It is shown that dimension five non-renormalizable interactions can produce light Dirac neutrinos in an extension of the minimal SU(5) GUT containing additional SU(5) singlets and global U(1) symmetries.

Recent developments on grand unified theories (GUTs) in the context of the LEP measurements of the coupling constants will be reviewed. The three coupling constants at the electroweak scale have been measured at LEP quite precisely. One can allow these couplings to evolve with energy following the renormalization group equations for the various groups and find out whether all the coupling constants meet at any energy. It was pointed out that the minimalSU (5) grand unified theory fails to satisfy this test. However, various extensions of the theory are still allowed. These extensions include (i) supersymmetricSU (5) GUT, with some arbitrariness in the susy breaking scale arising from the threshold corrections, (ii) non-susySU (5) GUTs with additional fermions as well as Higgs multiplets, which has masses of the order of TeV, and (iii) non-renormalizable effect of gravity with a fine tuned relation among the coupling constants at the unification energy. The LEP results also constrain GUTs with an intermediate symmetry breaking scale. By adjusting the intermediate symmetry breaking scale, one usually can have unification, but these theories get constrained. For example, the left-right symmetric theories coming from GUTs can be broken only at energies higher than about ∼ 10¹⁰GeV. This implies that if right handed gauge bosons are found at energies lower than this scale, then that will rule out the possibility of grand unification. Another recent interesting development on the subject, namely, low energy unification, will be discussed in this context. All the coupling constants are unified at energies of the order of ∼ 10⁸GeV when they are embedded in anSU (15) GUT, with some particular symmetry breaking pattern. But even in this case the results of the intermediate symmetry breaking scale remain unchanged.

Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to discriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet Higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.

First-principle calculations are carried out to explore magnesium composition-dependent structural and optoelectronic features of wurtzite Mg$_x$Zn$_{1−x}$Se ternary alloys. Analyses show a nearly linear enhancement in lattice constants (a0, c0) but a reasonably nonlinear reduction in bulkmodulus (B0)with increasingMg composition. Successive incorporation of Mg atom(s) in place of Zn in the w-ZnSe crystal results in three direct-band gap ($\Gamma–\Gamma$) semiconductor ternary alloys. The fundamental band gap shows fairly nonlinear enhancement with increasing Mgcomposition. Each of the considered wurtzite specimens is optically anisotropic. The computed components of the refractive index give uniaxial birefringence. Peaks in the dielectric function spectrum of all the specimens in the ultraviolet (UV) region are contributed exclusively or collectively by Se-4p to Mg-4s, 3p and Zn-5s, 4p electronic excitations. With the enhancement in the fundamental band gap, static optical constants ε1(0), n(0) and R(0) of the specimens reduce, while critical point energy in their ε2(ω), k(ω), σ(ω), α(ω) spectra enhances.