PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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It is evident that the masses of the heavy charged leptons obtained from Eqs. (3.33) and (3.35) are approximately the same as that obtained for the neutral heavy fermion using Eq. (3.22). Indeed a comparison of these equations show that at tree level, the difference between the neutral and charged heavy fermions are of the order of the neutrino mass and can be hence neglected. One-loop effects bring a small splitting between the masses of the heavy charged and neutral fermions, which is of the order of hundred MeV. This allows the decay channel Σ ± = Σ 0 +π ± at colliders, as discussed in detail in [14,15]. In this work we neglect this tiny difference and assume that the masses of all heavy fermions are the same. The matrices ˜m † l ˜m l and ˜M † ˜M H H are diagonalized by U l and Uh L giving, ( ) Ul 0 U L = 0 Uh L . (3.36) Similarly the ˜m l˜m † l and ˜M H ˜M† H matrices are diagonalized by U r and Uh R and hence give, ( ) Ur 0 U R = 0 Uh R . (3.37) Finally, the low energy observed neutrino mass matrix is given by U PMNS = U † l U 0. (3.38) Here both U l and U 0 are unitary matrices and hence U PMNS is unitary. 3.3 A µ-τ Symmetric Model As discussed in the introduction we wish to impose µ-τ symmetry on our model in order to comply with the neutrino data so that θ 13 = 0 and θ 23 = π/4. Henceforth, we impose the µ-τ exchange symmetry on both the neutrino Yukawa matrix Y Σ and the Majorana mass matrix for the heavy fermions M. Therefore, the neutrino Yukawa matrix takes the form ⎛ Y Σ = ⎝ a ⎞ 4 a 11 a 11 a ′ 11 a 6 a 8 ⎠, (3.39) a ′ 11 a 8 a 6 In addition to the µ-τ symmetry, we also assume (for simplicity) that a ′ 11 = a 11, which reduces the number of parameters in the theory. For simplicity, we also assume all entries of Y Σ to be real. The heavy Majorana mass matrix is given by ⎛ ⎞ M 1 0 0 M = ⎝ 0 M 2 0 ⎠, (3.40) 0 0 M 2 42
Sin 2 Θ 12 a 4 0.38 0.38 a 11 0.36 0.36 m o =0.95 m o =0.006 0.34 0.34 0.32 0.32 0.3 0.3 0.28 0.28 0.26 0.26 0.24 0.24 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0.1 0.2 0.3 0.4 0.5 0.6 Sin 2 Θ 12 Sin 2 Θ 12 0.38 0.36 0.34 0.32 0.3 0.28 0.26 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a 6 R 0.04 m o =0.95 m o =0.006 0.038 0.036 0.034 0.032 0.03 0.028 0.026 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 a 4 R 0.04 0.038 0.036 0.034 0.032 0.03 0.028 R 0.04 0.038 0.036 0.034 0.032 0.03 0.028 0.026 0.026 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a 11 a 6 Figure 3.1: Scatter plots showing variation of sin 2 θ 12 (upper panels) and R = ∆m 2 21 /|∆m2 31 | (lower panels) as a function of a 4, a 11 and a 6 . All Yukawa couplings apart from the one plotted on the x-axis, are allowed to vary freely. Only points which predict oscillation parameters within their current 3σ values are shown. Blue points are for m 0 = v ′2 /(2M 1 ) = 0.95 eV while the green points are for m 0 = 0.006 eV. a 6 a 8 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 m o =0.95 m o =0.006 m o =0.0021 -0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 a 4 a 11 a 11 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 a 6 a 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 0.7 1 0.9 0.8 0.7 0.6 0.8 0.6 0.5 0.7 0.5 0.6 0.4 0.4 0.5 0.3 0.4 0.3 0.2 0.3 0.2 0.1 0.2 0.1 0 0.1 0 a 4 a 8 a 6 -0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 a 11 a 8 Figure 3.2: Scatter plot showing the values of the Yukawa couplings which give all oscillation parameters within their current 3σ allowed ranges. Allowed points are shown for m 0 = 0.96 eV (blue), 0.006 eV (green) and 0.0021 eV (red). All Yukawa couplings apart from the ones plotted in the x-axis and y-axis are allowed to vary freely, in each panel. 43
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Neutrinos and Some Aspects of Physi
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Declaration This thesis is a presen
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Acknowledgments First and foremost,
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iii
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trino masses are bounded within 0.1
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softly broken Z 2 symmetry, the mas
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tribimaximal mixing in the neutrino
Page 20 and 21: Bibliography [1] Two Higgs doublet
Page 23 and 24: Contents 1 Introduction 1 1.1 Stand
Page 25: 6.2.2 Charged Lepton Masses and Mix
Page 29 and 30: Chapter 1 Introduction 1.1 Standard
Page 31 and 32: For positive µ 2 and λ, the Higgs
Page 33 and 34: type of Yukawa interaction between
Page 35 and 36: interaction with the Higgs as λ f
Page 37 and 38: where ˆΦ is the MSSM chiral super
Page 39: (2004); A. Ghosal, hep-ph/0304090;
Page 44 and 45: active flavor. In recent years, sev
Page 46 and 47: Figure 2.1: The possible neutrino s
Page 48 and 49: Majorana mass term breaks lepton nu
Page 50 and 51: The kinetic term of the Higgs tripl
Page 52 and 53: ight handed neutrino N R can be exa
