PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

More documents

Recommendations

Info

mally two. However the R-parity violating supersymmetric framework enables a viable description of the neutrino mass and mixing even with one generation of triplet matter chiral superfield which has R-parity −1 [2]. R-parity which is a discrete symmetry is defined as R p = (−1) 3(B−L)+2S and has been implemented in the minimal supersymmetric extension of the standard model to forbid the baryon number (Ûc ˆDc ˆDc ) and the lepton number violating (ˆLˆLÊc , ˆLˆQ ˆD c ) operators. Non-observation of proton decay constrains the simultaneous presence of lepton and baryon number violation, however leaving some space for the individual presence of either of these two. To accommodate the Majorana mass term of the standard model neutrino, lepton number violation is required. Spontaneous violation of R-parity meets both ends, it generates neutrino mass and satisfies the proton decay constraint, as in this scheme, the R-parity violating operators are generated very selectively. In our model R-parity is spontaneously broken by the vacuum expectation value of the different sneutrino fields. As a consequence, only the lepton number violating bilinear operators are generated while working in the weak basis. Sticking to the framework of the perturbative renormalizable field theory, the baryon number violating operators (Ûc ˆDc ˆDc ) would never be generated, hence naturally satisfying the proton decay constraint. Because of the R-parity violation, the standard model neutrinos ν i mix with the triplet fermion Σ 0 , as well as with the Higgsino ˜h 0 u and gauginos ˜λ 0 3,0 . Hence, in our model we have a 8×8 color and charge neutral fermionic mass matrix. With one generation of the triplet matter chiral superfield and the R-parity violation, two of the standard model neutrino masses can be generated as a consequence of the conventional seesaw along with the gaugino seesaw, while the third neutrino still remains massless. Hence, in this scenario viable neutrino masses and mixings are possible to achieve. In addition, the standard model charged leptons (l ± ), triplet fermions (Σ ± ) and the charginos (˜λ ± ,˜h ± u,d ) mixing is also determined by the different R-parity violating vacuum expectation values, as well as the different couplings of the superpotential. Hence, the charged lepton mass matrix is an extended 6×6 matrix. In our model the spontaneous violation of R-parity is not associated with any global U(1) lepton number breaking, since we break lepton number explicitly. Hence, the spontaneous R-parity violation is not associated with generation of any Majoron. We have explicitly analyzed the scalar potential and the minimization condition and have shown that the different R-parity violating sneutrino vacuum expectation values u, ũ in our model share a proportionality relation. From the neutrino phenomenology these vacuum expectation values are bounded to be small u,ũ < 10 −3 GeV, where we have considered gaugino masses of the order of few hundred GeV. We have discussed very briefly about the possible collider signatures which this model can offer. While the smallness of the neutrino mass can be explained via the seesaw mechanism, the very particular mixing of the standard model neutrinos can be well explained by invoking a suitable flavor symmetry. Among the widely used flavor symmetry groups, A 4 and S 3 are very promising ones. We have discussed in detail about the group theoretical aspects of the flavor symmetry groups A 4 and as well as S 3 in chapter 2, while 172
in chapter 5 [3] we have build a model based on the group A 4 . We have considered the most generic scenario with all possible one dimensional Higgs representations that can be accommodated within this A 4 model. The Higgs fields which are charged under the symmetry group A 4 , are standard model gauge singlets and they are knows as flavons. In our model [3] we have two flavon fields φ S,T which transform as three dimensional irreducible representation of the groupA 4 . In addition, we also have three other flavons ξ,ξ ′ ,ξ ′′ which transform as 1, 1 ′ and 1 ′′ respectively. The Lagrangian describing the Yukawa interaction between the different standard model leptons, Higgs and the flavons follows the effective field theoretical description. The different flavon fields take the vacuum expectation values, thereby resulting in a spontaneous breaking of the symmetry group A 4 . We have explored the conditions on VEVs and Yukawa couplings needed for obtaining exact TBM mixing in this present set-up. In particular, we have checked which combinations of the different one dimensional Higgs fields ξ, ξ ′ and ξ ′′ would produce TBM mixing and under what conditions. We have explicitly shown that the A 4 triplet field φ S can alone generate the tribimaximal mixing in the neutrino sector if all the vacuum expectation values v si of its component fields areequal. However it gives the atmospheric mass splitting ∆m 2 31 = 0, and hence is clearly incompatible with the neutrino oscillation data. To generate viable neutrino mass splittings in association with tribimaximal mixing, the one dimensional representations has to be included. Although the representation 1 which was originally proposed by Altarelli and Feruglio is the minimalistic choice to recover the correct mass, this particular choice ends up with a severe fine-tuning between the different parameters of the theory. The product of the VEV and Yukawa of this singlet is determined completely by the VEV and Yukawa of the triplet. Other than this, the normal hierarchy (∆m 2 31 > 0) between the standard model neutrino masses is the only allowed possibility. Inverted hierarchy can be possible if we have at least two or all three Higgs scalars with nonzero VEVs. The extreme fine-tuning in the parameter space is also gets reduced if one introduces two or three flavon fields at a time. Deviation from the particular relations between thedifferent Higgs vacuum expectation values andYukawas will lead to deviation from tribimaximal mixing. In the charged lepton sector the diagonal charged lepton mass matrix emerges as a consequence of an additional discrete symmetry Z 3 , as well as the vacuum alignment of the flavon field φ T . In chapter 6 we have constructed aflavor model based onthesymmetry groupS 3 [4], which reproduces the observed neutrino mass and mixing, as well as the standard model charged lepton mass hierarchy. We use two SU(2) Higgs triplets (∆) with hypercharge Y = 2, arrangedinadoublet of S 3 , andthe standardmodel singlet Higgs(φ e , ξ) which are also put as doublets of S 3 . Due to the appropriate charge assignment under additional discrete symmetry groups Z 4 and Z 3 , the flavon φ e enters only in the charged lepton Yukawa, whereas the other flavon ξ enters both in the neutrino as well as in the charged lepton Yukawa. The Higgs triplets ∆ and the flavon field ξ take vacuum expectation value, and generate standard model neutrino masses. To reproduce the observed lepton masses and mixings, the symmetry group S 3 has to be broken such that the neutrino 173
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 and 32:
For positive µ 2 and λ, the Higgs
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
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 98 and 99:
Page 100 and 101:
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 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
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
Page 168 and 169: 140
Page 170 and 171: 142
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
Page 182 and 183: 0.08 0.25 0.06 0.2 10 -3 m νee (eV
Page 184 and 185: We show the values of |U e3 | ≡ s
Page 186 and 187: while the branching ratio for this
Page 188 and 189: 6.4 The Vacuum Expectation Values I
Page 190 and 191: where we have defined B = (b+f 1 +f
Page 192 and 193: VEV alignments. Another way the VEV
Page 194 and 195: (2006); M. Maltoni, T. Schwetz, M.
Page 196 and 197: 168
Page 198 and 199: metric standard model in chapter 1.
Page 202 and 203: sector contains the exact/approxima
show all

PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Create successful ePaper yourself

Delete template?

Save as template?