Regular Series


Vol. 30 (1999), No. 4, pp. 863 – 1148


Searching for a Universal Integrable System

abstract

It is argued for the hypothesis that the SDYM equations for the Moyal bracket algebra (the master equation) is in a sense a universal integrable system. We show how the su(\(N\)) SDYM equations, the KP equation and the integrable equations in two dimensions can be encoded in the master equation.


Transformation of Non-Markovian Kinetic Equation for TCF to Markovian Type

abstract

It is shown that the non-Markovian kinetic equation of relaxation takes on the Markovian form if the non-Markovity parameter (Phys. Lett. A148, 199 (1990)) goes to infinity.


Acoustic Phase Lenses in Superfluid Helium as Models of Composite Space-Times in General Relativity: Classical and Quantum Features

abstract

In the spirit of the well-known analogy between inviscid fluids and pseudo-Riemannian manifolds we study spherical singular hypersurfaces in the static superfluid. Such hypersurfaces turn out to be the interfaces dividing superfluid into the pairs of spherical domains, examples of which are “superfluid A–superfluid B” or “impurity–superfluid” phases. It is shown that these shells form the acoustic lenses which are the sonic counterparts of the usual optical lenses. The exact equations of motion for the lens interfaces are obtained. Also some quantum aspects of the theory are considered. We calculate energy spectra for bound states of acoustic lenses in dynamical equilibrium taking into account the analogy to a material shell model of a black hole (we consider the cases of spatial topology of a black hole and a wormhole type).


Calogero Model and \(\mathrm {sL}(2,\mathbb {R})\) Algebra

abstract

The Calogero model with external harmonic oscillator potential is discussed from sL(2,\({R}\)) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are constructed and their involutivness demonstrated. The superintegrability of the model appears to be a simple consequence of the formalism.


On Calogero Wave Functions

abstract

Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the sL(\(2,R)\) structure of the Calogero–Moser wave functions.


On the Calogero Model with Negative Harmonic Term

abstract

The Calogero model with negative harmonic term is shown to be equivalent to the set of negative harmonic oscillators. Two time-independent canonical transformations relating both models are constructed: one based on the recent results concerning quantum Calogero model and one obtained from dynamical sL(\(2,R)\) algebra. The two-particle case is discussed in some detail.


Tagging \(b\)-Jets Using Low-\({p_{\rm T}}\,\)Electrons

abstract

This note presents a study of \(b\)-jet tagging in ATLAS using soft electrons from semileptonic \(b\)-quark decays. Both Inner Detector and EM Calorimeter information is used by the \(b\)-tagging algorithm to identify signal electrons inside jets. The performance of this algorithm in terms of expected \(b\)-tagging efficiency and non-\(b\) jet rejection is discussed in detail over the small central rapidity range and for low luminosity operation. For an algorithm efficiency of \(50\%\) (and an overall efficiency of \(7.2\%\) taking into account the branching ratio of \(b\rightarrow e\) decays), rejections of \(554\) against \(u\)-jets, \(192\) against gluon jets and of \(47\) against \(c\)-jets can be achieved. Such a soft-electron b-tagging algorithm can be combined with the higher-efficiency vertexing algorithm to improve the \(b\)-jet tagging performance.


\(\langle T^{\mu }_{\nu }\rangle _{\rm ren}\) of the Quantized Conformal Fields in the Schwarzschild Spacetime: Israel–Hartle–Hawking State

abstract

The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Israel–Hartle–Hawking state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric. Specifically, the relation of the results of the present approach to the stress tensor constructed within the framework of the Hadamard renormalization is analysed. Finally, the semi-analytic models reconstructing the numerical estimates of the tangential component of the stress-energy tensor with the maximal deviation not exceeding \(0.7 \%\) are constructed.


Consistent Effective Field-Theoretic Treatment of Resonances with Non Zero Width

abstract

A systematic field theoretic formalism for treating Fermionic resonances with non zero width is given. The implication of unitarity to coupling constants of non local interactions is shown. The extension of the formalism to Bosonic resonance field operators is straight forward.


On the Consistency of LEAR and FENICE Experimets in the Sector of \(p\bar p\) Interaction Near the Threshold

abstract

Some experiments at LEAR showed unusual behavior of the \(p\bar p\) interaction near the threshold. The experiments on \(p\bar p\) forward scattering detected zeros and a big variation of \(\rho \) and at the same time a smooth rising of \({\sigma }_{\rm tot}\) with lowering energy. Many models have difficulties in explaining this fact. In the PS-170 experiment with a good statistical accuracy, the unexpected behavior of the proton electromagnetic form factor was found. All these experiments can be considered as an indication for the existence of a low-lying \(p\bar p\) bound state ’baryonium’. This statement coincides with that made for interpreting of the energy dependence of the total cross-section of the reaction \(e^{+}e^{-}\to hadrons\) in FENICE. There is a model (based on analyticity) which explains afore-mentioned experiments and the fact that the ’baryonium’ is not seen in the OBELIX \(p\bar p\) annihilation cross-section. Thus, LEAR and FENICE experiments are consistent near the \(p\bar p\) threshold and testify to the existence of ’baryonium’.


