PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

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where ˜H = iτ 2 H ∗ . The electron, up quark and down quark masses are generated from the above equation and are respectively the following, m e = Y e v; m u = Y u v; m d = Y d v. (1.15) The neutrino has been considered massless in the standard model. 1.2 Problems of the Standard Model Standard model gives a definite quantum description of the elementary particles. The model gives many successful predictions. For example, it predicts the existence of three massive gauge bosons which have experimentally been verified in LEP experiments at CERN, Geneva [5]. In addition, it predicts nine massless gauge bosons and the existence of massive quarks and leptons. Among its different successes one major success is the top quark discovery. Standard model predicted the existence of the top quark before it was discovered. The top quark was later observed at the Tevatron [6]. The electroweak properties of the standard model have been verified to a large degree of accuracy in experiments such as LEP and Tevatron [5,6]. However,there are many issues which this theory does not explain or address. Here we list a few of them: • Aseriesofoutstandingexperimentslikesolarandatmosphericneutrinoexperiments, KamLAND, K2K, MINOS, CHOOZ provide information about the standard model neutrino mass splittings and its very peculiar mixing angles. Combined with cosmological bound specially from WMAP data, the sum of the light neutrino masses are bounded to 0.19 eV [7], while the observed solar and atmospheric mass splitting are ∆m 2 21 ∼ 10 −5 eV 2 and ∆m 2 31 ∼ 10 −3 eV 2 respectively. This extremely small neutrino masses (< eV) point towards a 10 12 order mass hierarchy between the top quark and the neutrino. Other than the extremely small neutrino masses, the mixing in the leptonic sector is also a puzzle. Unlike the mixing in the quark sector, in the leptonic sector two of the mixing angles θ 12 and θ 23 are quite large (sin 2 θ 12 ∼ 0.32, sin 2 θ 23 ∼ 0.46) [8] while at present there is an upper bound on the third mixing angle θ 13 as sin 2 θ 13 < 0.05 at 3σ Confidence Level (C.L) [8]. The observed mixing angles are in very close agreement with the tribimaximal mixing [9] pattern where the solar mixing angle is sin 2 θ 12 = 0.33, reactor mixing angle sin 2 θ 13 = 0.0 and the atmospheric mixing angle is maximal sin 2 θ 23 = 0.5. The maximal mixing angle θ 23 and θ 13 = 0 points towards a possible µ−τ symmetry [10] in the neutrino sector. The standard model of particle physics does not have any neutrino mass itself. In addition, the standard model does not shed any light if there is any fundamental principle governing this extremely small neutrino masses as well as the peculiar mixing. It is possible to extend the standard model by introducing gauge singlet neutrinos and to explain the observed neutrino mass as a consequence of the Dirac 4
type of Yukawa interaction between this gauge singlet neutrinos, lepton doublet and the Higgs. However to explain the eV-neutrino mass one eventually will need a Yukawa which is O(10 12 ) order of magnitude suppressed as compared to the top Yukawa, thereby leading to a fine-tuning problem. If the neutrino is a Majorana particle, then there is a very natural explanation to the smallness of the neutrino mass, which is the novel seesaw mechanism. The neutrino mass in this mechanism is generated from a dimension-5 operator and naturally suppressed by the mass scale of the new physics. The origin of such a higher dimensional operator requires some more ingredient than the standard model physics. We discuss in detail about the neutrino oscillation and mass generation in the next chapter. • The fermion mass hierarchy is a puzzle in nature. In the standard model, all the fermionmassesaregeneratedidentically, fromagaugeinvariantYukawaLagrangian. Still we have a O(10 6 ) order of magnitude mass hierarchy between top quark and electron masses. With the evidence of non-zero neutrino masses which are eV order, the hierarchy increases to O(10 12 ). The standard model does not provide any answer to the mass hierarchy puzzle. Apart from this, there are 19 free parameters in the standard model. These are three lepton masses, six quark masses, three CKM mixing angles, one CP violating phase δ CKM , three gauge coupling constants g, g ′ and g S , the QCD vacuum angle θ QCD , the Higgs quadratic coupling µ and self interacting Higgs quartic coupling λ. Except for the couplings µ and λ, the numerical values of all other parameters were fixed by experimental observation. With the inclusion of the neutrino mass, the number of free parameters increases even further. But, the standard model does not give any theoretical predictions for these parameters. • One of the major theoretical drawback of the standard model is the hierarchy or the naturalness problem. The Higgs particle which is an essential ingredient of the standard model is not stable under quantum corrections. In the standard model the Higgs mass is not protected by any symmetry and the one loop correction to the Higgs mass is quadratically divergent. The one loop correction to the Higgs mass goes as Λ 2 UV , where the Λ UV is the cut-off scale beyond which new physics is expected. Considering the validity of the standard model upto the Planck scale, the Higgs mass gets a quantum correction O(10 18 ) GeV [11,12]. Beyond standard model physics such as supersymmetry [11–13] gives a very natural solution to the hierarchy problem. We will discuss in detail the hierarchy problem and the minimal supersymmetric standard model in the next section. • Cosmological and astrophysical observation suggest [14,15] that the total matter density of the universe is Ω M h 2 ∼ 0.13, while the observed baryonic matter density isΩ h h 2 ∼ 0.02. Takentogether, theseobservationsstronglyleadustotheconclusion that 80-85% [16] of the matter in the universe is non-luminous and non-baryonic 5
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 and 30: Chapter 1 Introduction 1.1 Standard
Page 31: For positive µ 2 and λ, the Higgs
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
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
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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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Page 100 and 101:
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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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