Chiral fields at GUT scale SU(5), SU(7) GUTs

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3 Chiral fields at GUT scale SU(5), SU(7) GUTs UGUTF: Kim, PRL 45, 1916 (1980); arxiv: ; JEK, D.Y.Mo, S. Nam, JKPS 66, 894 (2015) [arxiv: ]

4 Flavor GUT

5 Flavor GUT Georgi

6 Flavor GUT Georgi

7 Flavor GUT No Grand Unification Georgi With INQ

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9 Flipped SU(5)

10 Flipped SU(5)

11 Flipped SU(5)

12 From Z(12-I) orbifold

13 From Z(12-I) orbifold With Kang-Sin Choi

14 From Z(12-I) orbifold With Kang-Sin Choi With Bumseok Kyae

15 With Kang-Sin Choi With Bumseok Kyae

16 With Kang-Sin Choi With Bumseok Kyae

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18 CKM matrix

19 CKM matrix

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21 J determinant

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23 J determinant as a phase in CKM matrix

24 J determinant as a phase in CKM matrix With Min-Seok Seo & Doh Young Mo

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27 To have physical effects of CP violation, the J must be non vanishing. Our form for the CKM matrix is, with the 1st row real,

28 To have physical effects of CP violation, the J must be non vanishing. Our form for the CKM matrix is, with the 1st row real, The individual element of determinant is

29 To have physical effects of CP violation, the J must be non vanishing. Our form for the CKM matrix is, with the 1st row real, The individual element of determinant is

30 Is Im(V11 V22 V33) the Jarlskog determinant?

31 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}*

32 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V

33 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V

34 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V

35 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V

36 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V

37 Is Im(V11 V22 V33) the Jarlskog determinant? The Jarlskog determinant is J= Im V_{11} V_{22} V_{12}* V_{21}*, or Im V_{ii}V_{jj}V_{ij}*V_{ji}* Let J be J=Im V_{11} V_{33} V_{13}* V_{31}*. Then, on 1=Det V Similar considerations for other elements give the imaginary part as [(1- V_{21} ^2) - V_{31} ^2 +(1- V_{11} )^2]J=J

38 Kim-Seo form of J: J=Im (V_{31}* V_{22}* V_{13}*)

39 Kim-Seo form of J: J=Im (V_{31}* V_{22}* V_{13}*) JEK, M-S. Seo, PoS DSU2012 (2012) 009 [arxiv: [hep-ph]] JEK, D.Y. Mo, S. Nam, JKPS 66 (2015) 894 [arxiv: [hep-ph]]

40 Kim-Seo form of J: J=Im (V_{31}* V_{22}* V_{13}*) JEK, M-S. Seo, PoS DSU2012 (2012) 009 [arxiv: [hep-ph]] JEK, D.Y. Mo, S. Nam, JKPS 66 (2015) 894 [arxiv: [hep-ph]] By looking at the KS form of J, we can see the importance of physical CP violation effect.

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42 We used Det(V)=1. If it were not so, we can multiply a common phase to all q=2/3 quarks to make Det=1. It corresponds to a rotation of J triangle.

43 We used Det(V)=1. If it were not so, we can multiply a common phase to all q=2/3 quarks to make Det=1. It corresponds to a rotation of J triangle. Making Det=real with 1st row real is rotating it such that the phase appears at origin.

44 We used Det(V)=1. If it were not so, we can multiply a common phase to all q=2/3 quarks to make Det=1. It corresponds to a rotation of J triangle. Making Det=real with 1st row real is rotating it such that the phase appears at origin. The 1st row is real. One side becomes x-axis.

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46 There are 6 Jarlskog triangles. One of them corresponds to B-meson decay to K. PDG gives alpha or our delta almost 90 degrees.

47 There are 6 Jarlskog triangles. One of them corresponds to B-meson decay to K. PDG gives alpha or our delta almost 90 degrees. We can consider another J: B decaying to pi meson. This has two long sides.

48 There are 6 Jarlskog triangles. One of them corresponds to B-meson decay to K. PDG gives alpha or our delta almost 90 degrees. We can consider another J: B decaying to pi meson. This has two long sides. So, delta=90 degrees is a maximal CP violation! in KS parametrization. In other parametrizations too.

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50 This is PDG compilation. or is our.

51 This is PDG compilation. or is our. PDG determines

52 This is PDG compilation. or is our. PDG determines This implies that the weak CP violation in the quark sector is almost maximal with some real angles fixed. Here, the parametrization must allow 90 degrees.

