PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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C H0 ,L 1√ ll 2 (T 11Y † l S 11 cosα+T 21Y † Σ S 11 sinα) C H0 ,R ll 1√ 2 (S 11Y † † l T 11cosα+S 11Y † † Σ T 21sinα) C H0 ,L √2 1 lΣ (T † − 11 Y lS 12 cosα+T † 21 Y ΣS 12 sinα) C H0 ,R lΣ − √2 1 (S † 11 Y † l T 12cosα+S † 11 Y † Σ T 22sinα) C H0 ,L √2 1 Σ − Σ (T † − 12 Y lS 12 cosα+T † 22 Y ΣS 12 sinα) C H0 ,R Σ − Σ − √2 1 (S † 12 Y † l T 12cosα+S † 12 Y † Σ T 22sinα) C h0 ,L ll C h0 ,L lΣ − C h0 ,L Σ − Σ − C A0 ,L ll C A0 ,L lΣ − C A0 ,L Σ − Σ − C G0 ,L ll C G0 ,L lΣ − C G0 ,L Σ − Σ − √ −1 2 (T 11Y † l S 11 sinα−T 21Y † Σ S 11 cosα) C h0 ,R √−1 2 (T 11Y † l S 12 sinα−T 21Y † Σ S 12 cosα) C h0 ,R ll lΣ − √−1 2 (T † 12 Y lS 12 sinα−T † 22 Y ΣS 12 cosα) C h0 ,R Σ − Σ − √i 2 (T † 11 Y lS 11 sinβ +T † 21 Y ΣS 11 cosβ) C A0 ,R √ i 2 (T 11Y † l S 12 sinβ +T 21Y † Σ S 12 cosβ) C A0 ,R ll lΣ − √i 2 (T 12Y † l S 12 sinβ +T 22Y † Σ S 12 cosβ) C A0 ,R Σ − Σ − √−i 2 (T † 11 Y lS 11 cosβ −T † 21 Y ΣS 11 sinβ) C G0 ,R √−i 2 (T † 11 Y lS 12 cosβ −T † 21 Y ΣS 12 sinβ) C G0 ,R ll lΣ − √ −i 2 (T 12Y † l S 12 cosβ −T 22Y † Σ S 12 sinβ) C G0 ,R Σ − Σ − √ −1 2 (S 11Y † † √−1 2 (S 11Y † † l T 11sinα−S † 11Y † Σ T 21cosα) l T 12sinα−S † 11Y † Σ T 22cosα) √−1 2 (S † 12 Y † l T 12sinα−S † 12 Y † Σ T 22cosα) √−i 2 (S † 11 Y † l T 11sinβ +S † 11 Y † Σ T 21cosβ) √ −i 2 ((S 11Y † † √−i 2 (S 12Y † † l T 12sinβ +S † 11Y † Σ T 22cosβ) l T 12sinβ +S † 12Y † Σ T 22cosβ) √i 2 (S † 11 Y † l T 11cosβ −S † 11 Y † Σ T 21sinβ) √i 2 (S † 11 Y † l T 12cosβ −S † 11 Y † Σ T 22sinβ) √ i 2 (S 12Y † † l T 12cosβ −S 12Y † † Σ T 22sinβ) Table 3.13: The vertex factors for P L (P R ) and their corresponding exact expression in termsoftheYukawacouplingsandmixingmatricesaregiveninthefirst(third)andsecond (forth) column respectively. The vertex factors listed here are for Yukawa interactions of the charged leptons with neutral Higgs. C H0 ,L νν C H0 ,L νΣ 0 C H0 ,L Σ 0 Σ 0 C h0 ,L νν C h0 ,L νΣ 0 C h0 ,L Σ 0 Σ 0 C A0 ,L νν C A0 ,L νΣ 0 C A0 ,L Σ 0 Σ 0 C G0 ,L νν C G0 ,L νΣ 0 C G0 ,L Σ 0 Σ 0 sinα 2 (UT 21 Y ΣU 11 ) C H0 ,R νν sinα 2 (UT 21 Y ΣU 12 ) C H0 ,R νΣ 0 sinα 2 (UT 22 Y ΣU 12 ) C H0 ,R Σ 0 Σ 0 cosα 2 (UT 21 Y ΣU 11 ) C h0 ,R νν cosα 2 (UT 21 Y ΣU 12 ) C h0 ,R νΣ 0 cosα 2 (UT 22 Y ΣU 12 ) C h0 ,R Σ 0 Σ 0 icosβ (U T 2 21Y Σ U 11 ) C A0 ,R νν icosβ (U T 2 21 Y ΣU 12 ) C A0 ,R νΣ 0 icosβ (U T 2 22 Y ΣU 12 ) C A0 ,R Σ 0 Σ 0 isinβ (U T 2 21Y Σ U 11 ) C G0 ,R νν isinβ (U T 2 21Y Σ U 12 ) C G0 ,R νΣ 0 isinβ (U T 2 22Y Σ U 12 ) C G0 ,R Σ 0 Σ 0 sinα 2 (U† 11 Y † Σ U∗ 21 ) 2 (U† 11Y † Σ U∗ 22 ) 2 (U† 12Y † Σ U∗ 22 ) 2 (U† 11 Y † Σ U∗ 21 ) 2 (U† 11 Y † Σ U∗ 22 ) 2 (U† 12 Y † Σ U∗ 22 ) sinα sinα cosα cosα cosα − icosβ (U † 2 11Y † Σ U∗ 21) − icosβ (U † 2 11 Y † Σ U∗ 22 ) − icosβ (U † 2 12 Y † Σ U∗ 22 ) − isinβ (U † 2 11Y † Σ U∗ 21) − isinβ (U † 2 11Y † Σ U∗ 22) − isinβ 2 (U † 12Y † Σ U∗ 22) Table 3.14: The vertex factors for P L (P R ) and their corresponding exact expression in termsoftheYukawacouplingsandmixingmatricesaregiveninthefirst(third)andsecond (forth) column respectively. The vertex factors listed here are for Yukawa interactions of the neutral leptons with neutral Higgs. 80
