Q. Ma, Eur. Phys. J. Plus, 127:7(2012)
[22]	X. Zhang and B.-Q. Ma, Phys. Rev. D, 86:093002(2012)
[23]	X. Zhang, Y.-J. Zheng, and B.-Q. Ma, Phys. Rev. D, 85:097301(2012)
[24]	Y. Zhang, X. Zhang, and B.-Q. Ma, Phys. Rev. D, 86:093019(2012)
[25]	N. Haba, K. Kaneta, and R. Takahashi, Europhys. Lett., 101:11001(2013)
[26]	H. W. Ke, T. Liu, and X. Q. Li, Phys. Rev. D, 90:053009(2014)
[27]	J. M. Gerard and Z. Z. Xing, Phys. Lett. B, 713:29(2012)
[28]	F. del Aguila, G. L. Kane, and M. Quiros, Phys. Lett. B, 196:531(1987)
[29]	F. Vissani, hep-ph/9708483
[30]	V. D. Barger, S. Pakvasa, T. J. Weiler, and K. Whisnant, Phys. Lett., B, 437:107(1998)
[31]	A. J. Baltz, A. S. Goldhaber, and M. Goldhaber, Phys. Rev. Lett. 81:5730(1998)
[32]	N. Cabibbo, Phys. Lett. B, 72:333(1978)
[33]	L. Wolfenstein, Phys. Rev. D, 18:958(1978)
[34]	K. S. Babu, E. Ma, and J. W. F. Valle, Phys. Lett. B, 552:207(2003)
[35]	E. Ma and G. Rajasekaran, Phys. Rev. D, 64:113012(2001)
[36]	C. Hagedorn, M. Lindner, and R. N. Mohapatra, JHEP, 0606:042(2006)
[37]	E. Ma, Phys. Lett. B, 632:352(2006)
[38]	G. Altarelli and F. Feruglio, Nucl. Phys. B, 741:215(2006)
[39]	X. G. He, Y. Y. Keum, and R. R. Volkas, JHEP, 0604:039(2006)
[40]	H. Qu and B. Q. Ma, Phys. Rev. D, 88:037301(2013)
[41]	C. Y. Yao and G. J. Ding, Phys. Rev. D, 92:096010(2015)