53 In the quark sector, we can consider the leading CP violation term is maximal!! Also, simple in formulae. Further corrections may lower the value a bit. Since we know the weak CP phase, the final state interaction phase can be estimated. D. Y. Mo has already talked about this: the first try in particle physics to calculate the phase shift analysis problem in quantum mechanics. The order is about -180(Delta I=1/2), and 27(penguin) degrees.

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55 In the recent T2K experiment [Y. Oyama at Planck 2015, A. Fiorentini here], seems to be deltapmns degrees at 2 sigma level. Whether it is true or not, it is worthwhile to ask a question on it. See also, D.V. Forero- M. Tortola-J. Valle, arxiv: Determination of may choose in certain deltapmns deltackm models.

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57 15 +1 chiral fields are grouped into

58 15 +1 chiral fields are grouped into GG model

59 15 +1 chiral fields are grouped into GG model Anti-SU(5) model

60 15 +1 chiral fields are grouped into GG model Anti-SU(5) model

61 N(N-1)/2+ N chiral fields are grouped into

62 N(N-1)/2+ N chiral fields are grouped into Anti-SU(N) model

63 N(N-1)/2+ N chiral fields are grouped into Anti-SU(N) model

64 N(N-1)/2+ N chiral fields are grouped into Anti-SU(N) model

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66 One SU(5) family

67 Two SU(5) One SU(5) family anti-family, and one SU(5) family

68 One SU(5) family Two SU(5) anti-family, and one SU(5) family Net result: 0 SU(5) family

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72 Deadend of SO(4N+2). Family unification in SU(N): Georgi (1979): SU(11) model

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79 The simplest case is SU(7) with

80 The simplest case is SU(7) with For example, SU(8) with contains more non-singlet fields.

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107 Triangle Cushion:SU(3)

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130 In our UGUTF with anti-su(5) subgroup, the CKM and PMNS matrices use W couplings.

131 In our UGUTF with anti-su(5) subgroup, the CKM and PMNS matrices use W couplings.

132 In our UGUTF with anti-su(5) subgroup, the CKM and PMNS matrices use W couplings. These W couplings define the CKM and PMNS matrices.

133 The CKM and PMNS matrices arise when diagonalizing quark and mass matrices. Quarks and leptons are related here: 5-bar

134 The CKM and PMNS matrices arise when diagonalizing quark and mass matrices. Quarks and leptons are related here: 5-bar

135 The CKM and PMNS matrices arise when diagonalizing quark and mass matrices. Quarks and leptons are related here: 5-bar

136 The CKM and PMNS matrices arise when diagonalizing quark and mass matrices. Quarks and leptons are related here: 5-bar Using the bases where e and d masses are diagonalized, only neutrino and u- quark masses are important.

137 The CKM and PMNS matrices arise when diagonalizing quark and mass matrices. Quarks and leptons are related here: 5-bar Using the bases where e and d masses are diagonalized, only neutrino and u- quark masses are important. Thus, CKM and PMNS matrices are related

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139 J = 2 sin(deltackm) c1c2c3s1s2s3

140 J = 2 sin(deltackm) c1c2c3s1s2s3 J = 2 sin(deltapmns) C1C2C3S1S2S3

141 J = 2 sin(deltackm) c1c2c3s1s2s3 J = 2 sin(deltapmns) C1C2C3S1S2S3 Even though si is not equal to Si, deltackm and deltapmns can be equal. We may satisfy the following in this program if CP violation is spontaneous a la Froggatt-Nielsen by ONE complex vev of a SM singlet X. [JEK-Nam, ]

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143 (i) There are three possibilities for :,, of PDG book.

144 (i) There are three possibilities for :,, of PDG book. (i) Make Det=1 as in KS. Make the real part of (22) element is very large as in many parametrizations.

145 (i) There are three possibilities for :,, of PDG book. (i) If 1st row = real, or 1st column = real a is Kobayashi-Maskawa parametrization, Kim-Seo parametrization (i) If both 1st row = real, and 1st column = real, then = : Chau-Keung-Maiani parametrization

146 (i) There are three possibilities for :,, of PDG book. (i) If 1st row = real, or 1st column = real a is Kobayashi-Maskawa parametrization, Kim-Seo parametrization (i) If both 1st row = real, and 1st column = real, then = : Chau-Keung-Maiani parametrization (i) The identity = Imaginary part of V(31)*V(22)*V(13)* was very useful.

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