PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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Here M 1,2 are the soft supersymmetry breaking gaugino mass parameters (see Appendix B), whereas M corresponds to the triplet-fermion bilinear term. We define the 3 × 5 matrix m D as ⎛ ⎞ m T D = √ 1 ⎝ −g′ u 1 gu 1 0 Y Σ1 ũ Y Σ1 v 2 −g ′ u 2 gu 2 0 Y Σ2 ũ Y Σ2 v 2 ⎠. (4.36) 2 −g ′ u 3 gu 3 0 Y Σ3 ũ Y Σ3 v 2 Defined in this way, the 8×8 neutral fermion mass matrix can be written as ( ) M ′ m M n = D m T , (4.37) D 0 where M ′ represents the 5×5 matrix ⎛√ ⎞ 2M 1 √ 0 −g ′ v 1 g ′ v 2 0 M ′ = √ 1 0 2M 2 gv 1 −gv 2 0 2 ⎜ −g ′ v 1 gv 1 0 − √ 2µ 0 ⎝ g ′ v 2 −gv 2 − √ ∑ 2µ 0 i Y ⎟ ∑ Σ i u i ⎠ . (4.38) 0 0 0 i Y √ Σ i u i 2M The low energy neutrino mass would be generated once the neutralino and exotic triplet fermions get integrated out. Hence the low energy neutrino mass matrix m ν is m ν ∼ −m T D M′ −1 m D . (4.39) For M ′ in the TeV range, m ν ∼ 1 eV demands that m D should be 10 −3 GeV. If one takes v 2 ∼ 100 GeV then this sets Y Σ ∼ 10 −5 and the scale of u to be 10 −3 GeV. Since in our model for small value of u, the ũ and u are proportional to each other, hence we naturally get ũ ∼ u ∼ 10 −3 GeV. We have discussed in more detail in Appendix C how the smallness of neutrino mass can restrict the vacuum expectation values u i , ũ and the Yukawas Y Σi . One can clearly see from Eq. (4.35) that in the u = 0 and ũ = 0 limit, the gaugino-higgsino sector completely decouples from the standard model neutrino-exotic neutrino sector and the low energy neutrino mass would be governed via the usual type- III seesaw only. In the work presented in the previous chapter, we have taken a large Yukawa coupling Y Σ ∼ 1. In the present work since we do not extend the Higgs sector than the minimal supersymmetric standard model and in addition we choose a TeV scale triplet fermion mass parameter M, hence from the neutrino mass constraint the Yukawa is bounded to take such a small value Y Σ < 10 −5 . However, as of the two Higgs doublet type-III seesaw model presented in the previous chapter, one can further extend the Higgs sector of this model by two SU(2) doublet, so that one of the new Higgs contributes to the neutrino mass generation. In that case, one can choose a small VEV of the new Higgs doublet and take the large Yukawa. 98
4.5 Chargino-Charged Lepton Mass Matrix Liketheneutralino-neutrinomixingasdiscussedintheprevioussection, R-parityviolation will also result in chargino-charged lepton mixing, which in our model is significantly different compared to the other existing models of spontaneous and explicit R-parity violation, because of the presence of extra heavy triplet charged fermionic states in our model. Like the enlarged neutrino sector (ν Li ,Σ 0c R ) we have also an extended charged lepton sector. With one generation of ˆΣ c R we have two additional heavier triplet charged leptons Σ +c R and Σ−c R in our model, in addition to the standard model charged leptons. Hence we get mixing between the charginos and the standard model charged leptons as well as the heavier triplet charged leptons. The possible contributions to the different mixing terms would come from the superpotential as well as from the kinetic terms of the different superfields. Since we have written down explicitly the charginos-charged leptonsneutrino interaction terms in Appendix, it is straightforward to see the contribution to 0c the mass matrix coming from Eq. (B5), Eq. (B6) and Eq. (B8) once the ˜Σ R and ˜ν L i states get vacuum expectation values. The chargino-charged lepton mass matrix in the basis ψ1 T = (˜λ + ,˜H + u ,lc 1 ,lc 2 ,lc 3 ,Σ−c R )T and ψ 2 = (˜λ − ,˜H − d ,l 1,l 2 ,l 3 ,Σ +c R )T is where L c = −ψ T 1 M cψ 2 +h.c, (4.40) ⎛√ √ √ √ √ ⎞ 2M 2 √ √ 2gv1 2gu1 2gu2 2gu3 gũ M c = √ 1 2gv2 2µ YΣ1 ũ Y Σ2 ũ Y Σ3 ũ − ∑ √ i 2YΣi u i 0 − √ √ 2Y e1 u 1 2Ye1 v 1 0 0 0 2 ⎜ 0 − √ √ 2Y e2 u 2 0 2Ye2 v 1 0 0 ⎝ 0 − √ (4.41) √ ⎟ 2Y e3 u 3 √ 0 √ 0 √ 2Ye3 v 1 0 ⎠ √ −gũ 0 2YΣ1 v 2 2YΣ2 v 2 2YΣ3 v 2 2M Thechargino-chargedleptonmassmatrixwouldbediagonalizedbybi-unitarytransformation M c = TM d cS † . 4.6 Neutrino Mass and Mixing R-parity violation can contribute significantly to the 3×3 standard model light neutrino mass matrix. In this section we concentrate on determining the neutrino mass square differences andtheappropriatemixings. Withonly onegenerationofsinglet/triplet heavy Majorana neutrino it is not possible to get viable neutrino mass square differences and mixings in the R-parity conserving type-I or type-III seesaw scenario. Since R-parity 99
