Regular Series

Vol. 34 (2003), No. 8, pp. 3887 – 4310

Photons Produced Inside a Cavity with a Moving Wall

Acta Phys. Pol. B 34, 3887 (2003)

page 3887 •


The production of particles inside one-dimensional cavity with a moving wall is discussed. Cavities with periodically driven wall motions are analyzed numerically for long times. We formulate the conditions under which the particle production is being efficiently run. The conditions are independent of a specific type of cavity motions.

Contractions of Lie Algebras and Generalized Casimir Invariants

Acta Phys. Pol. B 34, 3901 (2003)

page 3901 •


We prove that if \(\mathfrak {g}^{\prime }\) is a contraction of a Lie algebra \(\mathfrak {g}\) then the number of functionally independent invariants of \(\mathfrak {g}^{\prime }\) is at least that of \(\mathfrak {g}\). This allows to obtain some criteria to ensure the non-existence of non-trivial invariants for Lie algebras, as well as to deduce some results on the number of derivations of a Lie algebra. In particular, it is shown that almost any even dimensional solvable complete Lie algebra has only trivial invariants. Moreover, with the contraction formula we determine explicitly the number of invariants of Lie algebras carrying a supplementary structure, such as linear contact or linear forms whose differential is symplectic, without having explicit knowledge on the structure of the contracting algebra. This in particular enables us to construct Lie algebras with non-trivial Levi decomposition and none invariants for the coadjoint representation as deformations of frobeniusian model Lie algebras.

Quantized Massive Scalar Fields in the Spacetime of a Charged Dilatonic Black Hole. Energy Conditions

Acta Phys. Pol. B 34, 3921 (2003)

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Employing the approximate effective action constructed from the coincidence limit of the Hadamard–Minakshisundaram–DeWitt (HaMiDeW) coefficient \(a_{3},\) the renormalized stress-energy tensor of the quantized massive scalar field in the spacetime of a static and electrically charged dilatonic black hole is calculated. Special attention is paid to the minimally and conformally coupled fields propagating in geometries with \(a=1,\) and to the power expansion of the general stress-energy tensor for small values of charge. A compact expression for the trace of the stress-energy tensor is presented. Finally, various pointwise energy conditions are considered.

On Friedmann Equation and the Radion Stabilization in Two-Brane Models with Dynamical Matter

Acta Phys. Pol. B 34, 3947 (2003)

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The consequences of a gravitational stabilization of a two-brane system are studied in the presence of matter and tensions of both branes as well as the cosmological constant in the bulk. An explicit calculation shows that the usual form of the Friedmann equation can be retained in this situation, even though the model is not a realistic one.

Quantized Massive Fields and Semiclassical Electrically Charged Black Holes

Acta Phys. Pol. B 34, 3957 (2003)

page 3957 •


Constructed within the framework of the Schwinger–DeWitt method, the renormalized stress-energy tensor of the quantized massive scalar, spinor and vector fields in a general spherically-symmetric and static spacetime is employed as a source term of the Einstein field equations. The semiclassical solutions describing the electrically charged black holes are obtained and their properties are studied. Special emphasis is put on the semiclassical extremal configurations: it is shown that the near-horizon geometry, when expanded into a whole manifold, is described by the Bertotti–Robinson line element.

Lagrangian Theory of Hamiltonian Reduction

Acta Phys. Pol. B 34, 3977 (2003)

page 3977 •


Lagrangian formalism corresponding to Hamiltonian reduction procedure is presented. Two versions are considered which lead to unbroken or explicitly broken gauge symmetries, respectively.

Fermions in 2d Lorentzian Quantum Gravity

Acta Phys. Pol. B 34, 3987 (2003)

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We implement Wilson fermions on 2d Lorentzian triangulation and determine the spectrum of the Dirac–Wilson operator. We compare it to the spectrum of the corresponding operator in the Euclidean background. We use fermionic particle to probe the fractal properties of Lorentzian gravity coupled to \(c=1/2\) and \(c=4\) matter. We numerically determine the scaling exponent of the mass gap \(M \sim N^{-1/d_{\rm H}}\) to be \(d_{\rm H}=2.11(5)\), and \(d_{\rm H}=1.77(3)\) for \(c=1/2\) and \(c=4\), respectively.

