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Masses and Mixing of Neutral Leptons in a Grand Unified E6 Model with Intermediate Pati-Salam Symmetry

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Abstract

A brief review of the assignment of elementary fermions and bosons to irreducible multiplets in grand unified \(E_{6}\) models is followed by a discussion of different, hierarchical symmetry breaking chains from \(E_{6}\) down to \(SU(3)_{C} \times U(1)_{EM}\). We concentrate here on a model with an intermediate Pati-Salam symmetry for which \((B-L)\) is conserved. In particular, the mass/mixing matrix of electrically neutral fermions (i.e.neutrinos) that would be derived from Yukawa couplings is constructed. The pattern of neutrino masses and some bounds on mixing parameters are discussed.

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Notes

  1. We make the most economical Higgs multiplet assignment. Higher Higgs multiplets \(\{351\}\) and \(\{\bar {351}\}\) may also be considered, for example, to implement supersymmetry [30].

  2. The alternative symmetry breaking chain with intermediate \(SU(5)\) symmetry instead of the Pati-Salam symmetry leads to a mass matrix with the same non-vanishing entries as above except the entry \(M_{13} \sim (-1,-1,-2)\) that vanishes. This is the case considered in Rosner [36].

  3. Here and in what follows, lower case m’s correspond to “small” parameter values while the upper case M’s correspond to “large” ones [35]. All the mass parameters are assumed positive.

  4. It is interesting to note that these bounds are independent of \(M_{13}\). Then they would remain the same if the broken symmetry chain had an intermediate \(SU(5)\) instead.

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Acknowledgments

S.B. thanks Koç University for a Graduate Student Scholarship. We are grateful to Dr.Emre Mengi for discussions on matrix analysis.

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  1. Department of Physics, Koç University, Sarıyer, Istanbul, 34450, Turkey

    Seçil Benli & Tekin Dereli

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Benli, S., Dereli, T. Masses and Mixing of Neutral Leptons in a Grand Unified E6 Model with Intermediate Pati-Salam Symmetry. Int J Theor Phys 57, 2343–2358 (2018). https://doi.org/10.1007/s10773-018-3757-8

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