[1]	W. M. Seif , A. S. Hashem . Constraints on the nuclear symmetry energy and its density slope from the α decay process. Chinese Physics C, 2018, 42(6): 064104. doi: 10.1088/1674-1137/42/6/064104
[2]	Ya-Fei Guo , Peng-Hui Chen , Fei Niu , Hong-Fei Zhang , Gen-Ming Jin , Zhao-Qing Feng . Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions. Chinese Physics C, 2017, 41(10): 104104. doi: 10.1088/1674-1137/41/10/104104
[3]	. Erratum and Addendum: A unified model with a generalized gauge symmetry and its cosmological implications. Chinese Physics C, 2017, 41(12): 129101.
[4]	LÜ Li-Jun , BAI Hong-Bo , ZHANG Jin-Fu , DONG Hong-Fei . Mixed symmetry states and electromagnetic transition in the N=Z nucleus ²⁸Si. Chinese Physics C, 2014, 38(10): 104102. doi: 10.1088/1674-1137/38/10/104102
[5]	LIU Bei-Bei , OUYANG Fei , CHEN Wei . Influence of coupling constants on nuclear symmetry energy. Chinese Physics C, 2013, 37(4): 044103. doi: 10.1088/1674-1137/37/4/044103
[6]	Kaushal Thakkar , Ajay Majethiya . Electromagnetic transition properties of Δ→Nγ in a hypercentral scheme. Chinese Physics C, 2012, 36(5): 385-389. doi: 10.1088/1674-1137/36/5/001
[7]	ZHANG Ying , WANG Qing . Parameterization of general Z-γ-Z’ mixing in an electroweak chiral theory. Chinese Physics C, 2012, 36(4): 298-306. doi: 10.1088/1674-1137/36/4/001
[8]	LIU Min , LI Zhu-Xia , WANG Ning , ZHANG Feng-Shou . Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei. Chinese Physics C, 2011, 35(7): 629-634. doi: 10.1088/1674-1137/35/7/006
[9]	LI Fang-Qiong , ZHAO Peng-Wei , LIANG Hao-Zhao . Perturbative pseudospin symmetry limit with linear spin-orbit potential. Chinese Physics C, 2011, 35(9): 825-828. doi: 10.1088/1674-1137/35/9/007
[10]	DONG Hong-Fei , BAI Hong-Bo , . Isospin and mixed symmetry structure in ²⁶Mg. Chinese Physics C, 2011, 35(9): 817-820. doi: 10.1088/1674-1137/35/9/005
[11]	LI Kang , Dulat Sayipjamal , . Non-commutative phase space and its space-time symmetry. Chinese Physics C, 2010, 34(7): 944-948. doi: 10.1088/1674-1137/34/7/003
[12]	L. Ya. Glozman . Chiral symmetry restoration in excited hadrons and dense matter. Chinese Physics C, 2010, 34(9): 1212-1217. doi: 10.1088/1674-1137/34/9/012
[13]	GUO Feng-Kun . Heavy quark spin symmetry and heavy flavor hadronic molecules. Chinese Physics C, 2010, 34(9): 1294-1297. doi: 10.1088/1674-1137/34/9/027
[14]	MAO Shi-Jun , HUANG Xu-Guang , ZHUANG Peng-Fei . Viscosities in chiral symmetry breaking phase. Chinese Physics C, 2010, 34(9): 1440-1442. doi: 10.1088/1674-1137/34/9/065
[15]	A. J. Buchmann . Excited nucleon electromagnetic form factors from broken spin-flavor symmetry. Chinese Physics C, 2009, 33(12): 1257-1260. doi: 10.1088/1674-1137/33/12/034
[16]	C. Garcia-Recio , V. K. Magas , T. Mizutani , J. Nieves , A. Ramos , L. L. Salcedo . Charmed baryon resonances with heavy-quark symmetry. Chinese Physics C, 2009, 33(12): 1323-1326. doi: 10.1088/1674-1137/33/12/046
[17]	LÜ Li-Jun , BAI Hong-Bo , ZHANG Jin-Fu . Isospin and mixed symmetry structure in ²⁴Mg. Chinese Physics C, 2008, 32(3): 177-181. doi: 10.1088/1674-1137/32/3/003
[18]	Li Ziping . Canonical Symmetry in a System with Singular Lagrangian and Ward Identities. Chinese Physics C, 1994, 18(S3): 265-274.
[19]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[20]	Liu Baohua , Li Jiarong . The Mean-Field Analysis for Chiral Symmetry Phase Transition. Chinese Physics C, 1988, 12(S4): 373-378.

Access

Get Citation

Hong-Wei Ke, Song-Xue Zhao and Xue-Qian Li. Implications of equalities among the elements of CKM and PMNS matrices[J]. Chinese Physics C, 2016, 40(5): 053101. doi: 10.1088/1674-1137/40/5/053101

Hong-Wei Ke, Song-Xue Zhao and Xue-Qian Li. Implications of equalities among the elements of CKM and PMNS matrices[J]. Chinese Physics C, 2016, 40(5): 053101. doi: 10.1088/1674-1137/40/5/053101 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2015-09-28

Fund

Supported by National Natural Science Foundation of China(11375128, 11135009)

Article Metric

Article Views(1901)
PDF Downloads(310)
Cited by(0)

Policy on re-use

To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Implications of equalities among the elements of CKM and PMNS matrices

Corresponding author: Hong-Wei Ke,

Corresponding author: Xue-Qian Li,

1. School of Science, Tianjin University, Tianjin 300072, China

2. School of Physics, Nankai University, Tianjin 300071, China

Received Date: 2015-09-28

Available Online: 2016-05-05

Fund Project: Supported by National Natural Science Foundation of China(11375128, 11135009)

Abstract: Investigating the CKM matrix in different parameterization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal i.e. there exist several relations among the CP phases. Using those relations, several approximate equalities among the elements of CKM matrix are established. The case can also be generalized to the PMNS matrix for the lepton sector. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in the literature are obtained. Other authors have derived several mixing textures by using presumed symmetries; amazingly, some, though not all, of their forms are the same as those we obtained. This hints at the existence of a hidden symmetry which is broken in the practical world. Nature makes its own selection of the underlying symmetry and the way to break it, while we just guess what it is.

HTML

Reference (41)

Implications of equalities among the elements of CKM and PMNS matrices

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article