Narrow Results

Several ideas for solving the problem of fermion mass hierarchy and mixing and specific supersymmetric models that realize it are reviewed. In particular, we discuss many models based on SO(10) in four dimensions combined with a family symmetry to accommodate fermion mass hierarchy and mixing, including the case of neutrinos. These models are compared and various tests that can be used to distinguish these models are suggested. We also include a discussion of a few SO(10) models in higher space–time dimensions.

In supersymmetry, there are gauge invariant dimension 5 proton decay operators which must be suppressed by a mass scale much larger than the Planck mass. It is natural to expect that this suppression should be explained by a mechanism that explains the hierarchical structure of the fermion mass matrices. We apply this argument to the case where wave functions of chiral multiplets are localized under a kink background along an extra spatial dimension and the Yukawa couplings as well as the coefficients of the proton decay operators are determined by the overlap of the relevant wave functions. A configuration is found in the context of SU(5) supersymmetric grand unified theory that yields realistic values of quark masses, mixing angles, CP phase and charged lepton masses and sufficiently small genuine dimension 5 proton decay operators. Inclusion of SU(5) breaking effects is essential in order to obtain non-vanishing CP phase as well as correct lepton masses. The resulting mass matrix has a texture structure in which texture zeros are a consequence of extremely small overlap of the wave functions. Our approach requires explicit breaking of supersymmetry in the extra dimension, which can be realized in (de)constructing extra dimension.

In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and indistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the Lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group . We explain why we have chosen E₆ as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the Standard Model with only three fermion families. We suggest a possible symmetry breaking pattern of that could explain quark, lepton and neutrino masses and mixings.

We present a preliminary study of the fermion-mass generation in the Einstein-Cardan gravitational theory.

Flavor violating processes in the quark and lepton sectors are investigated within a realistic supersymmetric SO(10)×A₄ grand unification model. By employing exotic heavy fermion fields, this model successfully describes various features of the fermion masses and mixings including large neutrino mixings accompanied by small quark mixings. In this model the flavor violation is induced at GUT scale, at which A₄ flavor symmetry is broken, as a consequence of the large mixings of the light fermion fields with these exotic heavy fields. The stringent experimental constraint from μ→eγ decay rate necessitates a high degree of degeneracy of the supersymmetry breaking soft scalar masses of the exotic heavy fields and supersymmetric scalar partners of the light fermion fields. The choice of slepton masses of order 1 TeV is found to be consistent with the constraints from branching ratio of μ→eγ and with all other flavor changing neutral current processes being sufficiently suppressed.

It is shown that if, from the starting point of a universal rank-one mass matrix long favored by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only six real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles θ₁₂, θ₁₃, θ₂₃ in ν-oscillation, and the masses m_c, m_μ, m_e) agree well with experiment, mostly to within experimental errors; four others (m_s, m_u, m_d, m_ν2), the experimental values for which can only be inferred, agree reasonably well; while two others (m_ν1, δ_CP for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass m_νR and (ii) the strong CP angle θ inherent in QCD. One notes in particular that the output value for sin² 2 θ₁₃ from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit two new testable constraints: (i) that θ₂₃ must depart from its "maximal" value: sin² 2 θ₂₃ ~ 0.935 ±0.021, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only |sinδ_CP| ≤ 0.31 if not vanishing altogether.

In a warped 6D world with an extra two-dimensional sphere, we propose an exactly solvable model for fermion masses with zero mode. The warp factor is given by ϕ(θ, φ) = sin θcos φ, which is a solution to the 6D Einstein equation with the bulk cosmological constant Λ and the energy–momentum tensor of the bulk matter fields. Our model provides another possibility of obtaining fermion zero mode, rather than traditional model based on Dirac's monopole.

Grand Unified Theories (GUTs) are attractive candidates for more fundamental elementary particle theories. They cannot only unify the Standard Model (SM) interactions but also different types of SM fermions, in particular quarks and leptons, in joint representations of the GUT gauge group. We discuss how comparing predictive supersymmetric GUT models with the experimental results for quark and charged lepton masses leads to constraints on the SUSY spectrum. We show an example from a recent analysis where the resulting superpartner masses where found just beyond the reach of LHC Run 1, but fully within the reach of a 100 TeV $pp$ collider.

We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that correct leptonic mixing angles can be generated with normal hierarchical neutrino masses if the relation between mixing angle and mass ratio is restricted to 1–2 and 1–3 mixing in both charged lepton and neutrino sectors leaving the 2–3 mixing angles as free parameters. We then restrict the lightest neutrino mass as well as the difference between 2–3 mixing angles in charged lepton and neutrino sectors from the requirement of producing correct leptonic mixing angles. We constrain the lightest neutrino mass to be around 0.002 eV and leptonic Dirac CP phase ${\delta }_{\mathrm{\text{CP}}}$ such that ${sin}^2{\delta }_{\mathrm{\text{CP}}}\sim (0.35\text{–}0.50)$. We also construct the leptonic mass matrices in terms of 2–3 mixing angles and lightest neutrino mass and briefly comment on the possibility of realizing texture zeros in the neutrino mass matrix.

Grand Unified Theories (GUTs) are attractive candidates for more fundamental elementary particle theories. They cannot only unify the Standard Model (SM) interactions but also different types of SM fermions, in particular quarks and leptons, in joint representations of the GUT gauge group. We discuss how comparing predictive supersymmetric GUT models with the experimental results for quark and charged lepton masses leads to constraints on the SUSY spectrum. We show an example from a recent analysis where the resulting superpartner masses where found just beyond the reach of LHC Run 1, but fully within the reach of a 100 TeV pp collider.