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Non-zero |U e3 | and Quark-Lepton in Discrete Symmetry Y.H.Ahn based on Phys.Rev.D83:076012,2011. working with Hai-Yang Cheng and S.C.Oh 1 2011 년 8 월 17 일 수요일

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Outline 2 Present Knowledges and Motivations Tri-Bimaximal Mixing and Non-zero |U e3 | A4 symmetry+TBM and its Deviations in Seesaw Charged fermion mixing angles Low energy phenomenology and leptogenesis Conclusion 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 3 Neutrino oscillation (arXiv: 1106, 6028 G.L.Fogli, E.Lisi, A.Marrone,A.Palazzo, A.M.Rotunno ) Analysis by Fogli etal. Including the latest T2K and MINOS results Bi-Large mixing angles These results should be compared with Theta13 which is very small, and with the quark mixing angles in the V CKM. Some new flavor symmetries A clue to the nature among quark-lepton physics beyond SM 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 4 Neutrino oscillation (arXiv: 1106, 6028 G.L.Fogli, E.Lisi, A.Marrone,A.Palazzo, A.M.Rotunno ) Analysis by Fogli etal. Including the latest T2K and MINOS results Bi-Large mixing angles These results should be compared with Theta13 which is very small, and with the quark mixing angles in the V CKM. Some new flavor symmetries A clue to the nature among quark-lepton physics beyond SM 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 5 Neutrino oscillation (arXiv: 1106, 6028 G.L.Fogli, E.Lisi, A.Marrone,A.Palazzo, A.M.Rotunno ) Analysis by Fogli etal. Including the latest T2K and MINOS results Bi-Large mixing angles These results should be compared with Theta13 which is very small, and with the quark mixing angles in the V CKM. Some new flavor symmetries A clue to the nature among quark-lepton physics beyond SM 2011 년 8 월 17 일 수요일 The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a "quark–lepton complementarity" which can be expressed in the relations “Raidal 2004” “Smirnov and Minakata”

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Present Knowledges and Motivations 6 Neutrino oscillation (arXiv: 1106, 6028 G.L.Fogli, E.Lisi, A.Marrone,A.Palazzo, A.M.Rotunno ) Analysis by Fogli etal. Including the latest T2K and MINOS results Bi-Large mixing angles These results should be compared with Theta13 which is very small, and with the quark mixing angles in the V CKM. Some new flavor symmetries A clue to the nature among quark-lepton physics beyond SM 2011 년 8 월 17 일 수요일 The disparity that nature indicates between quark and lepton mixing angles has been viewed in terms of a "quark–lepton complementarity" which can be expressed in the relations “Raidal 2004” “Smirnov and Minakata” Accidental or not ?

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Present Knowledges and Motivations 7 Nothing is known about all three CP-violating phases If δ CP and θ 13 ≠0, CP is violated in ν oscillations. δ CP : Not directly related to leptogenesis, but would be likely in most leptogenesis models. Dirac phase : CP violation in ν oscillation Leptogenesis Majorana phases : Neutrinoless Double beta decay Leptogenesis A relatively large Theta13>0 (T2K and MINOS) opens up : CP-violation in neutrino oscillations Exps. (T2K, NO ν A…) Matter effects can experimentally determine the type of ν mass spectrum : normal or inverted mass ordering (goal of future LBL ν oscillation Exps. program) 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 8 Nothing is known about all three CP-violating phases If δ CP and θ 13 ≠0, CP is violated in ν oscillations. δ CP : Not directly related to leptogenesis, but would be likely in most leptogenesis models. Dirac phase : CP violation in ν oscillation Leptogenesis Majorana phases : Neutrinoless Double beta decay Leptogenesis A relatively large Theta13>0 (T2K and MINOS) opens up : CP-violation in neutrino oscillations Exps. (T2K, NO ν A…) Matter effects can experimentally determine the type of ν mass spectrum : normal or inverted mass ordering (goal of future LBL ν oscillation Exps. program) CP violations in the lepton sector are imperative, if the baryon asymmetry of the Universe (BAU) originated from leptogenesis scenario in the seesaw models. So any observation of the leptonic CP violation, or demonstrating that CP is not a good symmetry of the leptons, can strengthen our belief in leptogenesis. 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 9 Nothing is known about all three CP-violating phases If δ CP and θ 13 ≠0, CP is violated in ν oscillations. δ CP : Not directly related to leptogenesis, but would be likely in most leptogenesis models. Dirac phase : CP violation in ν oscillation Leptogenesis Majorana phases : Neutrinoless Double beta decay Leptogenesis A relatively large Theta13>0 (T2K and MINOS) opens up : CP-violation in neutrino oscillations Exps. (T2K, NO ν A…) Matter effects can experimentally determine the type of ν mass spectrum : normal or inverted mass ordering (goal of future LBL ν oscillation Exps. program) CP violations in the lepton sector are imperative, if the baryon asymmetry of the Universe (BAU) originated from leptogenesis scenario in the seesaw models. So any observation of the leptonic CP violation, or demonstrating that CP is not a good symmetry of the leptons, can strengthen our belief in leptogenesis. 2011 년 8 월 17 일 수요일

