Nonlocal Yukawa interaction and fermion mass-scale nonlocality

A nonlocal Yukawa interaction between the Higgs boson and the fundamental fermions is introduced. A simple form of this interaction allows us to calculate a particular mass-scale nonlocality for all fundamental fermions. A prediction is given for the mass of the Higgs boson (m _H ≈ 200 GeV).     

Finite-N fluctuation formulas for random matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ _j ^N =1 (x _j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ _j ^N =1 (θ _j ?π) and ? Σ _j ^N =1 log 2 |sinθ _j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.     

Ambiguities in zeroth order fermion mass matrices

The six quark Weinberg-Salam model with the symmetry of the three generation permutation group S₃ has an extra O(2) pseudosymmetry when the Higgs fields lie in an S₃ doublet. We use this model as a prototype to question the derivation of zeroth order relations between fermion mixing angles and fermion masses.     

The fermion mass matrices near a fixed point

The structure of the fermion mass matrices is investigated in the neighbourhood of an infrared fixed point with special emphasis on the mixing angles which determine the charged current couplings. We find that it is necessary to introduce a fourth generation of quarks whose masses are predicted. The mass of the top quark is close to 35 GeV. The solution for a two family problem is found, which predicts very small charged current couplings of the very heavy to the lighter quarks.     

On determination of the analytical formulas for reduction matrices of tetrahedral-symmetry molecules

The formulas for the elements of ^(J)G matrices (J = 0, 1, 2 ?) determining reduction of irreducible representations D^(Jg) of the group 0(3) to the irreducible representations D^(Γ) of the T_d group have been obtained in an analytical form. It was shown how the transition was made from the G matrices of this paper to those determined by Moret-Bailly's basis [Cah. Phys., 15, 237–314 (1961)].     

Eigenvalue spectra of random matrices for neural networks

The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances.     

New formulas and predictions for running fermion masses at higher scales in SM, 2HDM, and MSSM

Including contributions of scale-dependent vacuum expectation values, we derive new analytic formulas and obtain substantially different numerical predictions for the running masses of quarks and charged leptons at higher scales in the SM, 2HDM and MSSM. These formulas exhibit significantly different behaviours with respect to their dependence on gauge and Yukawa couplings from those derived earlier. At one-loop level, the masses of the first two generations are found to be independent of the Yukawa couplings of the third generation in all three effective theories in the small mixing limit. Analytic formulas are also obtained for the running of in 2HDM and MSSM. Other numerical analyses include a study of the third generation masses at high scales as functions of the low-energy values of and the SUSY scale GeV. Received: 1 October 2000 / Revised version: 11 January 2001 / Published online: 12 April 2001     

Microscopic theory of Raman spectra of heavy fermion systems in the normal state

In this communication, we develop the microscopic theory of Raman spectra of the heavy fermion (HF) system in its normal state at low temperatures. The system is described by the Periodic Anderson Model along with the coupling of the phonon to the bare f-electrons as well as to the hybridization between the conduction band and the f-electrons. The phonon Green's function and the phonon self-energy are evaluated by the equations of motion method of Zubarev. The phonon spectral density function (SDF) is evaluated at low temperatures in the long wavelength limit. The calculation depicts three Raman active modes one of which corresponds to the strongly renormalized phonon at the value of the reduced frequency ) around 0.57 denoted as (P₀), and the other two at low reduced frequencies of and in the SDF. The effect of electron–phonon (EP) coupling on Raman excitation peaks is investigated to probe the nature of the electronic states of the system.     

Different kind of textures of Yukawa coupling matrices in the two Higgs doublet model type III

The quark mass matrices ansätze proposed by Fritzsch, Du–Xing and Fukuyama–Nishiura in the framework of the general two Higgs doublet model are studied. The corresponding Yukawa matrices in the flavor basis in the various cases considered are discussed. The corresponding Cabibbo–Kobayashi–Maskawa matrix elements are computed in all cases and compared with their experimental values. The complex phases of the ansätze are taken into account, and the CP violating phase δ is computed. Finally, in order to observe the influence of the various kinds of texture of the Yukawa coupling matrices considered, some issues in the phenomenology of the two body decays of the top quark, the lightest Higgs boson and the charged Higgs boson are discussed.