Study of High Mass Higgs Using \(pp\rightarrow qqH\)

Acta Phys. Pol. B 34, 4001 (2003)

page 4001 •


The observability of the Higgs signal in the mass range of 200–800 GeV is investigated in the weak boson fusion channel at the CMS experiment at LHC. The weak boson fusion channel is characterized by two final state jets at large pseudorapidity. The forward calorimeter plays a key role in detecting these jets. The significant signals are obtained for \(H \rightarrow WW \rightarrow l\nu jj\), \(H \rightarrow ZZ \rightarrow lljj\) and \(H \rightarrow ZZ \rightarrow ll \nu \nu \). Importance of the forward jet tagging and the central jet veto is emphasized to extract the signal from the large QCD \(W/Z+\textrm {jets}\) and the top backgrounds. This analysis shows that the Higgs particle with mass 300 GeV to 800 GeV can be observed in \(WW\) and \(ZZ\) decay channels with an integrated luminosity of about 10 to 20 fb\(^{-1}\) in the low luminosity running conditions in CMS.

Vacuum Engineering at a Photon Collider?

Acta Phys. Pol. B 34, 4019 (2003)

page 4019 •


The aim of this paper is twofold: to provide a rather detailed and self-contained introduction into the physics of the Disoriented Chiral Condensate (DCC) for the photon (and linear) collider community, and to indicate that such physics can be searched and studied at photon colliders. Some side tracks are also occasionally followed during the exposition, if they lead to interesting vistas. For gourmets, the Baked Alaska recipe is given in the appendix.

Gluon Superpropagator as the Origin of QCD Potential

Acta Phys. Pol. B 34, 4073 (2003)

page 4073 •


We show that the confining term in the widely used Cornell form of QCD potential is derivable from the gluon superpropagator for an exponential form of gluon self-interaction, if one assumes that the gluon–gluon coupling constant has the character of a running coupling constant. We also consider a rational form of self-interaction.

Production of Excited Electrons at TESLA and CLIC Based \(e\gamma \) Colliders

Acta Phys. Pol. B 34, 4079 (2003)

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We analyze the potential of TESLA and CLIC based electron–photon colliders to search for excited spin-1/2 electrons. The production of excited electrons in the resonance channel through the electron–photon collision and their subsequent decays to leptons and electroweak gauge bosons are investigated. We study in detail the three signal channels of excited electrons and the corresponding backgrounds through the reactions \(e\gamma \rightarrow e\gamma \), \(e\gamma \rightarrow eZ\) and \(e\gamma \rightarrow \nu W\). Excited electrons with masses up to about \(90\%\) of the available collider energy can be probed down to the coupling \(f=f^{\prime }=0.05(0.1)\) at TESLA(CLIC) based \(e\gamma \) colliders.

\(\sigma \)-Meson and \(\omega \)–\(\rho \) Mixing Effects in \(\omega \rightarrow \pi ^+\pi ^-\gamma \) Decay

Acta Phys. Pol. B 34, 4095 (2003)

page 4095 •


We calculate the branching ratio of \(\omega \rightarrow \pi ^+\pi ^-\gamma \) decay in a phenomenological framework in which the contributions of VMD, chiral loops, \(\sigma \)-meson intermediate state amplitudes and the effects of \(\omega \)–\(\rho \) mixing are considered. We conclude that the \(\sigma \)-meson intermediate state amplitude and \(\omega \)–\(\rho \) mixing make substantial contribution to the branching ratio.

