PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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dark matter. The standard model can not explain this dark matter abundance. Beyond standard model physics, for example minimal supersymmetric standard model provide a natural dark matter candidate. • The universe is made by matter and not by antimatter. The observed value of the baryon asymmetry from the WMAP data and primordial nuclear abundance gives evidence for the matter and antimatter asymmetry n B nγ = (6.1±0.3)×10 −10 [17]. If the universe has been started with a matter-antimatter symmetric state, then this baryon asymmetry is indeed a puzzle which the standard model cannot explain. The explanation certainly needs beyond standard model physics. One of the novel mechanism which can explain the baryon asymmetry of the universe is leptogenesis [18], which is inherently linked with the Majorana neutrino mass generation scheme, i.e the novel seesaw mechanism. In leptogenesis the lepton asymmetry is generated in the decay of standard model gauge singlet states( also SU(2) triplet states [19, 20]) [21], which gets converted into baryon asymmetry due to the presence of nonpurturvative sphalaron transitions [22]. The same gauge singlet or SU(2) triplet fields generate the dimension-5 operator from which Majorana neutrino mass is generated. The detail about leptogenesis can be found in [17,23]. • From experiments we know there are three generations of fermions in the standard model. However, theoretically standard model does not shed any light on the fermion generations. • Aesthetically, we would like to have unification of the fundamental forces of nature. In nature we have the gravitational interaction, electromagnetic interaction, weak and strong interaction. Standard model unifies electromagnetic and weak interaction. But it fails to unify the other forces with the electroweak one and also it does not give a quantum description of gravity. These above mentioned problems motivate one to look for beyond standard model physics scenarios. In the next section we discuss the minimal supersymmetric standard model. In chapter 2 we discuss the neutrino oscillation and neutrino mass generation in detail. 1.3 Minimal Supersymmetric Standard Model Supersymmetry is a symmetry that transforms a boson into a fermion and vice versa. The main phenomenological motivation to extend the standard model into the minimal supersymmetric standard model lies in the quadratic divergence of the Higgs mass. In the standard model the Higgs mass is not protected by any symmetry and the one loop correction of the Higgs mass is quadratically divergent. The fermions which have Yukawa 6
interaction with the Higgs as λ f Hff, contributes to the one loop correction to the Higgs mass as [11,12] δm 2 H = −|λ f| 2 8π 2 Λ2 UV +..., (1.16) where Λ UV is the cut-off scale beyond which the new physics is expected. Considering the validity of the standard model upto the Planck scale, the Higgs mass gets a quantum correction O(10 18 ). Cancellation of this divergences with the bare mass parameter would require fine-tuning of order one part in 10 −18 , rendering the theory unnatural [11,12]. This huge quantum correction due to fermionic contribution is cancelled by the scalar contribution, if we introduce scalar particle ˜f with the quartic interaction λ˜f|H| 2 |˜f| 2 and with the property λ˜f = |λ f | 2 . Supersymmetry is the desired symmetry which naturally introducesascalarparticle ˜f forthefermionicfieldf withthesamemassandthenecessary criteria between the couplings λ˜f = |λ f | 2 . The contribution of the ˜f scalar to the one loop correction of the Higgs mass is the following, δm 2 H = (λ˜f) 8π 2 Λ2 UV . (1.17) The total contribution to quadratic divergence of the Higgs mass in this case would be, and hence will naturally vanish for λ˜f = |λ f | 2 . δm 2 H = (λ˜f −|λ f | 2 ) 8π 2 Λ 2 UV , (1.18) The operator Q that generates a supersymmetric transformation is an anticommuting spinor, with and Q|Boson〉 = |Fermion〉, (1.19) Q|Fermion〉 = |Boson〉 (1.20) The hermitian conjugate of Q i.e Q † is also a supersymmetry generator. Supersymmetry is a space-time symmetry and the possible form of supersymmetry is restricted by Haag-Lopuszanski-Sohnius extension of the Coleman-Mandula theorem [24]. For realistic theories like standard model, the theorem implies these following anticommutation and commutation relations between the different generators, {Q,Q † } = P µ (1.21) {Q,Q} = {Q † ,Q † } = 0 [P µ ,Q] = [P µ ,Q † ] = 0, 7
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: type of Yukawa interaction between
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
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the sinα term. However, decay to h
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Σ − m 1 ->ν m1 W Σ 0 m 1 ->ν
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Γ 2HDM (Σ 0 m → ν m H 0 ) ≃
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Decay modes Σ ± m 1 Σ ± m 2 Σ
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III seesaw model. Clearly, for our
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Sl no Channels Effective cross-sect
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• The other dominant decay channe
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Page 100 and 101:
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3.9 Conclusions The seesaw mechanis
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Appendix A: The Scalar Potential an
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B: The Interaction Lagrangian B.1:
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C H0 ,L 1√ ll 2 (T 11Y † l S 11
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c Z,L ll c Z,L lΣ − c Z,L Σ −
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Bibliography [1] S. Weinberg, Phys.
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Lett. B 615, 231 (2005); Phys. Rev.
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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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