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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
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Contents 1 Introduction 1 1.1 Stand
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6.2.2 Charged Lepton Masses and Mix
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Chapter 1 Introduction 1.1 Standard
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For positive µ 2 and λ, the Higgs
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type of Yukawa interaction between
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interaction with the Higgs as λ f
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where ˆΦ is the MSSM chiral super
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(2004); A. Ghosal, hep-ph/0304090;
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active flavor. In recent years, sev
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Figure 2.1: The possible neutrino s
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Majorana mass term breaks lepton nu
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The kinetic term of the Higgs tripl
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ight handed neutrino N R can be exa
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alternating group which is not a di
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The group contains two one-dimensio
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from neutral-current interactions i
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[31] K. S. Babu and R. N. Mohapatra
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of producing the heavy fermion trip
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where Σ ± Ri = Σ1 Ri ∓iΣ2 Ri
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while U ν diagonalizes m ν and ˜
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It is evident that the masses of th
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0.001 0.001 0.0001 0.0001 U e3 1e-0
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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
Page 120 and 121: neutralino-neutrinomassmatrixandins
Page 122 and 123: 4.3 Symmetry Breaking In this secti
Page 124 and 125: +(M 2 +m 2 Σ )ũ2 + ∑ m 2˜ν i
Page 128 and 129: is violated, we have neutrino-neutr
Page 130 and 131: (M 1,2 ,M,µ,Y Σi ,v 1,2 ,ũ,u i )
Page 132 and 133: In our model in addition to the sta
Page 134 and 135: 4.8 Conclusion In this work we have
Page 136 and 137: Y Σi √2 ĤuˆΣ 0 0c Rˆν L i
Page 138 and 139: while the parameter α 1 is α 1 =
Page 140 and 141: Bibliography [1] S. Roy and B. Mukh
Page 142 and 143: [15] M. C. Gonzalez-Garcia and J. W
Page 144 and 145: ν i A Σi • ˜ν i h,H,A × χ
Page 146 and 147: 118
Page 148 and 149: of the form ⎛ ⎞ A B B m ν =
Page 150 and 151: triplet representation of A 4 , l =
Page 152 and 153: m 0 =0.016 m 0 =0.024 m 0 =0.032 2
Page 154 and 155: Higgs Neutrino mass matrix Eigenval
Page 156 and 157: 5.3. The deviation of the mixing an
Page 158 and 159: Sin 2 θ 12 Sin 2 θ 13 Sin 2 θ 23
Page 160 and 161: Figure 5.5: Scatter plot showing th
Page 162 and 163: Figure 5.6: Same as Fig. 5.5 but fo
Page 164 and 165: mass matrix is then given as ⎛ m
Page 166 and 167: Bibliography [1] M. C. Gonzalez-Gar
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Page 172 and 173: a way that the residual µ−τ sym
Page 174 and 175: 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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