Search for the SM and MSSM Higgs Boson in the \(t \bar t H, H \to b \bar b\) Channel

abstract

A detailed study of the associated Standard Model Higgs boson production \({t \bar t H}\) with \({ H \to b \bar b}\) is presented for the SM and MSSM scenarios. For Higgs boson masses from 80 to 120 GeV and an integrated luminosity of \(3 \cdot 10^4~{\rm pb}^{-1}\) a clear evidence for an excess of events with four \(b\)-tagged jets over the background from \({W+{\rm jets}}\) and \({t \bar t}\) production should be observable. However, a clean reconstruction of the \({h \to b \bar b}\) mass peak will be difficult because of the combinatorial background from the signal itself. This problem can be to a large extent overcome if both top-quark decays are reconstructed in addition to the reconstruction of the \({h \to b \bar b}\) mass peak. In the MSSM scenario, the low \(\tan \beta \) region (up to \(\tan \beta \sim 6\)) for an integrated luminosity of \(3 \cdot 10^4~{\rm pb}^{-1}\) and most of the (\({m_A}\), \(\tan \beta \)) parameter space for an integrated luminosity of \(10^5~{\rm pb}^{-1}\) would be accessible with this channel. Excellent \(b\)-tagging capability and good efficiency for jet reconstruction are however necessary to explore this channel to its full potential.


Phenomenological Analysis of Data on Inclusive and Semi-Inclusive Spin Asymmetries

abstract

We present a phenomenological analysis of data on both inclusive and semi-inclusive spin asymmetries. We examine the impact of the semi-inclusive results presented by SMC on the determination of polarized parton distributions performing global fits with different sets of observables. We discuss the flavour dependence of the polarized sea inside a nucleon.


Phase Diagrams in Higher Dimensional U(1) Lattice Gauge Theory

abstract

In five or more dimensions, U(1) lattice gauge theory shows a strong first-order phase transition and metastable states in the region of the transition. Monte Carlo calculations carried out in dimensions up to seven illustrate this behavior. These metastable states are well reproduced by gauge-fixed mean-field theory for the “superheated state” (\(\beta \lt \beta _c\)) and by Padé approximants to the strong-coupling expansion for the “supercooled state” (\(\beta \gt \beta _c\)). In analogy to a Van der Waal’s system, a cubic equation of state is employed to connect the two metastable states in both the Monte Carlo and analytic calculations. A Maxwell construct is developed allowing for the identification of the transition point and a complete, analytic description of the phase diagram in five and higher dimensions.


Casimir Energy of Rotating String — Indirect Approach

abstract

Methods of calculating the Casimir energy which do not require the explicit knowledge of the oscillation frequencies are developed and applied to the model of the Nambu–Goto string with the Gauss–Bonnet term in the action.


\(\omega \to \pi \pi \) Decay in Nuclear Medium

abstract

We calculate the width for the \(\omega \to \pi \pi \) decay in nuclear medium. Chiral dynamics and low-density approximation are used. At densities around twice the nuclear saturation density we estimate the partial width for the decay of the longitudinal mode to be of the order of a few tens of MeV, and for the transverse mode a few times less.


Potential Gradient Parametrization in a Langevin Type Dissipative Dynamics

abstract

A parametrization of the conservative force in the dynamical coalescence and reseparation model is proposed. This model with one body dissipation formula, Yukawa plus exponential finite range potential, and shell effects included was recently adopted to follow Langevin trajectories for a collision of two very heavy nuclei which can end up as a compound system or reseparate. With our parametrization it is possible to speed up model calculations by a factor of 10 without loosing accuracy of trajectory integration. This can be of some importance in a case of Langevin trajectories calculation where many of them have to be traced in order to estimate probability for a process of interest, namely a fusion of two very heavy nuclei at beam energies close to the Coulomb barrier. Few examples of fusion excitation functions of heavy nuclei calculated with this faster version of the computer code are presented.


Transport Properties and Neutrino Emissivity of Dense Neutron-Star Matter with Localized Protons

abstract

As pointed out by Kutschera and Wójcik, very low concentration of protons combined with a specific density dependence of effective neutron–proton interaction could lead to a localization of “proton impurities” in neutron medium at densities exceeding four times normal nuclear matter density. We study consequences of the localization of protons for transport processes in dense neutron star cores, assuming random distribution of proton impurities. Kinetic equations, relevant for the transport of charge, heat and momentum, are solved using variational method. Localization of protons removes a \(T^{-2}\) factor from the transport coefficients, which leads, at lower temperatures, to a strong decrease of thermal conductivity, electrical conductivity and shear viscosity of neutron star matter, as compared to the standard case, where protons form a Fermi liquid. Due to the localization of protons a number of conventional neutrino emission processes (including modified URCA process) become inoperative in neutron star cores. On the other hand, the energy loss rate from neutrino–antineutrino pair bremsstrahlung due to electron and neutron scattering off (localized) protons, will have a specific \(T^6\) dependence, which could modify the cooling of the neutron star core, as compared to the standard case. Possible astrophysical implications of the localization of protons for neutron star evolution and dynamics are discussed.


Neutrino Emission Due to Electron Bremsstrahlung in Superfluid Neutron-Star Cores

abstract

We study neutrino energy emission rates (emissivities) due to electron bremsstrahlung produced by \(ee\) and \(ep\) collisions in the superfluid neutron star cores. The neutrino emission due to \(ee\) collisions is shown to be the dominant neutrino reaction at not too high temperatures (\(T \lesssim 10^8\) K) in dense matter if all other neutrino reactions involving nucleons are strongly suppressed by neutron and proton superfluidity. Simple practical expressions for the \(ee\) and \(ep\) neutrino emissivities are obtained. The efficiency of various neutrino reactions in the superfluid neutron–star cores is discussed for the cases of standard neutrino energy losses and the losses enhanced by the direct Urca process.


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