PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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Synopsis The standard model of particle physics which is based on the local gauge invariance of the gauge group SU(3) C × SU(2) L × U(1) Y has been extremely successful in describing the electromagnetic, weak and strong interactions between elementary particles. The theory has been verified to a high degree of accuracy in collider experiments such as the Large Electron-Positron Collider (LEP) at CERN in Europe and the Tevatron at Fermilab, USA. The other very profound characteristic of the standard model of particle physics is renormalizibility, which emerges because of its underlying quantum field theoretical description. However, although this theory gives a number of correct predictions, there are still certain issues which it is unable to explain, hence the standard model is considered a low energy description of some fundamental theory. The standard model of particle physics cannot explain the observed small neutrino mass and the peculiar mixing. It does not give any candidate for the dark matter of the Universe. It also fails to explain the observed matter-antimatter asymmetry of the Universe. In addition, one of its major theoretical drawback is the hierarchy or the naturalness problem. The Higgs particle which is an essential ingredient of the standard model is not stable under quantum corrections. There is no symmetry to protect its mass and hence the mass of the Higgs gets a quantum correction δm h ∼ 10 18 GeV, assuming the validity of the standard model up to the Planck scale. Beyond standard model physics such as supersymmetry gives a very natural solution to the hierarchy problem. In the minimal supersymmetric extension of the standard model, every standard model fermion/scalar is accompanied by its scalar/fermionic superpartner and hence the scalar and fermionic contributions mutually cancel each other, stabilizing the Higgs mass. Other than this, standard model does not give gauge coupling unification. It unifies electromagnetic and weak interaction, but fails to unify the electroweak and strong interactions. Also, it does not include gravity. Apart from these drawbacks, the mass hierarchy between the standard model particles is itself a puzzle. In the standard model, the left and right handed fermions interact with the Higgs via the gauge invariant Yukawa Lagrangian and their masses are generated when the Higgs takes a non-zero vacuum expectation value. The nonzero vacuum expectation value of the Higgs field breaks the SU(2) L ×U(1) Y symmetry of the standard model down to U(1) em . The fermion masses in the standard model is determined by this nonzero vacuum expectation value and the Yukawa couplings. Although the mass generation mechanism is the same for all the standard model fermions, still there exist a O(10 6 ) hierarchy between the top and electron masses. With the inclusion of neutrino mass, the hierarchy gets much enhanced. A series of outstanding experiments like solar and atmospheric neutrino experiments, KamLAND, K2K, MINOS provide information about the standard model neutrino mass splittings and its very peculiar mixing angles. Combined with cosmological bound specially from WMAP data, the sum of the light neu-
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 15 and 16: nomenology. The triplet fermions wh
Page 17 and 18: Non-observation of proton decay con
Page 19 and 20: interacts with the gauge bosons via
Page 21: Publication and Preprints 1. Two Hi
Page 24 and 25: 3.5.4 Comparison Between One and Tw
Page 28 and 29: xvi
Page 30 and 31: In the above equations the SU(2) L
Page 32 and 33: where ˜H = iτ 2 H ∗ . The elect
Page 34 and 35: dark matter. The standard model can
Page 36 and 37: where P µ is the four-momentum gen
Page 38 and 39: Bibliography [1] S. Weinberg, Phys.
Page 43 and 44: Chapter 2 Neutrino Mass and Mixing
Page 45 and 46: ∆m 2 21(10 −5 eV 2 ) 7.59 ±0.2
Page 47 and 48: Figure 2.2: Feynman diagram of neut
Page 49 and 50: theory. The fields which get integr
Page 51 and 52: H H H H µ ∆ H H Y † ν N R Y
Page 53 and 54: • The LL∆ term in Eq. (2.16) is
Page 55 and 56: Conjugacy Class Elements 1 1 ′ 2
Page 57 and 58: Bibliography [1] W. Pauli, “Dear
Page 59 and 60: [20] H. V. Klapdor-Kleingrothaus et
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Chapter 3 Two Higgs Doublet Type-II
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artifact of the imposed µ-τ symme
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we generate the following neutrino
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where m l = vY l , while D l and D
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Sin 2 Θ 12 a 4 0.38 0.38 a 11 0.36
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demand that v ′ ∼ 10 5 eV in or
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and ˜M H ˜M† H respectively. Fo
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Figure 3.4: Variation of production
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ν m . Accordingly m lj will repres
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Σ − m 1 -> e m H Σ − m 1 ->
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Σ 0 -> e m 1 m H + Σ 0 -> e m 2 m
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For the other two channels Σ 0 m
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Γ 1HDM (Σ ± m → l± m Z) ≃
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Decay modes Σ ± m 1 Σ ± m 2 Σ
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Decay modes h 0 H 0 A 0 b m¯bm 0.8
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The most important characteristics
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heavy fermions Σ ± → l ± h 0 a
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Sl no Channels Effective cross-sect
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Sl no Channels Effective cross-sect
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3.8.3 Backgrounds In Tables 3.8, 3.
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parameters depend on the model para
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The physical Higgs are given in ter
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−L H0 ν,Σ 0 = H0 {ν m (C H0 ,L
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C H− ,L lν −T 11Y † l U 11 s
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mixing between Higgs fields as disc
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[11] I. Gogoladze, N. Okada and Q.
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Chapter 4 R Parity Violation and Ne
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gaugino seesaw. We restrict ourself
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The SU(2) triplet fermions are Σ +
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In the above equations ... represen
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Hence for small u which is demanded
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4.5 Chargino-Charged Lepton Mass Ma
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We next discuss the neutrino oscill
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loop in Fig. 3 of [4]. For the sake
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neutralino states [7], as for the f
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Appendix A: Soft supersymmetry brea
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Similar interaction terms would be
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eaking mass terms in Eq. (4.33). Si
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ph]]; A. Bartl, M. Hirsch, A. Vicen
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[27] A. Bartl, M. Hirsch, T. Kernre
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117
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Chapter 5 A 4 Flavor Symmetry and N
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Lepton SU(2) L A 4 l 2 3 e R 1 1 µ
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5.3 Number of One Dimensional Higgs
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2 1 b 0 -1 -2 -1 0 1 a Figure 5.2:
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In Fig. 5.2 we present a scatter pl
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Higgs Neutrino mass matrix Eigenval
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d b 2 1 0 -1 -2 0.5 0 -0.5 2 1 0 -1
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Higgs Neutrino mass matrix Eigenval
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0.4 0.35 Sin 2 θ 12 0.3 -0.01 -0.0
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Also we have shown, while the tripl
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Rev. D 71, 033001 (2005); R. N. Moh
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141
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Chapter 6 S 3 Flavor Symmetry and L
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Field H l 1 D l e R µ R τ R ∆
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where u ′ 1 = u 1 Λ and it is le
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6.2.2 Charged Lepton Masses and Mix
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0.4 0.4 Sin 2 θ 12 0.35 0.3 Sin 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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Figure 6.5: The Jarlskog invariant
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The quantities e 1 , e ′ 1 , e 2
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Vertices Vertex factors F ab eµ H
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−4cu 1 u 2 +c ′ (u 2 1 +u2 2 )+
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Using the same arguments as above,
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Bibliography [1] E. Ma, Phys. Rev.
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167
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Chapter 7 Conclusion In this thesis
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with five physical degrees of freed
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in chapter 5 [3] we have build a mo
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Bibliography [1] Two Higgs doublet
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PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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