arXiv subjects
Publications and source records attributed to E. I. Lashin.
We study a specific texture of the neutrino mass matrix, namely the models with one $2\times 2$ subdeterminant equal to zero. We carry out a complete phenomenological analysis with all possible relevant correlations. Every pattern of the six possible ones is found able to accommodate the experimental data, with three cases allowing also for non-invertible mass matrices. We present symmetry realizations for all the models.
We examine the possibility that a certain class of neutrino mass matrices, namely those with two independent vanishing minors in the flavor basis, regardless of being invertible or not, is sufficient to describe current data. We compute generic formulae for the ratios of the neutrino masses and for the Majorana phases. We find that seven textures with two vanishing minors can accommodate the experimental data. We present an estimate of the mass matrix for these patterns. All the possible textures can be dynamically generated through the seesaw mechanism augmented with a discrete Abelian symmetry.
We propose a new texture for the light neutrino mass matrix. The proposal is based upon imposing zero-trace condition on the two by two sub-matrices of the complex symmetric Majorana mass matrix in the flavor basis where the charged lepton mass matrix is diagonal. Restricting the mass matrix to have two traceless sub-matrices may be found sufficient to describe the current data. Eight out of fifteen independent possible cases are found to be compatible with current data. Numerical and some approximate analytical results are presented.
We consider a special class of the tetrad theory of gravitation which can be considered as a viable alternative gravitational theories. We investigate cosmological models based on those theories by examining the possibility of fitting the recent astronomical measurement of supernova Ia magnitude versus shift. Our investigations result in a reasonable fit for the supernova data without introducing a cosmological constant. Thus, cosmological models based on tetradic theory of gravitation can provide alternatives to dark energy models.
The CP conserved non leptonic $K\to πππ$ decays are discussed within the chiral quark model, including chiral perturbation theory corrections. All amplitudes are parameterized in terms of quark and gluon condensate and the constituent quark mass. The same values for these parameters that can be obtained by a fit of the $ΔI = 1/2$ rule in $K\to 2 π$ give a reasonably good fit in the $K\to 3 π$ case. We compare with the work of other groups.
We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.
A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.
We show that for the triple well potential with non-equivalent vacua, instantons generate for the low lying energy states a singlet and a doublet of states rather than a triplet of equal energy spacing. Our energy splitting formulae are also confirmed numerically. This splitting property is due to the presence of non-equivalent vacua. A comment on its generality to multi-well is presented.
The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central well and the two other states are distributed only among the left and right well in anti-symmetric and symmetric way respectively. Due to the tunneling effects the energy eigenvalue of the ground state is approximately equal to the ground state energy for a harmonic oscillator localized at the central well, while the two others are nearly degenerate with approximate values equal to the ground state energy of a harmonic oscillator localized at the left or right well. The resulting pattern of the spectra are confirmed numerically. The failure of the instantonic approach recently applied for predicting the correct spectra is commented
We present Feynman rules for the strong and $ΔS = 1$ weak chiral Lagrangian which are relevant for calculating $K\to πππ$ decay amplitudes. Feynman rules for this specific case turn out to be too lengthy to be included in a research paper. Since they are not standard, we decide to include them in a separate article, making them available for any one who is interested in this kind of calculation. Any found mistakes and (/or) comments are warmly welcome so that corrections can be made.
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown that the method is capable of producing to a high accuracy the eigenvalues, eigenfunctions, and the expectation values $ $ of the corresponding unbounded ones as the separation between the two infinite walls becomes large.
Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between their minimal neighborhoods. We introduce notations and elementary facts known as Alexandroff space. The family of minimal neighborhoods forms a unique minimal base. We consider T_0 spaces. We give a link between finite $T_0$ spaces and the related partial order. Finally, we study some properties of multifunctions and their relationships with connected ordered topological spaces.
A scenario based on the TopFlavor model is presented to explain the origin of a light sterile neutrino as indicated by all combined neutrino oscillation experiments. The model is phenomenologically well motivated and compatible with all available low-energy data. The derived nuetrino mass matrix can qualitatively explain the observed hierarchy in the neutrino mass splittings as indicated by the neutrino oscillation data. Numerical results are obtained for special cases.