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Present Knowledges and Motivations 10 Nothing is known about all three CP-violating phases If δ CP and θ 13 ≠0, CP is violated in ν oscillations. δ CP : Not directly related to leptogenesis, but would be likely in most leptogenesis models. Dirac phase : CP violation in ν oscillation Leptogenesis Majorana phases : Neutrinoless Double beta decay Leptogenesis A relatively large Theta13>0 (T2K and MINOS) opens up : CP-violation in neutrino oscillations Exps. (T2K, NO ν A…) Matter effects can experimentally determine the type of ν mass spectrum : normal or inverted mass ordering (goal of future LBL ν oscillation Exps. program) CP violations in the lepton sector are imperative, if the baryon asymmetry of the Universe (BAU) originated from leptogenesis scenario in the seesaw models. So any observation of the leptonic CP violation, or demonstrating that CP is not a good symmetry of the leptons, can strengthen our belief in leptogenesis. 2011 년 8 월 17 일 수요일

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Present Knowledges 11 Cosmological limit (including WMAP 3-years result) upper bound on neutrino masses (astro-ph/0604335 : Uros Seljak, Anze Slosar, Patrick McDonald ) Uros SeljakAnze SlosarPatrick McDonald Starting to disfavor the degenerate spectrum of neutrinos BAU Astrophys. J. Suppl. 192 (2011) 18 Why is there only Matter in Universe but no antimatter ? No evidence of antimatter in our domain of Universe (~20Mpc ≈ 10 8 light-years) How can we generate η B ≈10 -10 from an initial condition for Big-Bang ? 2011 년 8 월 17 일 수요일

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Present Knowledges 12 Cosmological limit (including WMAP 3-years result) upper bound on neutrino masses (astro-ph/0604335 : Uros Seljak, Anze Slosar, Patrick McDonald ) Uros SeljakAnze SlosarPatrick McDonald Starting to disfavor the degenerate spectrum of neutrinos BAU Astrophys. J. Suppl. 192 (2011) 18 Why is there only Matter in Universe but no antimatter ? No evidence of antimatter in our domain of Universe (~20Mpc ≈ 10 8 light-years) How can we generate η B ≈10 -10 from an initial condition for Big-Bang ? 2011 년 8 월 17 일 수요일

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13 All data can be explained in terms of oscillation between just 3 known species : Two possible orderings of neutrino masses Earth matter effects(LBL) Quasi-Degenerate case 2011 년 8 월 17 일 수요일

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14 Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix Atmospheric and SBL reactor Solar and LBL accelerator LBL reactor Majorana phases Neutrinoless Double beta decay 2011 년 8 월 17 일 수요일 Goal: sin 2 2 13 ~ 0.02 @ 90% CL in 3 years

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15 Pontecorvo-Maki-NaKagawa-Sakata (PMNS) Matrix Atmospheric and SBL reactor Solar and LBL accelerator LBL reactor Majorana phases Neutrinoless Double beta decay 2011 년 8 월 17 일 수요일 Goal: sin 2 2 13 ~ 0.02 @ 90% CL in 3 years Not observable in oscillations