C H− ,L lν −T 11Y † l U 11 sinβ C H− ,R lν ( √ 1 2 S 11Y † † Σ U 21 ∗ −S 21Y † ∗ Σ U ∗ 11 )cosβ C H− ,L lΣ −T 11Y † 0 l U 12 sinβ C H− ,R lΣ 0 ( √ 1 2 S 11Y † † Σ U 22 ∗ −S 21Y † ∗ Σ U ∗ 12 )cosβ C H+ ,L νΣ ( 1 − √ 2 U21Y T Σ S 12 −U11Y T T Σ S 22 )cosβ C H+ ,R νΣ − −U 11Y † † l T 12sinβ C H− ,L Σ − Σ −T 12Y † 0 l U 12 sinβ C H− ,R Σ − Σ 0 ( √ 1 2 S 12Y † † Σ U 22 ∗ −S 22Y † ∗ Σ U ∗ 12 )cosβ C G− ,L lν T 11Y † l U 11 cosβ C G− ,R lν ( √ 1 2 S 11Y † † Σ U 21 ∗ −S 21Y † ∗ Σ U ∗ 11 )sinβ C G− ,L lΣ T 11Y † 0 l U 12 cosβ C G− ,R lΣ 0 ( √ 1 2 S 11Y † † Σ U 22 ∗ −S 21Y † ∗ Σ U ∗ 12 )sinβ C G+ ,L νΣ ( 1 − √ 2 U21Y T Σ S 12 −U11Y T T Σ S 22 )sinβ C G+ ,R νΣ − U 11Y † † l T 12cosβ C G− ,L Σ − Σ T 12Y † 0 l U 12 cosβ C G− ,R Σ − Σ 0 ( √ 1 2 S 12Y † † Σ U 22 ∗ −S 22Y † ∗ Σ U ∗ 12 )sinβ Table 3.15: The vertex factors for P L (P R ) and their corresponding exact expression in termsoftheYukawacouplingsandmixingmatricesaregiveninthefirst(third)andsecond (forth) column respectively. The vertex factors listed here are for Yukawa interactions of the charged as well as neutral leptons with charged Higgs. where the first term is for heavy triplet fermion field and the second term contains the corresponding contributions from all standard model fields. The covariant derivative is defined as D µ = ∂ µ +ig[W µ ,Σ]. (B13) Inserting the covariant derivative in Eq. (B12) one obtains the following interaction terms between leptons and gauge fields L int = L l,Σ− NC +Lν,Σ0 NC +L CC, (B14) where the first two terms contain the neutral current interactions between l ± andΣ ± (first term) and between ν and Σ 0 (second term) respectively. The last term gives the charged current interaction between the leptons. The neutral current interaction Lagrangian involving l and Σ − is given by where L l,Σ− NC = l m γ µ {c Z,R ll P R +c Z,L ll P L }l m Z µ +{l m γ µ {c Z,R lΣ P − R +c Z,L lΣ P − L }Σ − m Z µ +h.c} +Σ − m γµ {c Z,R Σ − Σ P − R +c Z,L Σ − Σ P − L }Σ − m Z µ, (B15) c Z,R ll c Z,R lΣ − c Z,R Σ − Σ − = g c w s 2 w (T† 11 T 11)−c w g(T † 21 T 21), = g c w s 2 w (T† 11T 12 )−c w g(T † 21T 22 ), = g c w s 2 w(T † 12T 12 )−c w g(T † 22T 22 ), (B16) 81
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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
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
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 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 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
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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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