PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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violating λ ′′ coupling are constrained as λ ′ 11k λ′′ 11k ≤ 10−24 (m˜k/100GeV). For other λ ′ and λ ′′ couplings the bound is λ ′ ijk λ′′ lmn ≤ 10−9 [11]. Comparable bound exist on the product of λ and λ ′′ couplings [12]. Once R-parity conservation is implemented, all the terms of W̸Rp−MSSM are forbidden and hence the minimal supersymmetric standard model does not suffer any proton decay constraint. However, only the absence of λ ′′ term is sufficient and minimalistic choice to avoid the proton decay constraint. Sticking to a renormalizable perturbation theory if R-parity is violated spontaneously, one can easily justify the absence of the baryon number violating λ ′′ operator in the superpotential W̸Rp−MSSM, while at the same time the bilinear R-parity violating operator and trilinear R-parity violating operators are possible to generate. In this scenario R-parity is conserved in the superpotential. Once the sneutrino fields acquire vacuum expectation values, R-parity breaking terms are generated spontaneously [9,10,13–17]. In presence of additional singlet or triplet matter chiral fields, this provides a natural explanation for the origin of the R-parity and lepton number violating bilinear term 1 ǫ, without generating the baryon number violating λ ′′ term in the superpotential. Therefore, one can generate neutrino masses without running into problems with proton decay in this class of supersymmetric models. TherehavebeenearlierattemptstoconstructspontaneousR-parityviolatingmodels within the MSSM gauge group [9,10,13,14] and with the MSSM particle contents. In all these models the R-parity is broken spontaneously when the sneutrino acquires a VEV. This automatically breaks lepton number spontaneously. If lepton number is a global symmetry, this will give rise to a massless Goldstone called the Majoron [18]. All models which predict presence of Majoron are severely constrained. The phenomenology of the models with singlet Majoron has been studied in detail in [10,14]. A possible way of avoiding the Majoron is by gauging the U(1) symmetry associated with lepton number such that the spontaneous R-parity and lepton number violation comes with the new gauge symmetry breaking. This gives rise to an additional neutral gauge boson and the phenomenology of these models have also been studied extensively in the literature [15,16]. This idea has been used in a series of recent papers [17]. In this work we study spontaneous R-parity violation in the presence of a SU(2) L triplet Y = 0 matter chiral superfield, where we stick to the gauge group of the minimal supersymmetric standard model. Lepton number is broken explicitly in our model by the Majorana mass term of the heavy fermionic triplet, thereby circumventing the problem of the Majoron. We break R-parity spontaneously by giving vacuum expectation values to the 3 MSSM sneutrinos and the one additional sneutrino associated with the triplet which leads to the lepton-higgsino and lepton-gaugino mixing in addition to the conventional Yukawa driven neutrino-triplet neutrino mixing. This opens up the possibility of generating neutrino mass from a combination of the conventional type-III seesaw and the 1 It is possible to realize the other terms λ and λ ′ from the R-parity conserving MSSM superpotential only after redefinition of basis [1]. 90
gaugino seesaw. We restrict ourself to just one additional SU(2) L triplet Y = 0 matter chiral superfield, and explore the possibility of getting viable neutrino mass splitting and the mixing angles at tree level. With one generation of heavy triplet we get two massive neutrinos while the third state remains massless. Like the neutralino sector we also have R-parity conserving mixing between the standard model charged leptons and the heavy triplet charged lepton states. The spontaneous R-parity breaking brings about mixing between the charginos and the charged leptons, and hence modifies the chargino mass spectrum. In addition to the usual charged leptons, our model contains a pair of heavy charged fermions coming from the fermionic component of the triplet superfield. Another novel feature of our model comes from the fact that the additional triplet fermions and sfermions have direct gauge interactions. Hence they offer a much richer collider phenomenology. We discuss in brief about the possibility of detecting our model at colliders and the predicted R-parity violating signatures. The main aspects of our spontaneous R-parity violating model are the following: • We introduce one chiral superfield containing the triplets of SU(2) L and with Y = 0. • We have an explicit breaking of the lepton number due to the presence of the mass term of this chiral superfield in the superpotential. Therefore unlike as in [9,10,13,14], the spontaneous breaking of R-parity does not create any Majoron in our model. Since we do not have any additional gauge symmetry, we also do not have any additional neutral gauge boson as in [15–17]. • Since we have only one additional triplet chiral superfield we have two massive neutrinos, with the lightest one remaining massless. One of the neutrinos get mass due to type-III seesaw and another due to gaugino seesaw. Combination of both gives rise to a neutrino mass matrix which is consistent with the current data. • The triplet chiral superfield in our model modifies not only the neutrino-neutralino mass matrix, but also the charged lepton – chargino mass matrix. Being a triplet, it contains one neutral Majorana fermion Σ 0 , two charged fermions Σ ± , one sneutrino ˜Σ 0 , and two charged sfermions ˜Σ ± . Therefore, our neutral fermion mass matrix is a 8 × 8 matrix, giving mixing between the gauginos, higgsinos as well as the new TeV-scale neutral fermion Σ 0 . Likewise, the new charged fermions Σ ± will mix with the charginos and the charged leptons. • There are thus new TeV-mass neutral and charged leptons and charged scalars in our model, which will have mixing with other MSSM particles. These could be probed at future colliders and could lead to a rich phenomenology. We give a very brief outline of the collider signatures in this work. The chapter is organized as follows. In section 4.2 we describe the model and in section 4.3 we present the symmetry breaking analysis. In section 4.4, we discuss the 91
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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
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 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 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 164 and 165: mass matrix is then given as ⎛ m
Page 166 and 167: 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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