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Register a new userLeptogenesis and fermion mass fit in a renormalizable $SO(10)$ model
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Venkata Suryanarayana Mummidi
Publication date
2021
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English
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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.
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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.
We present a renormalizable model for fermion masses based solely on the double tetrahedral group T. It does not include right handed neutrinos and majorana neutrino masses are generated radiatively. The scalar sector of the model involves three SU(2) doublets and a set of lepton number violating (charged) scalars needed to give mass to the neutrinos. In the quark sector the model leads to a Fritzsch type scenario that is consistent with all the existing data. In the lepton sector, the model leads to tribimaximal (and near tribimaximal) mixing, and an inverted mass hierarchy.
Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only ${bf 10}$ and $overline{bf 126}$ Higgs fields have been shown to realize the fermion masses and mixings economically. In previous works, the sum rule of the fermion mass matrices are given by inputting the quark matrices, and the neutrino mixings are predicted in this framework. Now the three neutrino mixings have been measured, and in this paper, we give the sum rule by inputting the lepton mass matrices, which makes clear certain features of the solution, especially if the vacuum expectation values of ${bf 126}+ overline{bf126}$ ($v_R$) are large and the right-handed neutrinos are heavy. We perform the $chi^2$ analyses to fit the fermion masses and mixings using the sum rule. In previous works, the best fit appears at $v_R sim 10^{13}$ GeV, and the fit at the large $v_R$ scale ($sim 10^{16}$ GeV) has been less investigated. Our expression of the sum rule has a benefit to understand the flavor structure in the large $v_R$ solution. Using the fit results, we perform the calculation of the $mu to egamma$ process and the electric dipole moment of electron, and the importance of $v_R$ dependence emerges in low energy phenomena. We also show the prediction of the CP phase in the neutrino oscillations, which can be tested in the near future.
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 discuss gauge coupling unification of the SM descending directly from SO(10) while providing solutions to the three outstanding problems: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry in the model calls for high-scale spontaneous symmetry breaking through ${126}_H$ Higgs representation. This naturally leads to the hybrid seesaw formula for neutrino masses mediated by heavy scalar triplet and right-handed neutrinos. The seesaw formula predicts two distinct patterns of RH$ u$ masses, one hierarchical and another not so hierarchical (or compact) when fitted with the neutrino oscillation data. Predictions of the baryon asymmetry via leptogenesis are investigated through the decays of both the patterns of RH$ u$ masses. A complete flavor analysis has been carried out to compute CP-asymmetries and solutions to Boltzmann equations have been utilized to predict the baryon asymmetry. The additional contribution to vertex correction mediated by the heavy left-handed triplet scalar is noted to contribute as dominantly as other Feynman diagrams. We have found successful predictions of the baryon asymmetry for both the patterns of RH$ u$ masses. The triplet fermionic dark matter at the TeV scale carrying even matter parity is naturally embedded into the non-standard fermionic representation ${45}_F$ of SO(10). In addition to the triplet scalar and the triplet fermion, the model needs a nonstandard color octet fermion of mass $sim 10^7$ GeV to achieve precision gauge coupling unification. Threshold corrections due to superheavy components of ${126}_H$ and other representations are estimated and found to be substantial. It is noted that the proton life time predicted by the model is accessible to the ongoing and planned experiments over a wide range of parameter space.
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