PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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metric standard model in chapter 1. Chapter 2 was devoted to neutrino mass and mixing, the different seesaw realizations. In chapter 3 [1] we built a model on type-III seesaw and have studied its detail phenomenology. In type-III seesaw, SU(2) triplet fermion gets integrated out and generate the dimension-5 Weinberg operator. The triplet fermions which transformasanadjointrepresentationofSU(2), containtwochargedfermionicstates(Σ ± ) and one charge neutral Majorana fermionic state (Σ 0 ). Being SU(2) triplet, the triplet fermions offers a distinctive feature as compared to the type-I seesaw mechanism, where the gauge singlet Majorana neutrino generate the Weinberg operator. The gauge singlet right handed neutrino field of type-I seesaw interacts with the lepton and Higgs via the Yukawa Lagrangian, while its interaction with the gauge bosons is suppressed by the standard model neutrino-gauge singlet right handed neutrino mixing. Compared to this, the SU(2) L triplet fermion interacts directly with the standard model gauge bosons through their kinetic term, as well as with the leptons and the Higgs via the Yukawa Lagrangian. Hence for the 100 GeV mass range, the triplet fermions can be produced copiously at LHC, opening up the possibility to test the seesaw at LHC. Since the standard model neutrino masses are M ν ≃ −Y T Σ M−1 Y Σ v 2 , hence for triplet fermion mass M = O(10 2 ) GeV, theYukawa couplingY Σ between thetriplet fermions-Higgsdoublet-leptonic doublet gets constrained as Y Σ ∼ 10 −6 by the eV neutrino mass. This inaway tentamounts to fine tuning of the Yukawas, and smothers out the very motivation for the seesaw mechanism, which was to explain the smallness of the neutrino mass without unnaturally reducing the Yukawa couplings. We show that the large Yukawa coupling and few hundred GeV triplet fermions are still possible with the addition of another SU(2) L ×U(1) Y Higgs doublet to this existing setup [1]. Inourmodel wehave considered threesets ofright handedtriplet fermionicfields Σ i , and one additional Higgs doublet Φ 2 . In addition, we also have introduced one discrete Z 2 symmetry, softly broken by the Higgs potential. The additional Higgs field Φ 2 (Z 2 odd) has the same SU(2) and U(1) Y transformations as the standard model Higgs doublet Φ 1 (Z 2 even), only differing in its Z 2 charge assignment. Hence in the Yukawa Lagrangian, the additional Higgs field Φ 2 interacts only with the standard model leptons (Z 2 even) and the triplet fermions (Z 2 odd), whereas the standard model Higgs Φ 1 interacts with all other standard model fermionic fields. Due to the very specific nature of the Yukawa Lagrangian, the standard model neutrino and the triplet fermionic neutral component mixing is governed by the vacuum expectation value v ′ of the additional Higgs doublet. Hence small vacuum expectation value v ′ ∼ 10 −4 GeV generates eV neutrino mass, even with large O(1) Yukawa coupling Y Σ . The charged lepton and quark masses in this model are determined by the large vacuum expectation value v ∼ 100 GeV of the standard model Higgs doublet. The choice of the small vacuum expectation value of the additional Higgs field has a significant impact on determining the Higgs mass spectra and the mixing angle between the neutral Higgses. With two Higgs doublets the Higgs sector in our model is enriched 170
with five physical degrees of freedom (H 0 , h 0 , A 0 , H ± ). Working within the framework of a softly broken Z 2 symmetry, the mass of the light Higgs h 0 is determined by the standard model Higgs vacuum expectation value (v ∼ 10 2 GeV) as well as by the extent of the Z 2 symmetry breaking coupling λ 5 , whereas all the other Higgs masses are governed by the standard model Higgs vacuum expectation value v. Hence, in our model it is possible to accommodate a light Higgs state h 0 . However, the presence of the light Higgs does not violate theLEP bound, due to thevanishingly small Z−Z−h 0 coupling. Dueto theorder of magnitude difference between the two vacuum expectation values v and v ′ , the mixing angle α between the two neutral Higgs h 0 and H 0 is proportional to the ratio of the two vacuum expectation values (tanβ = v′ v ) and is extremely small tan2α ∼ tanβ ∼ 10−6 . Wehavestudiedindetailtheproductionandsubsequent decayofthetripletfermions at LHC. Triplet fermion production at the LHC is mostly governed by the gauge boson mediated partonicsubprocesses. Once produced, thetriplet fermion candecay todifferent final state particles such as to a lepton+Higgs or to a lepton+ gauge boson. In our model, due to the large Yukawa coupling Y Σ and small value of the mixing angle α as well as tanβ, the triplet fermions (Σ ± , Σ 0 ) decay predominantly into standard model leptons along with the neutral and charged Higgses h 0 , A 0 , H ± . The other decay modes where triplet fermions decay into a standard model lepton along with the neutral Higgs H 0 or the standard model gauge bosons is highly suppressed. The dominant decay of the triplet fermion into a standard model lepton and a Higgs h 0 , A 0 , H ± is more than 10 11 times larger compared to the one Higgs doublet type-III seesaw scenario. The different decay modes of the triplet fermions are inherently linked with the neutrino phenomenology. In particular, the exact or approximate µ−τ symmetry in the neutrino sector distinguishes among the different leptonic states when the triplet fermion decays into a standard model lepton and a Higgs. The µ−τ symmetry in the neutrino sector provide equal opportunity to µ and τ states to be the leptonic final states, whereas it forbids the third generation of charged triplet fermions to decay into electron state e in the decay of 3rd generation of triplet fermions.. We have also looked into different Higgs decay modes and the possible collider signatures ofour model. In theHiggs sector, the different Higgsdecay modes aregoverned bytheYukawacouplingsandalsobythesmallmixingangleαaswellastanβ. Theneutral Higgs predominantly decays to 2b while the dominant decay mode for the charged Higgs H ± is H ± → W ± h 0 . Other than this, a distinctive feature of our model is the displaced vertex of the Higgs h 0 . Unlike the type-III seesaw with one Higgs doublet, in our model the triplet fermions do not have any displaced vertex. The type-III seesaw with two Higgs doublet canbeverified atLHC via thedifferent collider signatures which thismodel offers. We have calculated the effective cross sections for these channels. In charper 4 [2], we have build a model of R-parity violating supersymmetry and discussed the neutrino mass generation. The observed data on solar and atmospheric neutrino mass splitting constrains the number of triplet fermion generation to be mini- 171
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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
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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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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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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
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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
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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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Page 184 and 185: We show the values of |U e3 | ≡ s
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Page 188 and 189: 6.4 The Vacuum Expectation Values I
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Page 200 and 201: mally two. However the R-parity vio
Page 202 and 203: sector contains the exact/approxima
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PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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