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So far it is still unclear how to theoretically understand the observed neutrino mixing. 16 A tentative way is to start with the data of ν oscillation and conjecture a simple constant mixing pattern, for example, “Tri-Bimaximal mixing” matrix ( Harrison, Perkins and Scott; see also Wolfenstein(1970) and He and Zee ) It suggests that flavor structure for mixing should be divorced from trying to understand the mass eigenvalues. Correlations between mass matrix elements It is suggestive of a flavor symmetry. 2011 년 8 월 17 일 수요일

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So far it is still unclear how to theoretically understand the observed neutrino mixing. 17 A tentative way is to start with the data of ν oscillation and conjecture a simple constant mixing pattern, for example, “Tri-Bimaximal mixing” matrix ( Harrison, Perkins and Scott; see also Wolfenstein(1970) and He and Zee ) It suggests that flavor structure for mixing should be divorced from trying to understand the mass eigenvalues. Correlations between mass matrix elements It is suggestive of a flavor symmetry. 2011 년 8 월 17 일 수요일 Tri-maximal Θ 12 =35.3 O

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So far it is still unclear how to theoretically understand the observed neutrino mixing. 18 A tentative way is to start with the data of ν oscillation and conjecture a simple constant mixing pattern, for example, “Tri-Bimaximal mixing” matrix ( Harrison, Perkins and Scott; see also Wolfenstein(1970) and He and Zee ) It suggests that flavor structure for mixing should be divorced from trying to understand the mass eigenvalues. Correlations between mass matrix elements It is suggestive of a flavor symmetry. 2011 년 8 월 17 일 수요일

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So far it is still unclear how to theoretically understand the observed neutrino mixing. 19 A tentative way is to start with the data of ν oscillation and conjecture a simple constant mixing pattern, for example, “Tri-Bimaximal mixing” matrix ( Harrison, Perkins and Scott; see also Wolfenstein(1970) and He and Zee ) It suggests that flavor structure for mixing should be divorced from trying to understand the mass eigenvalues. Correlations between mass matrix elements It is suggestive of a flavor symmetry. If there exists such a flavor symmetry in Nature, the TBM pattern for the neutrino mixing will be a good zeroth order approximation to reality. 2011 년 8 월 17 일 수요일

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Deviations from Tri-Bimaximal 20 It is clear by now that the TBM is not consistent with the recent experimental data on the reactor mixing angle θ 13 because of the vanishing matrix element U e3 in U TBM. (arXiv: 1106.6028 ; G.L.Fogli, E. Lisi, A. Marrone, A. Palazzo and A.M. Rotunno) Recent data of the T2K Collaboration and the analysis based on global fits of neutrino oscillations enter into a new phase of precise measurements of the neutrino mixing angles and mass-squared differences, indicating that the TBM mixing for three flavors of leptons should be modified. 2011 년 8 월 17 일 수요일

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Seesaw 21 A simple and attractive explanation of the smallness of ν mass : Origin of operator SEESAW MECHANISM: (i) SM+RH ν (EW singlet) (ii) SM+SU(2) Triplet Higgs while Ł of the EW int. keeps invariant SU(2)×U(1) (iii) SM+SU(2) Triplet fermions (R.Foot, H.Lew, X.-G. He, G.C. Joshi 1989) 3×3 Seesaw model has 18 parameters: 12 real+6 phases (cf. Casas Ibarra ) Integrating out the heavy fermions leaves us with observable mass matrix (9 observables: 6 real+3 phases) Half of the parameters of the model get lost at low-E The 3 low-E CP-violating depend, in general, on all 6 seesaw phases. The effects of high-E CP-violating phases control the generation of the BAU in the leptogenesis scenario, in | | and in the leptonic CP-violating rephasing invariant Jcp. Complicated & many unknown parameters !! 2011 년 8 월 17 일 수요일

