Implications of equalities among the elements of CKM and PMNS matrices

  • 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.
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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
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Received: 2015-09-28
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    Supported by National Natural Science Foundation of China(11375128, 11135009)

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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
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.

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