PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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In the above equations the SU(2) L and the SU(3) C gauge coupling constants are represented by g and g s respectively. The gauge invariance of the standard model forbids us to write the bare mass term of the gauge bosons as, L m = mF µ F µ (1.3) where F µ generically represents the gauge fields Wµ i , B µ and G a µ . The term in Eq. (1.3) does not respect the gauge symmetry and hence is not allowed in the theory. Therefore, in the absence of any mass term of the gauge bosons, we should have twelve massless gauge bosons in the standard model. However, it is experimentally verified to a very large degree of accuracy through the experiments at LEP, CERN and Tevatron, Fermilab that in nature there are three massive gauge bosons W ± and Z. In the standard model, the masses of the gauge bosons are generated by the novel Higgs mechanism via spontaneous symmetry breaking (SSB). For this purpose an SU(2) L scalar doublet with hypercharge Y = +1 which is SU(3) gauge singlet has been included in the standard model. The Higgs spontaneously breaks the electroweak subgroup of the standard model gauge group to an U(1) em subgroup, thereby generating three massive gauge bosons. We discuss the Higgs mechanism and fermion mass generation in the following subsection. 1.1.1 Higgs Mechanism and Fermion Mass In the standard model the Higgs which is an SU(2) L complex scalar doublet with hypercharge Y = +1 is denoted as, ( ) H + H = H 0 (1.4) and transforms as (1,2,+1) under the standard model gauge group SU(3) C ×SU(2) L × U(1) Y . The neutral component of Higgs takes vacuum expectation value (VEV) v, breaking theSU(2) L ×U(1) Y → U(1) em spontaneously. The spontaneous breaking ofthecontinuous gauge symmetry generates three massive gauge bosons W µ ± and Z µ [3]. The photon A µ and the gluon G a µ remain massless due to the U(1) em symmetry and the unbroken SU(3) C symmetry. The gauge-invariant Lagrangian of the scalar field is, where the covariant derivative D µ is L = (D µ H) † (D µ H)−V(H), (1.5) D µ H = (∂ µ − i 2 gWj µ.τ j − iY H 2 g′ B µ )H. (1.6) In the above equation τ j are the Pauli matrices, Y H is the hypercharge of the Higgs field and g and g ′ are the SU(2) L and U(1) Y coupling constants. The potential of the Higgs field H is V(H) = −µ 2 H † H +λ(H † H) 2 . (1.7) 2
For positive µ 2 and λ, the Higgs field takes non-zero VEV v ( 0 〈0|H|0〉 = ; v v) 2 = µ2 2λ . (1.8) The gauge boson masses are generated from the first term of Eq. (1.5) and are the following, with L = M 2 WW + µ W −µ + 1 2 M2 ZZ µ Z µ , (1.9) W ± µ = W1 µ ∓iW2 µ √ 2 , and M 2 W = g2 v 2 2 , (1.10) Z µ = cosθ W W 3 µ −sinθ WB µ , tanθ W = g′ g ; M2 Z = v2 (g 2 +g ′2 ) . (1.11) 2 The angle of rotation θ W is refereed as Weinberg angle and is related to the masses of the W and Z gauge bosons as, M 2 W M 2 Z cos2 θ W = 1. (1.12) MW The ratio 2 MZ 2 cos2 θ W is defined as the ρ parameter. Experimentally the measured value of the Weinberg angle is sin 2 θ W = 0.23 [4]. The other linear combination of Wµ 3 and B µ is the photon A µ A µ = cosθ W Wµ 3 +sinθ WB µ (1.13) which remain massless due to the U(1) em invariance. The vacuum expectation value v is v ∼ 174 GeV in order to match the observed W and Z bosons masses, M W ∼ 80.4 GeV and M Z ∼ 91.19 GeV [4]. The Higgsgives masses not onlyto the gaugebosons, but also to the standardmodel fermions. Similar to the gauge bosons, one cannot write a bare mass term of the standard model fermions, because the bare mass term does not respect the gauge symmetry of the standard model. The fermion masses in the standard model are generated through the Yukawa Lagrangian which is −L Yuk = Y e LHe R +Y u Q L ˜HuR +Y d Q L Hd R +h.c, (1.14) 3
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: Chapter 1 Introduction 1.1 Standard
Page 33 and 34: type of Yukawa interaction between
Page 35 and 36: interaction with the Higgs as λ f
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
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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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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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