PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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if we neglect terms proportional to v ′2 . The mixing matrices U l and U r which diagonalize ˜m † l ˜m l (cf. Eq. (3.34)) and ˜m l˜m † l (cf. Eq. (3.32)) respectively, turn out to be unit matrices at leading order. ⎛ ⎞ ⎛ ⎞ 1 0 0 1 0 0 U l ≃ ⎝0 1 0⎠, U r ≃ ⎝0 1 0⎠, (3.44) 0 0 1 0 0 1 Finally, we show in Fig. 3.3 the impact of µ-τ symmetry breaking on the low energy neutrino parameters. For the sake of illustration we choose a particular form for this breaking, by taking M 3 ≠ M 2 . Departure from µ-τ symmetry results in departure of U e3 from zero and sin 2 θ 23 from 0.5. We show in Fig. 3.3 the U e3 (left hand panel) and |0.5−sin 2 θ 23 | generated as a function of the symmetry breaking parameter ǫ = M 3 −M 2 . The figure is generated for a 4 = −0.066, a 11 = 0.171, a 6 = 0.064, a 8 = 0.0037 and m 0 = 0.745 eV. We have fixed M 1 = M 2 = 299 GeV in this plot. For ǫ = 0, µ-τ symmetry is restored and both U e3 and 0.5−sin 2 θ 23 go to zero. We show only points in this figure for which the current data can be explained within 3σ. We note that for ǫ > 0 the curve extends to about M 3 = M 2 + 2.6 GeV, for this set of model parameters. For ǫ < 0, the allowed range for ǫ is far more restricted. We next turn our attention to the predictions of this model for the heavy fermion sector. The 6×6 mixing matrices, which govern the mixing of the heavy leptons with light ones, can also be obtained as discussed before. We will see in the next section that all the four 3×3 blocks of the matrices U, S and T are extremely important for phenomenology at the LHC. We denote these 3×3 blocks as U = S = T = ( ) U11 U 12 = U 21 U 22 ( ) (Wν ) 11 U 0 (W ν ) 12 U Σ , (3.45) (W ν ) 21 U 0 (W ν ) 22 U Σ ( ) ( S11 S 12 (WL ) = 11 U l (W L ) 12 Uh L S 21 S 22 (W L ) 21 U l (W L ) 22 Uh L ( ) ( T11 T 12 (WR ) = 11 U r (W R ) 12 Uh R T 21 T 22 (W R ) 21 U r (W R ) 22 Uh R ) , (3.46) ) , (3.47) The matrices W ν , W L and W R have been given in Eqs. (3.20), (3.30) and (3.31) respectively. Hence, the 3×3 blocks in S,T and in U can be estimated for our choice of m D , M and m l . In particular, we note that S 11 and T 11 are close to 1, while U 11 is given almost by U PMNS . The off-diagonal blocks U 12 , U 21 , S 12 and S 21 , are suppressed by ∼ m D /M, while T 12 and T 21 are suppressed by ∼ m D m l /M 2 . Finally, the matrices U 22 = (W ν ) 22 U Σ , S 22 = (W L ) 22 Uh L, and while T 22 = (W R ) 22 Uh R ≃ UR h . To estimate these we need to evaluate first the matrices which diagonalize the heavy fermion mass matrices ˜M, ˜M† ˜M H H , 46
and ˜M H ˜M† H respectively. For M and m D with µ-τ symmetry and with the parameters given in Table 3.1, it turns out that ⎛ 1 0 0 U Σ ≃ Uh L ≃ UR h ≃ ⎝ 0 1 √2 − 1 √ 2 0 1 √2 1 √2 ⎞ ⎠, (3.48) thereby yielding U 22 ≃ S 22 ≃ T 22 ≃ ⎛ 1 0 0 1 ⎝0 √2 −√ 1 2 ⎠. (3.49) 1 0 √2 1 √2 ⎞ ⎛ ⎞ 1 0 0 1 ⎝0 √2 −√ 1 2 ⎠. (3.50) 1 0 √2 √2 1 ⎛ 1 0 0 ⎝0 0 1 √2 √ 1 2 −√ 1 2 1 √2 ⎞ ⎠. (3.51) To be more precise, the structure of the 3rd column of U Σ , Uh L and UR h (and hence of U 22 , S 22 and T 22 ), is an immediate consequence of the µ-τ symmetry in M and m D . The matrices U Σ , Uh L and UR h will be almost unit matrices, only if M 1 ≪ M 2 ≪ M 3 . Breaking of the µ-τ symmetry either in m D or in M, will destroy this non-trivial form for U Σ , Uh R and Uh L. But having µ-τ symmetry in both Y Σ and M is both theoretically as well as phenomenologically well motivated. We will see later that this non-trivial form of the matrices U Σ , Uh L and UR h will lead to certain distinctive signatures at LHC. Among the different mixing matrices, while U Σ , Uh L and UR h have the form given by Eq. (3.48), U l and U r ≃ I, though both M and Y l were taken as real and diagonal. The main reason for this drastic difference is the following. While we take exact µ-τ symmetry for M, for Y l we take a largedifference between Y µ andY τ values. This choice was dictated by the observed charged lepton masses. We comment very briefly regarding the extent of deviation from unitarity. From the discussion of the previous section and Eq. (3.20), it is evident that the deviation from unitarity of the light neutrino mixing matrix is ∝ m 2 D /M2 Σ ≃ m ν/M Σ , where m ν and M Σ are the light neutrino and heavy lepton mass scales respectively. Therefore, an important difference between our model with TeV scale triplet fermion and the usual GUT seesaw models (for example type-I) is that the extent of non-unitarity for our model is much larger. This will result in comparatively larger lepton flavor violating decays. Detailed 47
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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
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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 70 and 71: It is evident that the masses of th
Page 72 and 73: 0.001 0.001 0.0001 0.0001 U e3 1e-0
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
Page 120 and 121: neutralino-neutrinomassmatrixandins
Page 122 and 123: 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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