Primary vertex in the ALICE experiment in absence of the event reconstruction

ALICE is a general-purpose apparatus for the study of ultra-relativistic heavy-ion collisions at the Large Hadron Collider of the CERN. The study of such reactions demands the determination of the primary vertex in three dimensions with good resolution. We have developed an algorithm for finding the vertex position even in absence of the event reconstruction. The performances of such an algorithm have been studied as a function of the vertex position, particle multiplicity and magnetic field.     

The diagonalisation of the Lund fragmentation model I

We will in this note show that it is possible to diagonalise the Lund fragmentation model. We show that the basic original result, the Lund area law, can be factorised into a product of transition operators, each describing the production of a single particle and the two adjacent break up points (vertex positions) of the string field. The transition operator has a discrete spectrum of (orthonormal) eigenfunctions, describing the vertex positions (which in a dual way correspond to the momentum transfers between the particles produced) and discrete eigenvalues, which only depend upon the particle produced. The eigenfunctions turn out to be the well-known two-dimensional harmonic oscillator functions and the eigenvalues are the analytic continuations of these functions to timelike values (corresponding to the particle mass). In this way all observables in the model can be expressed in terms of analytical formulas. In this note only the 1+1-dimensional version of the model is treated, but we end with remarks on the extensions to gluonic radiation, transverse momentum generation etc., to be performed in future papers. Received: 7 April 2000 / Published online: 18 May 2000     

Localization and Propagation in Random Lattices

We analyze the motion of a particle on random lattices. Scatterers of two different types are independently distributed among the vertices of such a lattice. A particle hops from a vertex to one of its neighboring vertices. The choice of neighbor is completely determined by the type of scatterer at the current vertex. It is shown that on Poisson and vectorizable random triangular lattices the particle will either propagate along some unbounded strip or be trapped inside a closed strip. We also characterize the structure of a localization zone contained within a closed strip. Another result shows that for a general class of random lattices the orbit of a particle will be bounded with probability one.     

Magnetoconductivity of disordered two dimensional tight binding electrons in CPA

The magnetotransport properties of a tight binding model of electrons on a two dimensional square lattice with diagonal disorder and in a perpendicular magnetic field is investigated. The disorder is treated in the coherent potential approximation (CPA) and a quasiclassical solution of the Harper equation is used to calculate the one particle Green's function. Analytical expressions for the CPA vertex corrections to the magnetoconductivity are derived. Numerical results for the density of states and the diagonal magnetoconductivity are discussed. The vertex correction vanishes if the Harper band width is neglected.     

Extreme quantum field theory and particle physics with IZEST

The prospect of next-generation ultra-high-intensity laser sources has prompted recent renewed study of nonlinear QED processes, such as the Schwinger effect, in which the instability of the QED vacuum is probed by external fields. Experimental observation of these nonlinear QED effects would provide unprecedented controlled access to non-perturbative processes in quantum field theory under extreme conditions, which is of direct interest in particle physics and astrophysical applications. I summarize important theoretical issues, both conceptual and computational, related to these nonlinear QED effects.     

Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.     

Compact sensor for measuring nonlinear rotational dynamics of driven magnetic microspheres with biomedical applications

The nonlinear rotation response of a magnetic particle occurs when a driving magnetic field, used to rotate the magnetic particle, exceeds a critical frequency. This type of nonlinear rotational dynamic depends on several physical parameters, such as the rotational drag that the particle experiences. Shifts in this nonlinear rotational frequency offer a dynamic approach for the detection of bacteria, measurement of their growth, their response to chemical agents, and other biomedical applications. Therefore, we have developed a stand-alone prototype device that utilizes an elegant combination of a laser diode and photodiode to monitor particle rotation.     

Particle behavior in aesthetic field theory

We discuss the structure of a particle system obtained in “aesthetic” field theory and study the evolution of this system in time. We find the particle system to have more structure than particles found by other authors investigating particlelike behavior in nonlinear field theories. Our particle system has a maximum center in proximity to a minimum center. Thus, we can interpret our system as being constructed of two bodies. We find that the maximum center and the minimum center move in straight lines, to computer accuracy. Thus, we have not found any nontrivial force laws. This suggests that the situation with respect to basic principles be kept fluid. So far as we know, we are the first investigators to study the trajectories of a two-body system which arises as a consequence of nonlinear field equations.     

The equation of motion for the trajectory of a circling particle with an overdamped circle center

Inspired by biological microorganisms swimming in circles in liquid with low Reynolds number, I developed the dynamic theory for computing the helical trajectory of a circling particle with an overdamped circle center. The equation of motion for the circling particle is a hybrid equation of deterministic terms and stochastic terms. Observing the motion of a swimming microorganism, I found the strength of stochastic fluctuations should be much smaller than that governs deterministic dynamics. This dynamic theory predicts a nonlinear transverse motion perpendicular to the direction of external force. Both the living microorganism and artificial circling particle are applicable for an experimental check of this prediction. For the convenience of easy theoretical research, I further derived the probability conservation equations based on this dynamic theory both in two-dimensional and three-dimensional space.     

