abstract

Concept of the strong necessary condition for existence of the extremum of functional is discussed as an alternative to the Euler equation. This concept leads to field equations of the order lower than the order of the Euler equation. They appear as duality equations: Bogomolny decomposition or Bäcklund transformations. The derived formalism is presented and tested on some examples: nonlinear \(\sigma \)-model, nonlinear Klein-Gordon equations (both hyperbolic and elliptic) and nonlinear Schrödinger equation.

abstract

An asymptotic formula for Renyi entropies characterizing a Bernoulli distribution is derived and compared with numerical estimates. Its physical consequences are discussed.

abstract

Dynamics of hydrogen atom driven by microwave field of arbitrary polarization is approximated by the discrete mapping. The map describes the change of dynamical variables from an aphelion or a perihelion to the next one. The results are compared with numerical simulation and previous approximations.

abstract

This is the first paper of the series devoted to threshold amplitudes in quantum field theory. We consider here some aspects of tree approximation. The careful discussion of relevant generating functionals including the problem of boundary conditions is given. The general rules for constructing the field matrix elements between threshold states are rederived. Some features of amplitudes for all particles at the threshold are discussed. They are related to the properties of reduced classical Newton systems. In particular, the nullification and divergence of amplitudes are interrelated and explained in terms of dynamics of classical point particles.

abstract

The simplest non-trivial model of chaotic Bohmian dynamics is identified. We argue that its most important features can be observed in more complex models, above all, the presumable mechanism of the appearance of chaos in the Bohmian-type dynamical systems.

abstract

A Hamiltonian BRST deformation procedure for obtaining consistent interactions among fields with gauge freedom is proposed. The general theory is exemplified on the three-dimensional Chern–Simons models and two-dimensional nonlinear gauge theories.

abstract

We have estimated the contributions to the moments of polarized nucleon structure function \(g_1(x,Q^2)\) coming from the region of the very low \(x\) (\(10^{-5}\lt x\)). Our approach uses the nucleon structure function extrapolated to the region of low \(x\) by the means of the double \(\ln ^2(1/x)\) resummation. The \(Q^2\) evolution of \(g_1\) was described by the unified evolution equations incorporating both the leading order Altarelli–Parisi evolution at large and moderate \(x\), and the double \(\ln ^2(1/x)\) resummation at small \(x\). The moments were obtained by integrating out the extrapolated nucleon structure function in the region \(10^{-5}\lt x\lt 1\).

abstract

An alternative equation, resumming of the \(\ln ^2 1/x\) terms for the polarized nonsinglet structure function \(g_1^{\rm NS}\) at small \(x\) is presented. Construction of the DGLAP-like formula for the auxiliary function, corresponding to the \(g_1^{\rm NS}\) at rescaled \(Q^2\) variable is shown. Predictions of this approach for the \(g_1^{\rm NS}\) function at small \(x\) in a case of a flat as well as a dynamical input are given. The role of the fixed coupling constant and the running one is also discussed.

abstract

This paper continues the study of the consequences of the Bjorken–Gottfried hypothesis for the HBT parameters measured in \(e^+e^-\) annihilation. It is shown that introducing a natural cut-off for transverse momenta of emitted particles, one can describe the observed ratio of transverse and longitudinal HBT radii for pions without destroying the good description of the mass dependence of the HBT parameters for heavier particles.

abstract

We discuss a model with a massless scalar field coupled to the Yang–Mills SU(2) gauge field in four-dimensional space-time. The solutions from static, pointlike color source are given. There exists not only solutions with finite energy but also a singular one which describes confinement. The confining potential depends on the \(\delta \) parameter of our model. The regular magnetic monopole solutions as well as the singular dyon configurations are also obtained. We fit the \(\delta \) parameter to the experimental data.

abstract

We investigate the radiative \(\rho ^+\rightarrow \pi ^+\gamma \) decay in the framework of the light cone QCD sum rules. We estimate the coupling constant \(g_{\rho \pi \gamma }\) for this decay and using this value of the coupling constant, we calculate the decay width of the \(\rho ^+\rightarrow \pi ^+\gamma \) decay. Our result is in good agreement with the experimental value.

abstract

A selection of the Photon Gluon Fusion (PGF) process with light quarks for deep inelastic scattering events is presented. This process is directly sensitive to gluon polarization and our goal is to find out the most effective selection on a sample of events simulated for the SMC experiment. We compare two general multi-class classification methods — Bayes method and neural network with a conventional selection procedure. The neural network algorithm presented here is a modification of method belonging to the family of directional minimization algorithms. This method is convenient and effective for photon gluon fusion selection and determination of gluon polarization. Finally we present the estimation for precision of gluon polarization for neural network method.

