The String Unufication of Gauge Cuoplings and Gauge Kinetic Mixings

In the superstring models we have not only the complete {\bf 27} multiplets of $E_6$ but also extra incomplete $({\bf 27}+{\overline {\bf 27}})$ chiral supermultiplets being alive at low energies. Associated with these additional multiplets, when the gauge symmetry contains more than one $U(1)$ gauge group, there may exist gauge kinetic mixings among these $U(1)$ gauge groups. In such cases the effect of gauge kinetic mixings should be incorporated into the study of unification of gauge couplings. We study these interesting effects systematically in these models. The string threshold effect is also taken into account. It is found that in the four-generation models we do not have a advisable solution of string unification of gauge couplings consistent with experimental values at the electroweak scale. We also discuss the possible scenarios to solve this problem.Comment: 27 pages, LaTeX, DPNU-93-16, AUE-03-9

Quark CP-Phase and Froggatt-Nielsen Mechanism

On the basis of the Froggatt-Nielsen mechanism, we study quark flavor mixings in the $SU(6) \times SU(2)_R$ model. The characteristic structure of the CKM matrix is attributed to the hierarchical effective Yukawa couplings due to the Froggatt-Nielsen mechanism and also to the state-mixings beyond the MSSM. We elucidate the detailed form of the CKM matrix elements and find interesting relations between the \textit{CP} violating phase and three mixing angles. Taking the existing data of three mixing angles, we estimate the quark \textit{CP}-phase at $\delta = (75 \pm 3)^{\circ}$. This result is in accord with observations.Comment: 14 pages, no figure. To be published in Physics Letters B. Several sentences are added. arXiv admin note: text overlap with arXiv:1210.376

The Aligned SU(5)×U(1)2SU(5) \times U(1)^2 Model

In Calabi-Yau string compactification, it is pointed out that there exists a new type of $SU(5) \times U(1)^2$ model (the aligned $SU(5) \times U(1)^2$ model) in which the $SU(5)$ differs from the standard $SU(5)$ and also from the flipped $SU(5)$. With the aid of the discrete symmetry suggested from Gepner model, we construct a simple and phenomenologically interesting three-generation model with the aligned $SU(5) \times U(1)^2$ gauge symmetry. The triplet-doublet splitting problem can be solved. It is also found that there is a realistic solution for solar neutrino problem and for the $\mu$-problem. At low energies this model is in accord with the minimal supersymmetric standard model except for the existence of singlet fields with masses of $O(1)$TeV.Comment: LaTeX 24 page

Students with dyslexia: research projects at Northumbria University

Northumbria University has about 700 registered disabled students, the majority of whom (around 58 per cent) are registered as having dyslexia and account for approximately two per cent of the total student population. Therefore dyslexic students represent the largest single group of disabled students and are those with whom most staff are likely to come into contact. The research authors were keen to ascertain whether there was a difference in academic performance between dyslexic and non-dyslexic students in respect of degree classification and assignment marks and to investigate whether dyslexic students generally felt supported in their academic studies. Research involved both qualitative and quantitative strands and the areas explored include pre expectations; general support throughout study; methods, flexibility and clarity of learning tasks, in particular assessment and levels of performance throughout and at the end of their study. This research is ongoing, however, findings have proved invaluable as a basis in the construction of good practice guidelines in dealing with the pedagogic needs of this diverse student grou

The Weak-Scale Hierarchy and Discrete Symmetries

In the underlying Planck scale theory we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the $\mu$-problem and the tadpole problem can be solved simultaneously without relying on some fine-tuning of parameters. Instead, it is required that doublet Higgs and color-triplet Higgs fields reside in different irreducible representations of the gauge symmetry group at the Planck scale and that they have distinct charges of the discrete symmetry group.Comment: 13 pages, LATEX, 1 figures(not included, available on request by fax or Postscript file

Semidirect product gauge group [SU(3)c×SU(2)L]⋊U(1)Y[SU(3)_{\rm c} \times SU(2)_{\rm L}]\rtimes U(1)_{\rm Y} and quantization of hypercharge

In the Standard Model the hypercharges of quarks and leptons are not determined by the gauge group $SU(3)_{\rm c} \times SU(2)_{\rm L} \times U(1)_{\rm Y}$ alone. We show that, if we choose the semidirect product group $[SU(3)_{\rm c} \times SU(2)_{\rm L}] \rtimes U(1)_{\rm Y}$ as its gauge group, the hyperchages are settled to be $n/6 \mod {\mathbb{Z}}\;(n = 0,1,3,4)$. In addition, the conditions for gauge-anomaly cancellation give strong constraints. As a result, the ratios of the hypercharges are uniquely determined and the gravitational anomaly is automatically canceled. The standard charge assignment to quarks and leptons can be properly reproduced. For exotic matter fields their hypercharges are also discussed.Comment: 17 pages, 2 tables; LaTeX; typos corrected, references added or replaced, argument in Secs. 2 and 3 revised, results unchanged; to be published in Phys. Rew.

SU(3)L⋊(Z3×Z3)SU(3)_{\rm L} \rtimes (\mathbb{Z}_3 \times \mathbb{Z}_3) gauge symmetry and Tri-bimaximal mixing

We study an effective gauge theory whose gauge group is a semidirect product $G = G_c \rtimes \mathit{\Gamma}$ with $G_c$ and $\mathit{\Gamma}$ being a connected Lie group and a finite group, respectively. The semidirect product is defined through a projective homomorphism $\gamma$ (i.e., homomorphism up to the center of $G_c$) from $\mathit{\Gamma}$ into $G_c$. The (linear) representation of $G$ is made from $\gamma$ and a projective representation of $\mathit{\Gamma}$ over $\mathbb{C}$. To be specific, we take $SU(3)_L$ as $G_c$ and $\mathbb{Z}_3 \times \mathbb{Z}_3$ as $\mathit{\Gamma}$. It is noticed that the irreducible projective representations of $\mathit{\Gamma}$ are three-dimensional in spite of its Abelian nature. We give a toy model on the lepton mixing which illustrates the peculiar feature of such gauge symmetry. It is shown that under a particular vacuum alignment the tri-bimaximal mixing matrix is reproduced.Comment: 10 page