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A4 22 In approaches to reconstruct the high-energy physics from low-energy data, one can assume a flavor symmetry, which may reduce the unknown parameters. Unless flavor symmetries are assumed, particle masses and mixings are generally undetermined in gauge theory: To understand the present data we consider A4 flavor symmetry. (E.Ma and G.Rajarasekaran; G.Altarelly and F.Feruglio; X.G.He, Y.Y.Keum and R.Volkas) Tri-Bimaximal in neutrino mixing & No Quark mixing Non-zero |U e3 | and correct CKM matrix : Higher order corrections In seesaw + A4 : Leptogenesis scale ~ 10 13 -10 15 GeV, due to the equal size of moduli of neutrino Yukawa couplings (strong wash-out) Without the aid of higher order corrections or soft-breaking term, non-zero |U e3 | as well as Leptogenesis are not possible TeV-scale Resonant-Leptogenesis 2011 년 8 월 17 일 수요일

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A4 23 2011 년 8 월 17 일 수요일

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A4 24 2011 년 8 월 17 일 수요일

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A4 25 2011 년 8 월 17 일 수요일

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A4 26 A4 is the symmetry group of the tetrahedron and the finite groups of all twelve the even permutation of four objects: its irreducible representations contain one triplet 3 and three singlets 1,1’,1” with the multiplication rules 3×3=3+3+1+1’+1” and 1’×1’=1” Let’s denote two A4 triplets and where 2011 년 8 월 17 일 수요일

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Construction of Lagrangian 27 Under SU(2)×U(1)×A4×Z2 Hence its Yukawa interaction Z2: forbidden 2011 년 8 월 17 일 수요일

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Construction of Lagrangian 28 Under SU(2)×U(1)×A4×Z2 Hence its Yukawa interaction Z2: forbidden 2011 년 8 월 17 일 수요일

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Construction of Lagrangian 29 Under SU(2)×U(1)×A4×Z2 Hence its Yukawa interaction Z2: forbidden 2011 년 8 월 17 일 수요일

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Construction of Lagrangian 30 Under SU(2)×U(1)×A4×Z2 Hence its Yukawa interaction Z2: forbidden 2011 년 8 월 17 일 수요일

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Construction of Lagrangian 31 Under SU(2)×U(1)×A4×Z2 Hence its Yukawa interaction Z2: forbidden 2011 년 8 월 17 일 수요일

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32 In the charged fermion sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, Charged fermion mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) 2011 년 8 월 17 일 수요일

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33 In the charged fermion sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, Charged fermion mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) 2011 년 8 월 17 일 수요일

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34 In the charged fermion sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, “ Tri-maximal ” Lepton -sector Charged fermion mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) 2011 년 8 월 17 일 수요일

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35 In the charged fermion sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, “ Tri-maximal ” Lepton -sector Charged fermion mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) Quark sector In a weak eigenstate basis When diagonalizing the charged fermion mass matrices by rotating No Mixing !! it should be corrected !! 2011 년 8 월 17 일 수요일

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36 In the charged fermion sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, “ Tri-maximal ” Lepton -sector Charged fermion mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) Quark sector In a weak eigenstate basis When diagonalizing the charged fermion mass matrices by rotating No Mixing !! it should be corrected !! 2011 년 8 월 17 일 수요일

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37 In the neutrino sector: The Yukawa interaction, after EW symmetry breaking : Z 2 symmetry breaking No Leptogenesis and No low-E CP-violation Taking the scale of A4 symmetry breaking to be above EW scale, Heavy Majorana mass matrix : And assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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38 In the neutrino sector: The Yukawa interaction, after EW symmetry breaking : Z 2 symmetry breaking No Leptogenesis and No low-E CP-violation Taking the scale of A4 symmetry breaking to be above EW scale, Heavy Majorana mass matrix : And assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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39 In the neutrino sector: The Yukawa interaction, after EW symmetry breaking : Z 2 symmetry breaking No Leptogenesis and No low-E CP-violation Taking the scale of A4 symmetry breaking to be above EW scale, Heavy Majorana mass matrix : And assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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40 In the neutrino sector: The Yukawa interaction, after EW symmetry breaking : Z 2 symmetry breaking No Leptogenesis and No low-E CP-violation Taking the scale of A4 symmetry breaking to be above EW scale, Heavy Majorana mass matrix : And assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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41 In the neutrino sector: The Yukawa interaction, after EW symmetry breaking : Z 2 symmetry breaking No Leptogenesis and No low-E CP-violation Taking the scale of A4 symmetry breaking to be above EW scale, Heavy Majorana mass matrix : And assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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42 In the neutrino sector: If we consider Leptogenesis and low-energy CP-violation in our scenario, 2011 년 8 월 17 일 수요일