abstract

We address the question how the spin-dependent nucleon structure function \(g_1(x,Q^2)\) gets modified when the nucleon is bound inside a nucleus. We analyze the influence of nuclear interactions using the \({\mit \Delta }-\pi \) model, known to describe well the unpolarized effect, and the free polarized parton distributions. The results for the neutron in \(^3{\rm He}\) and proton in \(^3{\rm H}\), \(^7{\rm Li}\) and \(^{19}{\rm F}\) are presented, showing significant changes in the parton spin distributions and in their moments. Scattering processes off polarized \(^7{\rm Li}\) are suggested which could justify these theoretical calculations and shed more light on both nuclear spin structure and short distance QCD.

abstract

By analogy with an effective model of charged-lepton mass matrix that, with the inputs of \(m^{\rm exp}_e \) and \(m^{\rm exp}_\mu \), predicts (in a perturbative zero order) \(m_\tau = 1776.80 \) MeV close to \(m^{\rm exp}_\tau = 1777.03^{+0.30}_{-0.26}\) MeV, we construct such a model for quark mass matrices reproducing consistently the bulk of experimental information on quark masses and mixings. In particular, the model predicts \(|V_{u b}| = 0.00313\), \(\gamma = - \arg V_{u b} = 63.8^\circ \) and \(|V_{t d}| = 0.00785\), \(\beta = - \arg V_{t d} = 20.7^\circ \) (i.e., \(\sin 2\beta = 0.661\) to be compared with the BaBar value \(\sin 2\beta ^{\rm exp} = 0.59 \pm 0.14\)), if the figures \(|V^{\rm exp}_{u s}| = 0.2196\), \(|V^{\rm exp}_{c b}| = 0.0402\) and \(m^{\rm exp}_{s} = 123\) MeV, \(m^{\rm exp}_{c} = 1.25\) GeV, \(m^{\rm exp}_{b} = 4.2\) GeV are used as inputs. Also the rest of CKM matrix elements is predicted consistently by the experimental data. Here, quark masses and CKM matrix elements (ten independent quantities) are parametrised by eight independent model constants, what gives two independent predictions, e.g. for \(|V_{ub}|\) and \(\beta \). The considered model deals with the fundamental-fermion Dirac mass matrices, so that the neutrino Majorana mass matrix is outside the scheme. Some foundations of the model are collected in Appendix.

abstract

Single-particle Woods–Saxon Hamiltonian with the new set of parameters adjusted to the experimental single-particle nucleonic levels in spherical nuclei is used to evaluate the mean-square charge radii of even–even, odd–even and even–odd (spherical or deformed) nuclei. The results are compared with the experimental data and with the theoretical values obtained using the single-particle Nilsson potential in the realization of T. Seo. The odd–even staggering of nuclear charge radii is presented and shown to be satisfactorily reproduced by the calculations with the new parametrization.

abstract

Multistep direct cross sections including the contribution of incoherent particle–hole and collective excitations in the continuum, are calculated and combined with multistep compound and compound nucleus cross sections to give a complete description of neutron inelastic scattering by niobium at incident energy of 14.1 MeV. The multistep direct reactions are enhanced by using the non-DWBA matrix elements that include the biorthogonally conjugated distorted waves. The results reveal contributions from two- and three-step reactions in agreement with experiment.

abstract

The rapidity distributions of particles produced in nucleus–nucleus (Au–Au) collisions at the Alternating Gradient Synchrotron (AGS) energy (11–15\(A\) GeV) have been analyzed by the thermalized cylinder model and the three-fireball model. It is shown that the two models are successful at the AGS energy. The normalized rapidity distributions of produced particles (exclusion of protons) described by the two models do not depend on the forward energy and multiplicity. The rapidity shifts in the two models do not depend on the impact parameter. The proton and deuteron normalized rapidity distributions contributed by the participants in Au-Au collisions do not depend on the forward energy and multiplicity, but the final state proton and deuteron rapidity distributions depend on the forward energy and multiplicity due to the contributions of spectators.

abstract

The boost-invariant tunneling of particles along the hyperbolas of constant invariant time \(\tau =\sqrt {t^2-z^2}\) is included in the transport equations describing formation of the quark–gluon plasma in strong color fields. The non-trivial solutions of the transport equations exist if the boost-invariant distance between the tunneling particles, measured in the quasirapidity space \(\eta =1/2 \ln ((t+z)/(t-z))\), is confined to a finite interval \(\Delta \eta \). For realistic values of \(\Delta \eta \) the solutions of the transport equations show similar characteristics to those found in the standard approach, where the tunneling takes place at constant time \(t\). In the limit \(\Delta \eta \rightarrow \infty \), the initial color fields decay instantaneously.

