Regular Series


Vol. 36 (2005), No. 6, pp. 1901 – 2164


Diagonal Matrix Elements of the Effective Hamiltonian for \(K^{0}-\bar {K}^{0} \) System in One Pole Approximation

abstract

We study the properties of time evolution of the \(K^{0}\)–\(\bar {K}^{0} \) system in spectral formulation. Within the one-pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee–Oehme–Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT-invariant but CP-noninvariant.


Refinement of the Formulae for the Casimir Operators of \(w\mathfrak {u}(N)\) and Some of Its Contractions

abstract

The Casimir operators of the semidirect product Lie algebras \(w\frak {u}(N)\) and some contractions are obtained by purely determinantal methods, without involving the standard insertion method of Quesne.


Quantum Dynamics of Particles in a Discrete Two-Branes World Model: Can Matter Particles Exchange Occur Between Branes?

abstract

In a recent paper, a model for describing the quantum dynamics of massive particles in a non-commutative two-sheeted spacetime was proposed. This model considers a universe made with two spacetime sheets embedded in a 5D bulk where the fifth dimension is restricted to only two points. It was shown that this construction has several important consequences for the quantum dynamics of massive particles. Most notably, it was demonstrated that a coupling arises between the two sheets allowing matter exchange in presence of intense magnetic vector potentials. In this paper, we show that non-commutative geometry is not absolutely necessary to obtain such a result since a more traditional approach allows one to reach a similar conclusion. The fact that two different approaches provide similar results suggests that standard matter exchange between branes might finally occur contrary to conventional belief.


Comparison of Two Stationary Spherical Accretion Models

abstract

The general relativistic gas accretion onto a black hole is investigated in which the flow is steady and spherically symmetrical. Two models with different equations of state are compared. Numerical calculations show that the predictions of the models are similar in most aspects. In the ultrarelativistic regime the allowed band of the speed of sound and the mass accretion rate can be markedly different.


Pattern Formation in a Stochastic Model of Cancer Growth

abstract

We investigate noise-induced pattern formation in a model of cancer growth based on Michaelis–Menten kinetics, subject to additive and multiplicative noises. We analyse stability properties of the system and discuss the role of diffusion and noises in the system’s dynamics. We find that random dichotomous fluctuations in the immune response intensity along with Gaussian environmental noise lead to emergence of a spatial pattern of two phases, in which cancer cells, or, respectively, immune cells predominate.


Stationary Distributions of a Noisy Logistic Process

abstract

Stationary solutions to a Fokker–Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an unlimited growth. Positive correlations between the noises can lead to a minimum of the variance of the process and to the stochastic resonance if the system is additionally driven by a periodic signal.


\(E_6\) Multiplets and Unification in Extra Dimensions

abstract

We study the effect of all matter multiplets contained in 27 representation of \(E_6\) GUT on gauge coupling unification in extra dimensions. Extra members of 27 multiplets of all three generations have their ‘zero modes’ near \(m_{\rm t}\) such that they can be directly probed. From TeV scale onwards extra dimensions open up, theory becomes \(N=2\) supersymmetric and gauge couplings unify or they do not, depending on how we distribute matter fields and gauge fields in bulk and brane. We find three such possible embeddings which will lead to perfect gauge coupling unification below 100 TeV region for one extra dimension and lower than that if number of extra dimensions is larger.


\(a_0\rightarrow \pi ^0\eta \) Decay in QCD Sum Rules

abstract

We investigate the \(a_0\rightarrow \pi ^0\eta \) decay in the framework of QCD sum rules. We estimate the coupling constant \(g_{a_0\pi \eta }\) which plays an essential role in the analysis of physical processes involving \(a_0(980)\) meson. We also estimate the coupling constant \(g_{a_0\pi \eta }\) by using the experimental limits of the decay width of the \(a_0\rightarrow \pi ^0\eta \) decay and compare with our QCD sum rule result.


The \(B\to \pi \pi ,\ \pi K\) Puzzles in the Light of New Data: Implications for the Standard Model New Physics and Rare Decays

abstract

Recently, we developed a strategy to analyze the \(B\to \pi \pi ,\pi K\) data. We found that the \(B\to \pi \pi \) measurements can be accommodated in the Standard Model (SM) through large non-factorizable effects. On the other hand, our analysis of the ratios \(R_{\rm c}\) and \(R_{\rm n}\) of the CP-averaged branching ratios of the charged and neutral \(B\to \pi K\) modes, respectively, suggested new physics (NP) in the electroweak penguin sector, which may have a powerful interplay with rare decays. In this paper, we confront our strategy with recent experimental developments, addressing also the direct CP violation in \(B_d\to \pi ^\mp K^\pm \), which is now an established effect, the relation to its counterpart in \(B^\pm \to \pi ^0K^\pm \), and the first results for the direct CP asymmetry of \(B_d\to \pi ^0\pi ^0\) that turn out to be in agreement with our prediction. We obtain hadronic \(B\to \pi \pi ,\pi K\) parameters which are almost unchanged and arrive at an allowed region for the unitarity triangle in perfect accordance with the SM. The “\(B\to \pi K\) puzzle” persists, and can still be explained through NP, as in our previous analysis. In fact, the recently observed shifts in the experimental values of \(R_{\rm c}\) and \(R_{\rm n}\) have been predicted in our framework on the basis of constraints from rare decays. Conversely, we obtain a moderate deviation of the ratio \(R\) of the CP-averaged \(B_d\to \pi ^\mp K^\pm \) and \(B^\pm \to \pi ^\pm K\) rates from the current experimental value. However, using the emerging signals for \(B^\pm \to K^\pm K\) modes, this effect can be attributed to certain hadronic effects, which have a minor impact on \(R_{\rm c}\) and do not at all affect \(R_{\rm n}\). Our results for rare decays remain unchanged.