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43 In a weak eigenstate basis, the Yukawa interaction and charged gauge interaction Lagrangian Neutrino mass matrix as, which leads to an effective neutrino mass matrix at low energies Diagonalizing matrix of light neutrino mass matrix is 2011 년 8 월 17 일 수요일

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44 In a weak eigenstate basis, the Yukawa interaction and charged gauge interaction lagrangian Neutrino mass matrix as, which leads to an effective neutrino mass matrix at low energies Diagonalizing matrix of light neutrino mass matrix is 2011 년 8 월 17 일 수요일

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45 In a weak eigenstate basis, the Yukawa interaction and charged gauge interaction lagrangian By rotating From the charged lepton current 2011 년 8 월 17 일 수요일

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46 In a weak eigenstate basis, the Yukawa interaction and charged gauge interaction lagrangian By rotating From the charged lepton current Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector) Non-zero |U e3 | QLC Leptogenesis 2011 년 8 월 17 일 수요일

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47 In a weak eigenstate basis, the Yukawa interaction and charged gauge interaction lagrangian By rotating From the charged lepton current Tri-Bimaximal (Leptonic Sector)+No mixing (Quark Sector) Non-zero |U e3 | QLC Leptogenesis Consider Naïve and very simple corrections to the Quarks and lepton sectors 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 48 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 49 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 50 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 51 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 52 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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Deviations TBM from higher dimensional operators 53 In the Lagrangian level, assume that above the cutoff scale Λ there is no CP violation term in the Dirac Yukawa neutrino and charged fermion Yukawa interactions, which for scale below Λ is expressed in terms of 5-dimentional operators. In the presence of 5-D operators driven by χ -VEV alignment, the Yukawa interactions in the fermion sector, which is invariant under SU(2)×U(1)×A4×Z2 2011 년 8 월 17 일 수요일

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54 In the neutrino sector: Taking the scale of A4 symmetry breaking to be above EW scale, and assuming the vacuum alignment of heavy singlet scalar, where 2011 년 8 월 17 일 수요일

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55 In the neutrino sector: Taking the scale of A4 symmetry breaking to be above EW scale, and assuming the vacuum alignment of heavy singlet scalar, where The Yukawa interaction, after EW symmetry breaking : Z2 symmetry breaking The corrected neutrino Yukawa matrix : 2011 년 8 월 17 일 수요일

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56 In the neutrino sector: Taking the scale of A4 symmetry breaking to be above EW scale, and assuming the vacuum alignment of heavy singlet scalar, where The Yukawa interaction, after EW symmetry breaking : Z2 symmetry breaking The corrected neutrino Yukawa matrix : Leptogenesis low-E CP violation 2011 년 8 월 17 일 수요일

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57 In the charged fermion sector: VEV alignment The corrected charged fermion mass matrix where 2011 년 8 월 17 일 수요일

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58 In the charged fermion sector: VEV alignment The corrected charged fermion mass matrix where 2011 년 8 월 17 일 수요일

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59 In the charged fermion sector: VEV alignment The corrected charged fermion mass matrix where For the most natural case of hierarchical charged fermion Yukawa couplings the corrected off-diagonal terms are not larger than the diagonal ones in size 2011 년 8 월 17 일 수요일

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60 Only the mixing matrix takes part in PMNS and CKM mixing matrices Low-energy CP-violation 2011 년 8 월 17 일 수요일

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61 Only the mixing matrix takes part in PMNS and CKM mixing matrices Low-energy CP-violation There are empirical fermion mass ratios in the charged-lepton, up- and down-type quark sectors calculated from the measured values 2011 년 8 월 17 일 수요일

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62 Only the mixing matrix takes part in PMNS and CKM mixing matrices Low-energy CP-violation There are empirical fermion mass ratios in the charged-lepton, up- and down-type quark sectors calculated from the measured values 2011 년 8 월 17 일 수요일