abstract

Present day results for few-nucleon bound state and scattering observables based on modern high precision nuclear forces are briefly reviewed. While in relation to \(NN\) forces of that type three-nucleon (\(3N\)) forces are mandatory for binding energies and for quite a few \(3N\) scattering observables their effect is rather small in two-nucleon correlation functions as demonstrated for \(^3\)He and \(^4\)He. The old idea of the Coulomb sum rule as a way to extract the \(pp\) correlation function is reconsidered and the need for more accurate data is pointed out. It appears to be an ideal case to probe properties of the density operator and the ground state wave functions without disturbances of final state interactions (FSI). In the \(3N\) system below the pion threshold FSI is well under control and therefore the exclusive process \(^3{\rm He}(e,e'{NN})\) is also a very good test case for correlated nuclear wave functions and electromagnetic current operators. One specific kinematics is emphasized, which can lead to insights into the correlated ground state wave functions with little disturbance of FSI. Finally exclusive photodisintegration of \(^3\)He is regarded, which appears to be promising to identify \(3N\) force effects.

abstract

The creation of hot Ca-like fragments and the emission of intermediate velocity particles was studied in the 40Ca+197Au reaction at 35 AMeV. For peripheral collisions the primary projectile-like fragment was reconstructed using the AMPHORA \(4\pi \) detector system. The particle distributions are compared with the predictions of a Monte Carlo code which calculates the nucleon transfer and clustering probabilities according to the system density of states. The velocity distributions of charged particles projected on the beam direction can be explained if emissions from the hot projectile-like fragment and the target-like fragment are supplemented by an emission from an intermediate velocity source located between them. The properties of the intermediate velocity source are properly described, including the \(^2\)D/\(^3\)T/\(^3\)He effect.

abstract

Multifragment emission following Pb–Pb and Pb–Plastic collisions at 158 \(A\)GeV has been studied with a set of emulsion chambers of the EMU13 CERN experiment. It was found that the probability of nuclear multifragmentation increases with increasing mass of the target nucleus. For Pb–Pb collisions, multifragmentation events represent more than 30 % of the total charge changing cross section. On the other hand characteristics of multifragmentation are found to be independent of the mass of the target. A comparison is made with the results for Au multifragmentation after the collisions with emulsion nuclei at lower energies. The results suggest that above 10 \(A\)GeV the features of multifragmentation processes are energy independent.

abstract

In this paper we have estimated correction to the distance modulus, derived from the generalized Dyer–Roeder equation, due to a single clump of matter inducing gravitational lensing effect. To describe the influence of the gravitational lensing, we have used the “Swiss cheese” model and the Jacobi equation. In the case, when the source is at redshift \(z=1\) and the lensing object is a galaxy modeled by the Singular Isothermal Sphere (SIS) with mass \(M=10^{11}\times M_\odot \), we have found that the correction is about 0.01 mag. We have also show relations between the described approach and the convenient approach using the gravitational lens equation. In particular, we have derived the lens equation from the geodesic deviation equation and showed that the obtained dependence of the magnification factor on the impact parameter is well approximated (with accuracy \(\sim 0.2\%\)) by a function obtained from the lens equation for the SIS.

abstract

Mirror matter is predicted to exist if parity (i.e. left-right symmetry) is a symmetry of nature. Remarkably mirror matter is capable of simply explaining a large number of contemporary puzzles in astrophysics and particle physics including: Explanation of the MACHO gravitational microlensing events, the existence of close-in extrasolar gas giant planets, apparently ‘isolated’ planets, the solar, atmospheric and LSND neutrino anomalies, the orthopositronium lifetime anomaly and perhaps even gamma ray bursts. One fascinating possibility is that our solar system contains small mirror matter space bodies (asteroid or comet sized objects), which are too small to be revealed from their gravitational effects but nevertheless have explosive implications when they collide with the Earth. We examine the possibility that the 1908 Tunguska explosion in Siberia was the result of the collision of a mirror matter space body with the Earth. We point out that if this catastrophic event and many other similar smaller events are manifestations of the mirror world then these impact sites should be a good place to start digging for mirror matter. Mirror matter could potentially be extracted and purified using a centrifuge and have many useful industrial applications.