After updating the determination of the combination of Kobayashi-Maskawa elements $ \Im V_{td}V^*_{ts}$ according to our new estimate of the parameter $\hat B_K$, we study the CP-violating ratio $ε'/ε$ by means of hadronic matrix elements computed to $O(p^4)$ in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some $O(p^2)$ terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio $ε'/ε$ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find $ε'/ε= 1.7 ^{+1.4}_{-1.0} \times 10^{-3}$. Values positive and of the order of $10^{-3}$ are therefore preferred.
We calculate the hadronic matrix elements to $O(p^4)$ in the chiral expansion for the ($ΔS =1$) $K^0 \to 2 π$ decays and the ($ΔS=2$) $\bar K^0$-$K^0$ oscillation. This is done within the framework of the chiral quark model. The chiral coefficients thus determined depend on the values of the quark and gluon condensates and the constituent quark mass. We show that it is possible to fit the $ΔI =1/2$ rule of kaon decays with values of the condensates close to those obtained by QCD sum rules. The renormalization invariant amplitudes are obtained by matching the hadronic matrix elements and their chiral corrections to the short-distance NLO Wilson coefficients. For the same input values, we study the parameter $\hat B_K$ of kaon oscillation and find $\hat B_K = 1.1 \pm 0.2$. As an independent check, we determine $\hat B_K$ from the experimental value of the $K_L$-$K_S$ mass difference by using our calculation of the long-distance contributions. The destructive interplay between the short- and long-distance amplitudes yields $\hat B_K = 1.2 \pm 0.1$, in agreement with the direct calculation.
We compute the $\widehat B_K$ parameter and the mass difference $ΔM_{LS}$ of the $K^0-\bar K^0$ system by means of the chiral quark model. The chiral coefficients of the relevant $ΔS=2$ and $ΔS=1$ chiral lagrangians are computed via quark-loop integration. We include the relevant effects of one-loop corrections in chiral perturbation theory. The final result is very sensitive to non-factorizable corrections of $O(α_S N)$ coming from gluon condensation. The size of the gluon condensate is determined by fitting the experimental value of the amplitude $K^+ \to π^+π^0$. By varying all the relevant parameters we obtain $\widehat{B}_K= 0.87 \pm 0.33\ .$ We evaluate within the model the long-distance contributions to $ΔM_{LS}$ induced by the double insertion of the $ΔS = 1$ chiral lagrangian and study the interplay between short- and long-distance amplitudes. By varying all parameters we obtain $ΔM_{LS}^{th}/ΔM_{LS}^{exp} = 0.76 ^{+0.64}_{-0.34} .$ Finally, we investigate the phenomenological constraints on the Kobayashi-Maskawa parameter Im $λ_t$ entering the determination of $ε'/ε$.
We use the chiral quark model to estimate the coefficients of the weak chiral lagrangian as obtained from the bosonization of the ten relevant operators of the $ΔS = 1$ effective quark lagrangian. All contributions of order $N_c^2$ as well as $N_c$ and $α_s N_c$ are included. The chiral coefficients are given in terms of $f_π$, the quark and gluon condensates and the scale-dependent NLO Wilson coefficients of the corresponding operators. In addition, they depend on the constituent quark mass $M$, a parameter characteristic of the model. The $γ_5$-scheme dependence of the chiral coefficients, computed via dimensional regularization, and the Fierz transformation properties of the operator basis are discussed in detail. We apply our result to the evaluation of the hadronic matrix elements for the decay $K^0 \rightarrow 2 π$, consistently including the renormalization induced by the meson loops. The effect of this renormalization is sizable and introduces a long-distance scale dependence that matches in the physical amplitudes the short-distance scale dependence of the Wilson coefficients.
We give the complete $O(p^2)$ bosonization of the electroweak Penguin operators $Q_{7,8}$ and compare the result with that of the gluon Penguin operators $Q_{5,6}$. We find that, in addition to the usual (constant and current-current) parts, there are three new terms not discussed previously in the literature. Two of these are present in the factorization approximation and should be included in the standard definition of the $B_{7,8}$-factors. The impact of these corrections on the direct $CP$-violating parameter $\varepsilon '/\varepsilon$ is briefly discussed.