Free Massless Spin-5/2 Gauge Fields from the Lagrangian \(Sp(3)\) BRST Method

Acta Phys. Pol. B 34, 4105 (2003)

page 4105 •


An irreducible version of free massless spin-5/2 gauge fields is analyzed from the point of view of the Lagrangian \(Sp(3)\) BRST method. The irreducible formulation is obtained by means of introducing one purely gauge supplementary Majorana spinor. An appropriate gauge-fixing procedure is developed, such as to benefit from a direct link with the standard antifield-BRST method. The comparison with related results from the literature is discussed.

Bilarge Mixing Matrix and Its Invariance Under “Horizontal Conjugation” — a New Discrete Transformation for Neutrinos

Acta Phys. Pol. B 34, 4125 (2003)

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In the first part of the note, we consider a neutrino texture, where the Dirac and righthanded Majorana masses are proportional. If the former are approximately proportional also to the charged-lepton masses, then taking \({\mit \Delta } m^2_{32} \sim 3\times 10^{-3}\; {\rm eV}^2\) we estimate approximately that \({\mit \Delta } m^2_{21} \sim O(10^{-5}\; {\rm eV}^2)\), what is not very different from the recent KamLAND estimation \({\mit \Delta } m^2_{21} \sim 7\times 10^{-5}\;{\rm eV}^2\), consistent with the LMA solar solution. In the second part, we show generically that the invariance of neutrino mixing matrix under the simultaneous discrete transformations \(\nu _e \rightarrow -\nu _e \), \(\nu _\mu \rightarrow \nu _\tau \), \(\nu _\tau \rightarrow \nu _\mu \) and \(\nu _1 \rightarrow -\nu _1 \), \(\nu _2 \rightarrow -\nu _2 \), \(\nu _3 \rightarrow \nu _3 \) (neutrino “horizontal conjugation”) characterizes the familiar bilarge form of mixing matrix, favored phenomenologically at present. Then, in the case of this form, the mass neutrinos \(\nu _1, \nu _2 , \nu _3 \) get a new quantum number, covariant in their mixings (neutrino “horizontal parity”  equal to \(-1,-1,1\), respectively). Conversely, such a covariance may be the origin of the bilarge mixing matrix. In Section 5, the “horizontal parity” is embedded in a group structure.

QCD Sum Rule Analysis of the Coupling Constants \(g_{\rho \eta \gamma }\) and \(g_{\omega \eta \gamma }\)

Acta Phys. Pol. B 34, 4145 (2003)

page 4145 •


The coupling constants g\(_{\rho \eta \gamma }\) and g\(_{\omega \eta \gamma }\) are calculated using QCD sum rules method by studying the three point \({\rho \eta \gamma }\) and \({\omega \eta \gamma }\) correlation functions. A comparison of the results with the values of the coupling constants that are deduced from the experimentally measured decay widths of \(\rho \rightarrow \eta \gamma \) and \(\omega \rightarrow \eta \gamma \) decays is performed.

Limit on Quark–Antiquark Mass Difference from the Neutral Kaon System

Acta Phys. Pol. B 34, 4151 (2003)

page 4151 •


We quantify the limits on quark-antiquark mass differences imposed by the neutral kaon mass system. In particular, we find that an upper limit to the mass difference of \(10^{-3}\) eV exists if mass differences across quark flavors are uncorrelated. In the upcoming antihydrogen experiments this limit on quark mass difference would allow a measurement of electron-positron mass difference up to a relative precision level of \(10^{-15}\).

Is There a Dynamical Group Structure Behind the Bilarge Form of Neutrino Mixing Matrix?