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63 Quark-Lepton symmetry is broken by masses of quarks and lepton, therefore one does not expect that the quark mixing is transmitted to the lepton sector exactly. 2011 년 8 월 17 일 수요일

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64 Quark-Lepton symmetry is broken by masses of quarks and lepton, therefore one does not expect that the quark mixing is transmitted to the lepton sector exactly. However, there is some interesting empirical relation 2011 년 8 월 17 일 수요일

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65 Quark-Lepton symmetry is broken by masses of quarks and lepton, therefore one does not expect that the quark mixing is transmitted to the lepton sector exactly. However, there is some interesting empirical relation The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type one’s, on the other hand, the mass spectrum of up-type quark shows a strong hierarchy compared to the down-type one’s. 2011 년 8 월 17 일 수요일

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66 Quark-Lepton symmetry is broken by masses of quarks and lepton, therefore one does not expect that the quark mixing is transmitted to the lepton sector exactly. However, there is some interesting empirical relation The mass spectrum of the charged-leptons exhibit a similar hierarchy to the down-type one’s, on the other hand, the mass spectrum of up-type quark shows a strong hierarchy compared to the down-type one’s. In terms of the Cabbibo angle the fermion masses can be scaled as which may represent that the CKM matrix mainly generated from the down-type-quark sector, as well as charged-lepton mixing matrix is similar to the CKM matrix. 2011 년 8 월 17 일 수요일

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CKM Mixing Matrix 67 Up-type quark and its mixing matrix Due to the measured up-quark mass hierarchy, it is impossible to generate the Cabbibo angle : if let then, which is in discrepancy with the measured does not affect the leading order predictions in λ Cabbibo angle should arise from the first and second generation mixing in the down-type quark sector 2011 년 8 월 17 일 수요일

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CKM Mixing Matrix 68 Down-type quark and its mixing matrix From the measured down-quark mass hierarchies For letting in turn which means should be roughly Additional assumption to get a correct CKM matrix : 2011 년 8 월 17 일 수요일

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CKM Mixing Matrix 69 Down-type quark and its mixing matrix From the measured down-quark mass hierarchies For letting in turn which means should be roughly Additional assumption to get a correct CKM matrix : 2011 년 8 월 17 일 수요일

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70 Down-type quark and its mixing matrix From the measured down-quark mass hierarchies For letting in turn which means should be roughly Assumption to get a correct CKM matrix : 2011 년 8 월 17 일 수요일

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CKM Mixing Matrix 71 CKM mixing matrix When diagonalizing the charged-fermion mass matrices by rotating if we let Effects caused by CP violation are always proportional to Jalskog-invariant which is of the order 2011 년 8 월 17 일 수요일

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CKM Mixing Matrix 72 CKM mixing matrix When diagonalizing the charged-fermion mass matrices by rotating if we let 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 73 From the measured charged-lepton mass hierarchies Similar to down-type quark sector, if let, which means Scenario-I 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 74 From the measured charged-lepton mass hierarchies Similar to down-type quark sector, if let, which means Scenario-I 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 75 Scenario-II Similar to Down-type quark mixing matrix 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 76 Scenario-II Similar to Down-type quark mixing matrix 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 77 Scenario-II Similar to Down-type quark mixing matrix 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 78 Scenario-III 2011 년 8 월 17 일 수요일

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Charged-Lepton sector 79 Scenario-III 2011 년 8 월 17 일 수요일

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80 In a weak eigenstate basis When diagonalizing the charged-fermion mass matrices we can rotate In a mass eigenstate basis of the charged gauge interaction term 2011 년 8 월 17 일 수요일

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81 In a weak eigenstate basis When diagonalizing the charged-fermion mass matrices we can rotate In a mass eigenstate basis of the charged gauge interaction term 2011 년 8 월 17 일 수요일

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82 In a weak eigenstate basis When diagonalizing the charged-fermion mass matrices we can rotate In a mass eigenstate basis of the charged gauge interaction term 2011 년 8 월 17 일 수요일

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Neutrino sector 83 The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing An additional mixing matrix to diagonalize with the mixing angle and phases 2011 년 8 월 17 일 수요일 θ= ± π/4 +δ for δ«1

