abstract

We investigate a mechanical system consisting of infinite number of harmonically coupled pendulums which can impact on two rigid rods. Because of gravitational force the system has two degenerate ground states. The related topological kink, likely the simplest one presented in literature so far, is a compacton, that is it has strictly finite extension. In the present paper we elucidate the relation of such system with sine-Gordon model. Also, solutions describing waves with large amplitude, and an asymptotic formula for the width of the kink are obtained.

abstract

The entanglement at finite temperatures is analyzed by using thermal models for colored quarks making up the hadron physical states. We have found that these quantum correlations entirely vanish at \(T_{\rm c}\geq m_q\) / \(\ln (1.5)\). For temperatures larger than \(T_{\rm c}\) the correlations are classical. We have also worked out the entanglement for the transverse Ising spin chain. In dependence on both temperature \(T\) and transverse field \(\lambda \) we can identify a certain region, where the quantum effects are likely to dominate the system. We suggest the mutual information as a quantitative measure for the correlations in the ground state.

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Charmless \(B \rightarrow PP\) decays are studied using flavour SU(3) symmetry. Amplitude with charming penguin topology is considered for two cases: with zero and with arbitrary strong phase. Two sets of data (an older and the most recent one) are used in the fits, so that the stability of the fits is tested. It is shown that within the present uncertainties in the data the parameters of the fit may be significantly modified, especially the \(\gamma \) angle. The fits indicate the strong phase of the charming penguin amplitude to be around \(\pm 20^{\mathrm o}\).

abstract

We investigate perturbative unitarity constraints in a model for a singlet scalar dark matter candidate. Considering elastic two particle scattering processes of the Higgs particle and the dark matter candidate, a real Klein–Gordon scalar field, perturbative unitarity constrains the self-couplings of the scalar fields.

abstract

The model-independent determination of the Higgs-boson CP properties at the Photon Collider at TESLA has been studied in detail, for masses between 200 and 350 GeV, using realistic luminosity spectra and detector simulation. We consider a generic model with the CP violating Higgs tensor couplings to gauge bosons. We introduce a new variable describing angular distributions of the secondary \(WW\) and \(ZZ\) decay products which is very sensitive to the CP properties of the Higgs-boson. Understanding of the detector performance turns out to be crucial, as the influence of the acceptance corrections is similar to the effects of CP violation. From the combined measurement of invariant mass distributions and various angular distributions the phase describing a CP violation can be determined to about 50 mrad after one year of Photon Collider running.

abstract

Using the techniques developed by Ponsot and Teschner we derive the formulae for analytic continuation of the general 4-point conformal block.

abstract

Two sets of four \(3\times 3\) matrices 1\(^{(3)}, \varphi _1, \varphi _2, \varphi _3\) and 1\(^{(3)}, \,\mu _1, \,\mu _2, \,\mu _3\) are constructed, forming two unitarily isomorphic reducible representations \(\underline {3}\) of the group \(Z_2\times Z_2\) called often the four-group. They are related to each other through the effective neutrino mixing matrix \(U\) with \(s_{13} = 0\) and generate four discrete transformations of flavor and mass active neutrinos, respectively. If and only if \(s_{13} = 0\), the generic form of effective neutrino mass matrix \(M\) becomes invariant under the subgroup \(Z_2\) of \(Z_2\times Z_2\) represented by the matrices 1\(^{(3)}\) and \(\varphi _3\). In the approximation of \(m_1 = m_2\), the matrix \(M\) becomes invariant under the whole \(Z_2\times Z_2\) represented by the matrices 1\(^{(3)}, \,\varphi _1, \,\varphi _2, \,\varphi _3\). The effective neutrino mixing matrix \(U\) with \(s_{13} = 0\) is always invariant under the whole \(Z_2\times Z_2\) represented in two ways, by the matrices 1\(^{(3)}, \varphi _1,\;\varphi _2,\;\varphi _3\) and 1\(^{(3)},\;\mu _1, \;\mu _2,\;\mu _3\).

abstract

We compute the two-loop corrections to the thermodynamical pressure of an SU(2) Yang–Mills theory being in its electric phase. Our results prove that the one-loop evolution of the effective gauge coupling constant is reliable for any practical purpose. We thus establish the validity of the picture of almost noninteracting thermal quasiparticles in the electric phase. Implications of our results for the explanation of the large-angle anomaly in the power spectrum of temperature fluctuations in the cosmic microwave background are discussed.

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It is shown that the wounded nucleon model describes very well the recent PHOBOS data on particle production in \(D\)–Au collisions at 200 GeV. Contribution to particle production from a single wounded nucleon is determined. A two-component model is formulated and shown to account for most of the important features of the data.

abstract

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction patterns are calculated analytically both using “cut and project” and “average unit cell” method, taking advantage of the physical space properties of the structure.

abstract

One of great mysteries of the Tunguska event is its genetic impact. Some genetic anomalies were reported in the plants, insects and people of the Tunguska region. Remarkably, the increased rate of biological mutations was found not only within the epicenter area, but also along the trajectory of the Tunguska Space Body (TSB). At that no traces of radioactivity were found, which could be reliably associated with the Tunguska event. The main hypotheses about the nature of the TSB, a stony asteroid, a comet nucleus or a carbonaceous chondrite, readily explain the absence of radioactivity but give no clues how to deal with the genetic anomaly. A choice between these hypotheses, as far as the genetic anomaly is concerned, is like to the choice between “blue devil, green devil and speckled devil”, to quote late Academician N.V. Vasilyev. However, if another mysterious phenomenon, electrophonic meteors, is evoked, the origin of the Tunguska genetic anomaly becomes less obscure.