Acta Phys. Pol. B 34, 4157 (2003)

page 4157 •


We observe that the invariance of neutrino mixing matrix under the simultaneous discrete transformations \(\nu _1\,,\, \nu _2 \,,\, \nu _3 \rightarrow -\nu _1 \,,\, -\nu _2 \,,\, \nu _3 \) and \(\nu _e, \nu _\mu \,,\, \nu _\tau \rightarrow -\nu _e \,,\, \nu _\tau \,,\, \nu _\mu \) (neutrino “horizontal conjugation”) characterizes (as a sufficient condition for it) the familiar bilarge form of neutrino mixing matrix, favored experimentally at present. Thus, the mass neutrinos \(\nu _1, \nu _2 , \nu _3 \) get a new quantum number, covariant with respect to their mixings into the flavor neutrinos \(\nu _e, \nu _\mu , \nu _\tau \) (neutrino “horizontal parity”  equal to -1, -1,1, respectively). The “horizontal parity” turns out to be embedded in a group structure consisting of some Hermitian and real \(3\times 3\) matrices \(\mu _1, \mu _2 , \mu _3 \) and \(\varphi _1, \varphi _2 , \varphi _3 \), forming pairs interconnected through neutrino mixings. They generate some discrete transformations of mass and flavor neutrinos, respectively, in such a way that the group relations \(\mu _1 \mu _2 = \mu _3 \) (cyclic) and \(\varphi _1 \varphi _2 = \varphi _3 \) (cyclic) hold, while \(\mu _a \mu _b = \mu _b \mu _a \) and \(\varphi _a \varphi _b = \varphi _b \varphi _a \). Then, for instance, the \(\mu _3\) matrix may be chosen equal to the “horizontal parity”.

On Tachyon Potential in Boundary String Field Theory and Problems with Boundary Fermions

Acta Phys. Pol. B 34, 4167 (2003)

page 4167 •


A calculation of a partition function \(Z\) in a system of two coincident \(D1\)–\(\overline {D{1}}\) pairs of type I superstring theory is presented. According to the well known conjecture, this partition function is identified with a tachyon potential in a case of constant tachyon fields. Properties of this potential are discussed. On the way, a peculiar features of boundary fermions emerge. To solve the problems ensuing, a non-standard way of operator renormalization is required.

Inversion of the Photon Number Integral

Acta Phys. Pol. B 34, 4185 (2003)

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We consider the behavior of the photon number integral under inversion, concentrating on Euclidean space. The discussion may be framed in terms of an additive differential \(I\) which arises under inversions. The quantity \(\int \int I\) is an interesting integral invariant whose value characterizes different configurations under inversion.

Measurement of Cross Sections of Heavy Fragments Formed in the Interaction of 0.65–12.7 GeV \(^4\)He with \(^{209}\)Bi

Acta Phys. Pol. B 34, 4205 (2003)

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Formation of heavy fragments in the fission mass region during the interaction with \(^{209}\)Bi of the 0.65, 1.74, 5.1, 8.8 and 12.7 GeV \(^4\)He is studied using a sandwich configuration of the Makrofol polycarbonate track detector. Events are analyzed in which at least one heavy fragment is detected. Fragments produced in the experiment are identified and a model-free event-by-event analysis is performed in order to separate different production mechanisms. The cross sections and experimental features are determined for these reaction mechanisms, and so are their variations with the incident energy. Results are compared to the corresponding proton interaction data.

Analysis of the Freeze-out Parameters for RHIC, SPS and AGS Based on \({ {dE_{\rm T}} \over {d\eta } } / { {dN_{\rm ch}} \over {d\eta } }\) Ratio Measurements

Acta Phys. Pol. B 34, 4219 (2003)

page 4219 •


The ratio \(\frac {dE_{T}}{d\eta } /\frac {dN_{\rm ch}}{d\eta }\) is analyzed in the framework of a single-freeze-out thermal hadron gas model. Decays of hadron resonances are taken into account in evaluations of this ratio. The predictions of the model at the freeze-out parameters, established previously from observed particle yields, agree very well with the ratio measured at RHIC, SPS and AGS.

Collisional Effects in Isovector Response Function of Nuclear Matter at Finite Temperature

Acta Phys. Pol. B 34, 4229 (2003)

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The dipole response function of nuclear matter at zero and finite temperatures is investigated by employing the linearized version of the extended TDHF theory with a non-Markovian binary collision term. Calculations are carried out for nuclear dipole vibrations by employing the Steinwedel–Jensen model and compared with experimental results for \(^{120}\)Sn and \(^{208}\)Pb.

