PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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In our model in addition to the standard model neutrinos we also have a heavy triplet neutral fermion Σ 0c R . Hence in this kind of model where heavy triplet fermions are present, the lightest neutralino can also be Σ 0c R dominated. Here we present a very qualitative discussion on the possible neutralino, sneutrino, slepton and chargino decay modes. • (A) Neutralino two body decay: As R-parity is violated, the lightest neutralino can decay through R-parity violating decay modes. It can decay via the two body decay mode ˜χ 0 5 → lW or ˜χ0 5 → νZ. Other heavier neutralinos can decay to the lighter neutralino state ˜χ 0 i → ˜χ 0 jZ, or through the decay modes ˜χ 0 i → l ± W ∓ /νZ. The gauge boson can decay leptonically or hadronically producing ˜χ 0 i → l ± W ∓ → l ± l ∓ + ̸ E T , ˜χ 0 i → l ± W ∓ → l ± +2j, ˜χ 0 i → νZ → l ± l ∓ + ̸ E T , ˜χ 0 i → νZ → 2b+ ̸ E T . • (B) Sneutrino and slepton decay: Because of R-parity violation the slepton can decay to a charged lepton and a neutrino [27] via ˜l → νl. The sneutrino can also have the possible decay ˜ν → l + l − . In the explicit R-parity violating scenario, this interaction term between ˜νl ± l ∓ and ˜l¯lν would have significant contribution from λLLE C . Here l ± , ν and ˜l all are in mass basis. In the spontaneous R-parity violating scenario these interactions are possible only after basis redefinition. The different contributions to the above mentioned interaction terms will come from the MSSM R-parity conserving term ĤdˆLÊc as well as from the kinetic terms of the different superfields after one goes to the mass basis. • (C) Three body neutralino decay modes: The other possible decay modes for the neutralino are ˜χ 0 i → ν˜ν, l±˜l∓ , νh. If the lightest neutralino ˜χ 0 5 is the lightest supersymmetric particle, then the slepton or sneutrino would be virtual. The sneutrino or slepton can decay through the R-parity violating decay modes. Hence neutralino can have three body final states such as ˜χ 0 i → ν˜ν → νl± l ∓ , ˜χ 0 i → l±˜l∓ → l ± νl ∓ . Our special interest is in the case where the lightest neutralino state is significantly triplet fermion Σ 0 dominated. Besides the Yukawa interaction, the triplet fermion Σ ± ,Σ 0 have gauge interactions. Hence they could be produced at a significant rate in a proton proton collider such as LHC through gauge interactions. The triplet fermions Σ ± and Σ 0 could be produced via pp → W ± /Z → Σ ± Σ 0 /Σ ∓ 3 channels apart from the Higgs mediated channels. In fact the production cross section of these triplet fermions should be more compared to the production cross section of the singlet neutrino dominated 3 By Σ ± ,Σ 0 we mean chargino state ˜χ ± or neutralino state ˜χ 0 significantly dominated by Σ ± and Σ 0 respectively. 104
neutralino states [7], as for the former case the triplet fermions have direct interactions with the gauge bosons. The decay channels for these triplet neutral fermions are as Σ 0 → νZ, Σ 0 → l ± W ∓ , Σ 0 → νh and also Σ 0 → ν˜ν ∗ ,l˜l ∗ followed by R-parity violating subsequent decays of the slepton/sneutrino. Apart from the neutralino sector in our model, the charged higgsino and charged winos mix with standard model leptons and heavy charged leptons Σ ± . Hence, just like in the neutralino sector, there will also be R-parity violating chargino decay. The chargino ˜χ i ± can decay into the following states, ˜χ i ± → l ± Z, νW, νh ± and also to ˜χ i ± → l˜ν → ll ± l ∓ , ˜χ i ± → ν˜l → ννl. Just like as for the neutralinos, depending on the parameters, in this kind of model with heavy extra triplet fermions the lightest chargino could be as well Σ ± dominated. Moreover, because of R-parity violation, there will be mixing between the the slepton and charged Higgs and sneutrino and neutral Higgs. The sneutrinostate ˜Σ ± canhavethedecays ˜Σ ± → νl ± , ˜νW ± ,˜l ± Z. Similarly, ˜Σ0 candecayinto ˜Σ 0 → l + l − . Apart from these above mentioned decay channels, some other possible decay channels are, ˜Σ + → ¯du, ˜Σ 0 → uū, Σ + → ũ¯d. For the R-parity conserving seesaw scenario, these decay modes will be totally absent, as there is no mixing between the triplet/singlet fermion and the higgsino/gauginos and mixing between sfermions and Higgs bosons. We would also like to comment about the possibility of lepton flavor violation in our model. For the non-supersymmetric type-III seesaw, the reader can find detailed study on lepton flavor violation in [28]. Embedding the triplet fermions in a supersymmetric framework opens up many new diagrams which can contribute to lepton flavor violation, for example µ → eγ. In general the sneutrino, triplet sneutrino, different sleptons and the charginos or neutralinos can flow within the loop [23,29–31]. In our model the R-parity violating effect comes very selectively. The main contribution comes via the bilinear R-parity violating terms which get only generated spontaneously. Hence as discussed before, we ignore λ and λ ′ dominated diagrams [30] and we expect that the lepton flavor violating contribution would be mainly governed by the soft supersymmetry breaking offdiagonal slepton mass contribution. Since we stick to the universal soft supersymmetry breaking slepton masses, only RG running might generate the off diagonal supersymmetry breaking slepton masses [23]. In the R-parity conserving limit the soft supersymmetry breaking slepton masses get a contribution m 2 L ∝ (3m2 0 + A2 0 )(Y ΣYΣ T)log(M X M Σ ) 4 . For m 0 ,A 0 ∼TeV and Y Σ ∼ 10 −6 , m 2 L ∼ 10−6 log( M X M Σ )GeV 2 . The branching ratio would be roughly α3 |m 2 G 2 L |2 tan 2 β. However, because of extremely small Yukawa Y ˜m F 8 Σ ∼ 10 −6 − 10 −8 our model would not violate the bound coming from µ → eγ. 4 For simplicity we have taken Y Σ to be real. 105
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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
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calculations for lepton flavor viol
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fb. Therefore, it is obvious that t
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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 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 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
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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
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
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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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