Lepton Generation-Weighting Factors and Neutrino Mass Formula

abstract

A candidate for the simple empirical neutrino mass formula is found, predicting the mass proportion \(m_1 : m_2 : m_3 = 0 : 4 : 24\) and so, the mass ratio \(\Delta m^2_{32}\) / \(\Delta m^2_{21} = 35\) not inconsistent with its experimental estimate. It involves only one free parameter and three generation-weighting factors suggested by the successful mass formula found previously for charged leptons (the simplest neutrino mass formula would predict \(m_1 : m_2 : m_3 = 1 : 4 : 24\) and thus, \(\Delta m^2_{32}\) / \(\Delta m^2_{21} \simeq 37\)). A more involved variation of this equation follows from a special seesaw neutrino model with specifically “conspiring”  Dirac and Majorana neutrino mass matrices. In this variation \(m_1 : m_2 : m_3 \simeq \varepsilon ^{(\nu )} : 4 : 24\), where \(O(\varepsilon ^{(\nu )}) = 10^{-2}\).


A Scale-Invariant “Discrete-Time” Balitsky–Kovchegov Equation

abstract

We consider a version of QCD dipole cascading corresponding to a finite number \(n\) of discrete \(\Delta Y\) steps of branching in rapidity. Using the discretization scheme preserving the holomorphic factorizability and scale-invariance in position space of the dipole splitting function, we derive an exact recurrence formula from step to step which plays the rôle of a “discrete-time” Balitsky–Kovchegov equation. The BK solutions are recovered in the limit \(n=\infty \) and \(\Delta Y=0.\)


Pion-\(^{12}\)C Nucleus Optical Potential

abstract

Elastic and inelastic cross sections for pion scattering on \(^{12}\)C at pion kinetic energy ranging from 50 to 260 MeV are computed using three independent methods of \(\pi ^{\pm }\)-nucleus optical potential, the 3\(\alpha \)-particle model of the nucleus, the equivalent local Kisslinger potential, and the Laplacian one. Reasonable fits to the measured values are obtained for \(^{12}\)C without adjusting free parameters. The ability of these methods to account for elastic, inelastic, total, and reaction cross section data are somewhat similar. The Kisslinger-based local potential is the more suitable for describing the elastic and inelastic cross sections of \(\pi ^{\pm }\)-nucleus scattering. It seems that the 3\(\alpha \)-particle model of \(^{12}\)C is not useful in the description of pion scattering on \(^{12}\)C at least in the \({\mit \Delta }\)-resonance region.


Disentangling Spatial and Flow Anisotropy

abstract

Two generalisations of the blast-wave model to non-central nuclear collisions are constructed, and elliptic flow as well as azimuthal dependence of correlation radii are calculated. Particular attention is paid to how different azimuthal dependences of transverse flow direction can cause qualitatively different anisotropic fireballs to give same \(v_2\) as a function of the transverse momentum. The simultaneous dependence of \(v_2\) and the oscillation of correlation radii on both spatial and flow anisotropy is studied in great detail.


A Study on Even–Even Hf Isotopes Using the Cluster Model

abstract

In the present work the spectra of even–even Hf isotopes are studied through the selecting of core–cluster decomposition of the parent nucleus. The considered partition should give internal stability of the core–cluster combination. The modified Woods–Saxon and Coulomb potentials are used to reproduce the spectra of even–even Hf isotopes where the core-radius is taken as a free parameter. The theoretical calculations of the excitation energies and the transition probabilities \(B(E2)\) of the ground state band are compared to the experimental data of the considered Hf isotopes. The obtained results reflect the ability of describing the pure rotational ground state band of even–even Hf isotopes through the core–cluster decomposition model.


Hamiltonian Structures for Pais–Uhlenbeck Oscillator

abstract

The Hamiltonian structures for quartic oscillator are considered. All structures admitting quadratic Hamiltonians are classified.


Canonical Gauge-Invariant Variables for Scalar Perturbations in Synchronous Coordinates

abstract

Under an appropriate change of the perturbation variable Lifshitz–Khalatnikov propagation equations for the scalar perturbation reduce to d’Alembert equation. The change of variables is based on the Darboux transform.


all authors

V.V. Karbanovski, R.I. Maxioma, M.S. Bogdanov, O.V. Nefiodova, Yu.V. Kolesnikova, E.O. Panaite

On Status of Constant \(f\) in the Conformal Poincaré Gauge Theory of Gravitation

abstract

The status of constant \(f\) is analysed in the framework of the Conformal Poincaré Gauge Theory of gravitation. It is shown, that for the Morris–Thorne wormholes and the Bianchi I cosmology this constant should have the different signs. A possible interpretation of the obtained results is discussed.


Density Perturbations in Open Models of Early Universe with Positive Cosmological Constant

abstract

The analytical solutions of the density perturbation equation in the Friedman–Lemaître–Robertson–Walker (FLRW) open cosmological models with radiation and positive cosmological constant are provided. The perturbations are of two types: the first propagating as acoustical waves, and the second of non-wave nature. It is shown that there occurs dispersion on curvature and cosmological constant for acoustical perturbations. The wave solutions have anomalous dispersion.


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