abstract

The paper describes implementation details of the Cellular Automaton Algorithm (CAA) [I. Abt, D. Emeliyanov, I. Gorbounov, I. Kisel, Nucl. Instrum. Methods Phys. Res. A490, 546 (2002)] for reconstruction of the particles’ tracks in Transition Radiation Detector (TRD), designed for Compressed Baryonic Experiment (CBM) which will operate at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany. The application and performance of cellular automaton method for standalone track finding and first level event selection are presented.

abstract

Using the point canonical transformation method, we show that a large class of solvable potentials with Position-Dependent Effective Mass (PDEM) can be obtained by using the internal functions which are introduced by Levai for solvable potentials with constant mass. We also obtain the explicit expressions for some of these solvable potentials and show that their eigenfunctions can be obtained in terms of the known special functions such as Jacobi, generalized Laguerre and Hermit polynomials.

abstract

We propose a parallel introduction to Galilean and Einsteinian relativity based on the causal structure and inertial motions. Galilean and Poincaré transformations, as objects secondary to the geometrical structure, are left aside.

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For any semisimple subalgebra \(\mathfrak {s}^{\prime }\) of exceptional Lie algebras \(\mathfrak {s}\) satisfying the constraint \({\rm rank}(\mathfrak {s}^{\prime })={\rm rank}(\mathfrak {s})-1\) we analyze the branching rules for the adjoint representation, and determine the compatibility of the components with Heisenberg algebras. The analysis of these branching rules allows to classify the contractions of exceptional algebras onto semidirect products of semisimple and Heisenberg Lie algebras. Applications to the Schrödinger algebras are given.

abstract

The question of the relative size of tree and penguin amplitudes is analyzed using the data on \(B \to \pi \pi \), \(B^+ \to \pi ^+K^{\,0}\), and \(B^+ \to K^{\,+}\bar {\,K}^{\,0}\) decays. Our discussion involves an estimate of SU(3) breaking in the final quark-pair-creating hadronization process. The estimate is based on Regge phenomenology, which many years ago proved very successful in the description of soft hadronic physics. Accepting the Regge prediction as solid, it is then shown that the relative size and phase of the two parts of the penguin amplitude can be unambiguously extracted from the data on the decays considered. This enables fixing the \(C\) / \(T\) ratio of “true” tree amplitudes, which — on the basis of the existing data — is shown to be small (of the order of 0.2).

abstract

In the framework of the quasi-particle diquark model, we explore the validation of describing the baryon as made up of a cluster of quark and diquark. The mass of the diquark is reduced in this quasi-particle approximation. The scalar and vector diquark masses are calculated for various quark combinations and these are used to estimate ground state and excited state baryon masses. The results are found to be in good agreement with experimental data.

abstract

We discuss the ICARUS T600 detector capabilities in electromagnetic shower reconstruction through the analysis of a sample of 212 events, coming from the 2001 Pavia surface test run, of hadronic interactions leading to the production of \(\pi ^{0}\) mesons. Methods of shower energy and shower direction measurements were developed and the invariant mass of the photon pairs was reconstructed. The (\(\gamma \),\(\gamma \)) invariant mass was found to be consistent with the value of the \(\pi ^0\) mass. The resolution of the reconstructed \(\pi ^0\) mass was found to be equal to 27.3%. An improved analysis, carried out in order to clean the full event sample from the events measured in the crowded environment, mostly due to the trigger conditions, gave a \(\pi ^0\) mass resolution of 16.1%, significantly better than the one evaluated for the full event sample. The trigger requirement of the coincidence of at least four photo-multiplier signals favored the selection of events with a strong pile up of cosmic ray tracks and interactions. Hence a number of candidate \(\pi ^0\) events were heavily contaminated by other tracks and had to be rejected. Monte Carlo simulations of events with \(\pi ^0\) production in hadronic and neutrino interactions confirmed the validity of the shower energy and shower direction reconstruction methods applied to the real data.

abstract

In certain new physics (NP) models, such as the Littlest Higgs model with T-parity, a strict correlation between the \({K_{\rm L}\!\rightarrow \!\pi ^0\nu \bar \nu }\) and \({K^{\,+}\!\rightarrow \!\pi ^+\nu \bar \nu }\) branching ratios has been observed, allowing essentially only for two branches of possible points, while in other NP frameworks, such as the general MSSM or warped extra dimensional models, no visible correlation appears. We analyse the origin of the correlation in question and show it to be a direct consequence of the stringent experimental constraint on \(\varepsilon _K\), provided that the NP enters with comparable strength and a universal weak phase in both \(\Delta S=2\) and \(\Delta S=1\) transitions. This happens in many NP scenarios with either only SM operators, or where the NP induces exclusively right-handed currents while the left–right \(\Delta S=2\) operators are absent. On the other hand, if the NP phases in \(\Delta S=2\) and \(\Delta S=1\) processes are uncorrelated, \(\varepsilon _K\) has no power to put constraints on the \(K\to \pi \nu \bar \nu \) system. The latter appears in particular in those NP models where \(K^{\,0}\)–\(\bar K^{\,0}\) mixing receives contributions from the chirally enhanced left-right operators. We discuss the stability of the correlation in question against small deviations from the assumption of universal \(\Delta S=2\) and \(\Delta S=1\) weak phases, and in the presence of non-negligible NP contributions to \(\varepsilon _K\).

abstract

It is argued that a standard measurement of multiplicities in proton–proton collisions is sufficient to construct a single nucleon fragmentation function. A proposed method is based on measurement of mean values of produced particles \(\left \langle n\right \rangle \) and pairs of particles \(\left \langle n(n-1)\right \rangle \) in symmetric and asymmetric rapidity bins.

abstract

Predictions for the decay chains of the nuclei \(^{293}\)117 and \(^{294}\)117 are done within a macroscopic–microscopic model. The nuclei are planned to be synthesized in the reaction \(^{249}\)Bk + \(^{48}\)Ca (\(4n\) and \(3n\) channels), to be performed in Dubna. It is obtained in our study that at least three \(\alpha \) decays in both \(^{293}\)117 and \(^{294}\)117 chains should be observed. Thus, at least six new superheavy nuclides and one new superheavy element should be seen, if cross-sections for the reactions are sufficiently large. Additionally, it is expected that the decay chain of \(^{294}\)117 would be the first one in which the isotope of the element 113, \(^{286}\)113, has a chance to be studied chemically.

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Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on some invariance properties under the action of isometric and affine transformations we reviewed some new models of the mutual interaction between rotational and deformative degrees of freedom. Our methodology and some results may be useful in the theory of Raman scattering and nuclear radiation.

abstract

In this note general relativistic light deflection in the static, spherically symmetric spacetime is investigated as a means to determine the metric of the spacetime. It is shown that in this case derivation of spacetime metric is ambiguous from the light deflection angle only.