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Register a new userFlavour symmetries in a renormalizable SO(10) model
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In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a $mathbf{10} oplus mathbf{120} oplus bar{mathbf{126}}$ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by $Z_n$ symmetries, with suitable $n$, and one case is generated by a $Z_2 times Z_2$ symmetry. A numerical analysis of the 14 cases reveals that only two of them---dubbed A and B in the present paper---allow good fits to the experimentally known fermion masses and mixings.
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A non-supersymmetric renormalizable $SO(10)$ model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex $10_H$ and $overline{126}_H$ scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of ${cal O}(1)$. We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $m_{ u_1}$ between 2-8 meV, (b) the effective mass of neutrinoless double beta decay $m_{beta beta}$ between 4-10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases.
We study the Higgs potential of the next-to-minimal renormalizable SUSY SO(10) GUT with 120 Higgs representation on top of the standard minimal model Higgs sector spanning over 10, 126bar+126 and 210. All the GUT-scale Higgs sector mass matrices for the 592 Higgs states of the model are written down in detail with all the conventions fully specified. The consistency of the results is checked by the decoupling of 120 and independently by the analysis of the relevant Goldstone modes. The matching of the Yukawa sector sum-rules driving the matter fermion masses and mixing at the level of the effective theory is described thoroughly.
We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU(3)xSU(2)xU(1) for the most physically interesting cases of SU(5) or flipped SU(5)xU(1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU(5) symmetry there is at most one singlet of the residual symmetry in each SO(10) irreducible representation. We also point out on more general grounds in supersymmetric GUTs that some intermediate symmetries can be exactly realized and others can only be approximated by fine-tuning. In the first category, there could occur some tunneling between the vacua with exact and approximate intermediate symmetry. The flipped SU(5)xU(1) symmetry improves the unification of gauge couplings if (B-L) is broken by (B-L)=1 scalars yielding right handed neutrino masses below 10^{14} GeV}.
Obtaining realistic supersymmetry preserving vacua in the minimal renormalizable supersymmetric $Spin(10)$ GUT model introduces considerations of the non-trivial topology of the vacuum manifold. The $D$-parity of low energy unification schemes gets lifted to a one-parameter subgroup $U(1)_D$ of $Spin(10)$. Yet, the choice of the fields signaling spontaneous symmetry breaking leads to disconnected subsets in the vacuum manifold related by the $D$-parity. The resulting domain walls, existing due to topological reasons but not stable, are identified as topological pseudodefects. We obtain a class of one-parameter paths connecting $D$-parity flipped vacua and compute the energy barrier height along the same. We consider the various patterns of symmetry breaking which can result in either intermediate scale gauge groups or a supersymmetric extension of the Standard Model. If the onset of inflation is subsequent to GUT breaking, as could happen also if inflation is naturally explained by the same GUT, the existence of such pseudodefects can leave signatures in the CMB. Specifically, this could have an impact on the scale invariance of the CMB fluctuations and LSS data at the largest scale.
We analyse how $U(3)^5$ and $U(2)^5$ flavour symmetries act on the Standard Model Effective Field Theory, providing an organising principle to classify the large number of dimension-six operators involving fermion fields. A detailed counting of such operators, at different order in the breaking terms of both these symmetries, is presented. A brief discussion about possible deviations from these two reference cases, and a simple example of the usefulness of this classification scheme for high-$p_T$ analyses at the LHC, are also presented.
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