Elliptic Flow Fluctuations

Acta Phys. Pol. B 34, 4241 (2003)

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We suggest to perform systematic measurements of the elliptic flow fluctuations which are sensitive to the early stage dynamics of heavy-ion collisions at high-energies. Significant flow fluctuations are shown to be generated due to the formation of topological clusters and development of the filamentation instability. The statistical noise and hydrodynamic fluctuations are also estimated.

Application of the Nuclear Matter Approach to the Interaction Potential Between Heavy Ions

Acta Phys. Pol. B 34, 4257 (2003)

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A simple theory of the interaction potential between heavy ions \(\cal V\), based on the local density approach and the frozen density model, is applied to a number of pairs of nuclei with neutron excess. The energy density needed for calculating \(\cal V\) is expressed in a simple way through the equilibrium properties of nuclear matter, a phenomenological density gradient term, and nucleon density distributions in the two colliding nuclei. The Coulomb barrier in the calculated potential compares favorably with other estimates.

Effective Field Theory Approach to Electroweak Transitions of Nuclei Far From Stability

Acta Phys. Pol. B 34, 4269 (2003)

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In a previous paper, the convergence of the effective field theory approach of Furnstahl, Serot and Tang to the nuclear many-body problem was studied by applying it to selected doubly-magic, and neighboring single-particle and single-hole, nuclei far from stability. The success of that approach, interpreted through density functional theory, would imply reliable densities. In this paper, the single-particle (Kohn–Sham) wave functions are probed using weak transitions near the Fermi surface. The weak currents are the Noether currents derived from the effective Lagrangian. The general single-particle transition matrix elements, from which any semi-leptonic weak rate can be calculated, are obtained in terms of upper and lower components of the Dirac wave functions. Here beta-decays in nuclei neighboring \(^{132}\)Sn are studied and compared with available experimental data. Calibration of the theoretical results for such decays may also have useful application in element formation.

Are the Contemporary Financial Fluctuations Sooner Converging to Normal?

Acta Phys. Pol. B 34, 4293 (2003)

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Based on the tick-by-tick price changes of the companies from the U.S. and from the German stock markets over the period 1998–99 we reanalyse several characteristics established by the Boston Group for the U.S. market in the period 1994–95, which serves to verify their space and time-translational invariance. By increasing the time scales, in the region covered by the data, we find a significantly more accelerated departure from the power-law \((\alpha \approx 3)\) asymptotic behaviour of the distribution of returns towards a Gaussian, both for the U.S. as well as for the German stock markets. In the latter case the crossover is even faster. Consistently, the corresponding autocorrelation functions of returns and of the time averaged volatility also indicate a faster loss of memory with increasing time. This route towards efficiency, as seen in a fixed time scale, may reflect a systematic increase of the quality of information processing when going from past to present.

all authors

K. Kuwahara, H. Sagayama, K. Iwasa, M. Kohgi, S. Miyazaki, J. Nozaki, J. Nogami, M. Yokoyama, H. Amitsuka, H. Nakao, Y. Murakami

High Pressure X-Ray Diffraction Study of URu\(_{2}\)Si\(_{2}\)

Acta Phys. Pol. B 34, 4307 (2003)

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We have performed high pressure X-ray diffraction measurements on a powder sample of the tetragonal heavy-electron compound URu\(_{2}\)Si\(_{2}\) at low temperatures and pressure up to 3 GPa, in order to investigate a pressure-induced phase transition at \(P_{\rm c}={\sim }\,1.5\) GPa, which was indicated in the neutron diffraction experiment under pressure. The pressure variations of the lattice parameters \(a\) and \(c\) at 15 K decrease monotonously with increasing pressure. No discontinuity of the lattice parameters of URu\(_{2}\)Si\(_{2}\) around \(P_{\rm c}\) is observed within experimental error.


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