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Neutrino sector 84 The effective low-energy neutrino mass matrix can not be diagonalized by Bi-Maxiaml mixing An additional mixing matrix to diagonalize with the mixing angle and phases 2011 년 8 월 17 일 수요일 θ= ± π/4 +δ for δ«1

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85 The neutrino mass eigenvalues are given as From the above the solar and atmospheric mass squared differences are written as 2011 년 8 월 17 일 수요일

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86 The neutrino mass eigenvalues are given as From the above the solar and atmospheric mass squared differences are written as 2011 년 8 월 17 일 수요일

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PMNS Mixing matrix 87 that is, for the charged lepton correction is negligible In the limit of exact TBM is recovered. 3 σ (1 σ ) Exp. Bounds → this is disfavored in 1 σ Exp. Results due to the upper bounds 2011 년 8 월 17 일 수요일

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PMNS Mixing matrix 88 that is, for the charged lepton correction is negligible In the limit of exact TBM is recovered. 3 σ (1 σ ) Exp. Bounds → this is disfavored in 1 σ Exp. Results due to the upper bounds Therefore, sizable contributions from the charged lepton sector are required to reach accordance with the 1 σ Exp. results 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 89 Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are sensitive to the Dirac-phase, but insensitive to the Majorana phases. 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 90 Leptonic CP-violation at low-energies can be detected through neutrino oscillations which are sensitive to the Dirac-phase, but insensitive to the Majorana phases. 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 91 Solar mixing angle 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 92 Solar mixing angle For example, in the second scenario 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 93 Solar mixing angle For example, in the second scenario 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 94 Reactor mixing angle 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 95 Reactor mixing angle The parameter can be determined by the BAU if Leptogenesis is true. Subsequently, the parameter Φ(φ 21,θ,ψ 3 ) can be decided by the first QLC relation. And then, we can predict the value of reactor angle. 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 96 Atmospheric mixing angle where 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 97 Atmospheric mixing angle where If we consider Leptogenesis in this scenario, then we can pin down the value of ψ 1. 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 98 Solar Mixing Angle versus ψ 3 Atm. Mixing Angle versus ψ 1 θ 12 +θ q12 =45 ο θ 23 +θ q23 =45 ο 2011 년 8 월 17 일 수요일

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PMNS Mixing (charged lepton correction) 99 Non-zero |U e3 | Leptonic CP-violation J CP 2011 년 8 월 17 일 수요일

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Another very attractive feature of Seesaw ? 100 In addition to the explanation of neutrino masses, seesaw has another appearing feature so-called “Leptogenesis” Lepton asymmetry: It is independent of mixing angles and CP phases of neutrino oscillation. The loop function includes the 1-loop vertex and self energy corrections to the heavy neutrino decay amplitude. 2011 년 8 월 17 일 수요일

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Another very attractive feature of Seesaw ? 101 wash-out effects: The generated asymmetry survives if decays takes place out-of-equilbrium at otherwise, inverse decay and scattering processes cancel the asymmetry We are in the energy scale where A4 symmetry is broken but the SM gauge group remains unbroken. Choose leptogenesis scale Flavor effects: ( PRD49,6394 James M. Cline, Kimmo Kainulainen, Keith A. Olive ) Interactions involving the charged τ are out-of-equilibrium at Interactions involving the charged μ are out-of-equilibrium at Interactions involving the charged e are out-of-equilibrium at 2011 년 8 월 17 일 수요일

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A link between low-energy observables and Leptogenesis 102 Go into the physical basis of the RH neutrino Diagonalizing matrix 2011 년 8 월 17 일 수요일

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Conclusions 103 In the presence of 5-Dimensional operators driven by χ -field, A relatively large |U e3 | and CKM mixing matrix can be explained. QLC can be naturally explained in A4 flavor symmetry through phased-effects. The deviations from TBM can be fitted to Experimental data, especially a relatively large Theta13, through the phased effects from higher dimensional operators. If we consider the BAU through Leptogenesis in this scenario, we can have more informations and give predictions about neutrino data. 2011 년 8 월 17 일 수요일

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