Page 54 and 55: alternating group which is not a di
Page 56 and 57: The group contains two one-dimensio
Page 58 and 59: from neutral-current interactions i
Page 60: [31] K. S. Babu and R. N. Mohapatra
Page 64 and 65: of producing the heavy fermion trip
Page 66 and 67: where Σ ± Ri = Σ1 Ri ∓iΣ2 Ri
Page 68 and 69: while U ν diagonalizes m ν and ˜
Page 72 and 73: 0.001 0.001 0.0001 0.0001 U e3 1e-0
Page 74 and 75: if we neglect terms proportional to
Page 76 and 77: calculations for lepton flavor viol
Page 78 and 79: fb. Therefore, it is obvious that t
Page 80 and 81: Σ − -> e m 1 m h 0 Σ − -> e m
Page 82 and 83: We can also see that for Σ − m 1
Page 84 and 85: the sinα term. However, decay to h
Page 86 and 87: Σ − m 1 ->ν m1 W Σ 0 m 1 ->ν
Page 88 and 89: Γ 2HDM (Σ 0 m → ν m H 0 ) ≃
Page 90 and 91: Decay modes Σ ± m 1 Σ ± m 2 Σ
Page 92 and 93: III seesaw model. Clearly, for our
Page 94 and 95: Sl no Channels Effective cross-sect
Page 96 and 97: • The other dominant decay channe
Page 102 and 103: 3.9 Conclusions The seesaw mechanis
Page 104 and 105: Appendix A: The Scalar Potential an
Page 106 and 107: B: The Interaction Lagrangian B.1:
Page 108 and 109: C H0 ,L 1√ ll 2 (T 11Y † l S 11
Page 110 and 111: c Z,L ll c Z,L lΣ − c Z,L Σ −
Page 112 and 113: Bibliography [1] S. Weinberg, Phys.
Page 114: Lett. B 615, 231 (2005); Phys. Rev.
Page 118 and 119: violating λ ′′ coupling are co
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neutralino-neutrinomassmatrixandins
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4.3 Symmetry Breaking In this secti
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+(M 2 +m 2 Σ )ũ2 + ∑ m 2˜ν i
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Here M 1,2 are the soft supersymmet
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is violated, we have neutrino-neutr
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(M 1,2 ,M,µ,Y Σi ,v 1,2 ,ũ,u i )
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In our model in addition to the sta
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4.8 Conclusion In this work we have
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Y Σi √2 ĤuˆΣ 0 0c Rˆν L i
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while the parameter α 1 is α 1 =
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Bibliography [1] S. Roy and B. Mukh
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[15] M. C. Gonzalez-Garcia and J. W
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ν i A Σi • ˜ν i h,H,A × χ
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118
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of the form ⎛ ⎞ A B B m ν =
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triplet representation of A 4 , l =
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m 0 =0.016 m 0 =0.024 m 0 =0.032 2
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Higgs Neutrino mass matrix Eigenval
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5.3. The deviation of the mixing an
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Sin 2 θ 12 Sin 2 θ 13 Sin 2 θ 23
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Figure 5.5: Scatter plot showing th
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Figure 5.6: Same as Fig. 5.5 but fo
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mass matrix is then given as ⎛ m
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Bibliography [1] M. C. Gonzalez-Gar
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140
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142
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a way that the residual µ−τ sym
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where Λ is the cut-off scale of th
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m 2 . The eigenvectors are given as
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For λ ≃ 2 × 10 −2 ≃ λ2 c 2
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2 2 2 1 1 1 y 2 0 y 3 0 y 4 0 -1 -1
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0.08 0.25 0.06 0.2 10 -3 m νee (eV
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We show the values of |U e3 | ≡ s
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while the branching ratio for this
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6.4 The Vacuum Expectation Values I
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where we have defined B = (b+f 1 +f
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VEV alignments. Another way the VEV
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(2006); M. Maltoni, T. Schwetz, M.
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168
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metric standard model in chapter 1.
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mally two. However the R-parity vio
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sector contains the exact/approxima
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PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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