PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

More documents

Recommendations

Info

mass matrix is then given as ⎛ m ν = m 0 ⎝ a+2b ⎞ 1/3 d−b/3 d−b/3 d−b/3 d+2b/3 a−b 1 /3⎠ . (5.21) d−b/3 a−b 1 /3 d+2b/3 Of course for b 1 = b one would recover the case considered in the previous section and TBM mixing would result. The possibility of b 1 ≠ b gives rise to deviation from TBM mixing. In order to solve this matrix analytically we assume that b 1 = b + η and keep only the first order terms in η. The mass eigenvalues obtained are m 1 = m 0 (a+b−d+ η 3 ), m 2 = m 0 (a+2d), m 3 = m 0 (−a+b+d+ η ), , (5.22) 3 and the mixing matrix is ⎛ √ ( 2 1− η 3 √ ( 1 ⎜− ⎝ 6 √ − 1 6 3(3d−b) 1+ 2η 3(3d−b) ( 1+ 2η 3(3d−b) ) √ ) √ ) √ 1 3 1 3 1 3 ( 1+ 2η 3(3d−b) ( 1− η 3(3d−b) ( 1− η 3(3d−b) ) 0 ) √ − ) √ 1 2 Therefore, the only deviation from TBM comes in θ 12 and we have D 12 ≃ 1 2 ⎞ ⎟ ⎠ . (5.23) 4η 9(3d−b) . (5.24) We show in Fig. 5.7 variation of sin 2 θ 12 with η. As expected, sin 2 θ 12 is seen to deviate further and further from its TBM value of 1/3 as we increase the difference between v S and v S1 . The other two mixing angles are predicted to be exactly at their TBM values due to the presence of µ−τ symmetry in m ν . They would also deviate from TBM once we allow for either v S2 ≠ v S3 or c ≠ d, and in the most general case, both. 5.5 Conclusions InthisworkwehaveseentheimplicationofA 4 flavorsymmetry ontheneutrino oscillation datawhileemphasizingmostlyontribimaximalmixingpattern. Westicktoamostgeneric setup and we consider all the possibilities, where the one dimensional Higgses ξ, ξ ′ , ξ ′′ belong to 1, 1 ′ , 1 ′′ representation under the symmetry group A 4 . Other than this, we also haves two A 4 triplets φ T,S . We analyze the different cases by taking one, two and all three one dimensional A 4 Higgs fields at a time and show only few of them can give viable neutrinomassandmixing. TogettribimaximalmixingonewouldrequireVEValignments of the triplet and also specific relations between different VEV’s and Yukawa couplings. 136
Also we have shown, while the triplet alone is sufficient to provide the tribimaximal mixing, to get the viable neutrino mass splitting the one dimensional representation must be present. We have analyzed the possibilities to get normal and/or inverted hierarchy for these different viable scenarios. The most simple case with A 4 singlet ξ will lead to normal hierarchy, while inclusion of other one dimensional representation allows for inverted hierarchy as well. Finally we address the deviation from the tribimaximal mixing and give one illustrative example where the deviation is realized due to deviation from the triplet vacuum alignments. 137
Page 1:
Neutrinos and Some Aspects of Physi
Page 5:
Declaration This thesis is a presen
Page 9 and 10:
Acknowledgments First and foremost,
Page 11:
iii
Page 14 and 15:
trino masses are bounded within 0.1
Page 16 and 17:
softly broken Z 2 symmetry, the mas
Page 18 and 19:
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 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 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 98 and 99:
Page 100 and 101:
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 126 and 127: Here M 1,2 are the soft supersymmet
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 166 and 167: Bibliography [1] M. C. Gonzalez-Gar
Page 168 and 169: 140
Page 170 and 171: 142
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
Page 176 and 177: m 2 . The eigenvectors are given as
Page 178 and 179: For λ ≃ 2 × 10 −2 ≃ λ2 c 2
Page 180 and 181: 2 2 2 1 1 1 y 2 0 y 3 0 y 4 0 -1 -1
Page 182 and 183: 0.08 0.25 0.06 0.2 10 -3 m νee (eV
Page 184 and 185: We show the values of |U e3 | ≡ s
Page 186 and 187: while the branching ratio for this
Page 188 and 189: 6.4 The Vacuum Expectation Values I
Page 190 and 191: where we have defined B = (b+f 1 +f
Page 192 and 193: VEV alignments. Another way the VEV
Page 194 and 195: (2006); M. Maltoni, T. Schwetz, M.
Page 196 and 197: 168
Page 198 and 199: metric standard model in chapter 1.
Page 200 and 201: mally two. However the R-parity vio
Page 202 and 203: sector contains the exact/approxima
show all

PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?