A path integral formula for quark condensate states in?a?modified?PQCD

A modified version of PQCD considered in previous works is investigated here in the case of retaining only the quark condensate. The Green function generating functional is expressed in a form in which Dirac’s delta functions are now absent from the free propagators. The new expansion implements the dimensional transmutation effect through a single interaction vertex in addition to the standard ones in massless QCD. The new vertex suggest a way for constructing an alternative to the SM, in which the mass and CKM matrices could be generated by the instability of massless QCD under the production of the top quark and other fermions condensates, in a kind of generalized Nambu–Jona-Lasinio mechanism. The results of a two loop evaluation of the vacuum energy indicate that the quark condensate is dynamically generated. However, the energy as a function of the condensate parameter is again unbounded from below in this approximation. Assuming the existence of a minimum of the vacuum energy at the experimental value of the top quark mass m _q =173 GeV, we evaluate the two particle propagator in the quark–anti-quark channel in zero order in the coupling and a ladder approximation in the condensate vertex. Adopting the notion from the former top quark models in which the Higgs field corresponds to the quark condensate, the results suggest that the Higgs particle could be represented by a meson which might appear at energies around twice the top quark mass.     

Possibility of T-violating P-conserving magnetism and its contribution to the T-odd P-even neutron–nucleus forward elastic scattering amplitude

T-violating P-even magnetism is considered. The magnetism arises from the T-violating P-conserving vertex of a spin 1/2 particle interaction with the electromagnetic field. The vertex vanishes for a particle on the mass shell. Considering the particle interaction with a point electric charge we have obtained the T-violating P-even spin dependent potential, which is inversely proportional to the cubed distance from the charge. The matrix element of this potential is zero for particle states on the mass shell; nevertheless, the potential contributes to the T-odd P-even neutron forward elastic scattering amplitude by a deformed nucleus with spin . The contribution arises if we take into account incident neutron plane wave distortion by the strong neutron interaction with the nucleus. Received: 29 August 2000 / Revised version: 22 January 2001 / Published online: 23 March 2001     

The nonlinear Dirac equation in Bose-Einstein condensates: Foundation and symmetries

We show that Bose-Einstein condensates in a honeycomb optical lattice can be described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We present a rigorous derivation of the nonlinear Dirac equation from first principles. We provide a thorough discussion of all symmetries broken and maintained.     

Traffic of indistinguishable particles in complex networks

In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under different restrictive conditions the particle distributions satisfy different forms, including the Bose--Einstein distribution, the Fermi--Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose--Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions.     

Plasma wave frequency shift in a weak transverse magnetic field due to trapped particle acceleration

A simple model of nonlinear electrostatic wave–particle interaction in a weak magnetic field perpendicular to the direction of wave propagation is developed. The damping of the wave loaded with the phase bunched groups of trapped particles is considered with the aid of the model equations. To determine the nonlinear frequency shift of the wave in the process of the trapped particle acceleration, the nonlinear dispersion equation is derived. It is shown that the corresponding variation of the phase velocity may affect the interaction process and hence must be taken into account in the self-consistent treatment of the time evolution of the wave.     

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincaré invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark?Cantiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space?Ctime hyperboloid could be advantageous.     

Regularization of the interaction and renormalization of the physical constants in the clothed particle representation within the quantum field theory

The possibility of covariant regularization of trilinear Yukawa-type interaction has been investigated within the simplified standard quantum field theory. The properties of the vertex functions, conditioned by the Lorentz invariance of particle mass shifts, and regularizing functions in the lowest interaction orders have been studied within the clothed-particle representation.     

Fast electrons generation by RF and random fields near the antenna I. One dimensional model and regular fields

Test particle motion and acceleration has been explored in strong radio frequency (RF) fields, for which quasilinear ponderomotive force approximation is not valid. By nonlinear acceleration in spatially varying wave amplitude of RF travelling wave, electrons may be accelerated to time averaged velocities significantly larger than the RF wave phase velocity, and than the boundary plasma thermal velocity, in RF fields of several Volts per centimeter at wave frequency of 7 MHz. It is also demonstrated that even weak spatial gradients, much weaker than those expected in experiments, of the RF wave field amplitude, have significant consequences for the particle motion. Estimates are presented of the total energy transferred from the near antenna RF field to the plasma due to the nonlinear electron acceleration effects.     

The analysis of the charge on a cylindrical dielectric particle in unipolar corona field

In this study, a nonlinear integro-differential equation is derived to express the charging kinetics of stationary and rotational cylindrical dielectric particle in unipolar corona field. An algorithm is developed to solve the derived equation numerically by using Euler method. The variation of charge on the dielectric cylindrical particle is presented and evaluated by considering the variable parameters of the particle, medium and field. Assessments of the numerical results demonstrate that the limit charge value on stationary cylindrical dielectric particle during the charging process in unipolar corona field is less in comparison with the rotational cylindrical particle in identical conditions. Also this is an important factor for electron–ion technology in the aspect of charging kinetic problems.     

Structure of elementary particles in a nonlinear field theory

Characteristics of nonlinear gauge-invariant singularity-free field theories of elementary particles are discussed. It is shown that the electromagnetic field, in conjunction with a scalar field which is required for gauge invariance, provides a potential mechanism for the creation of the spin and magnetic moment of the particle, in addition to its mass and charge.     

On Nonstationary Inhomogeneities of the Nonlinear Klein—Gordon Equation

JETP Letters - A system consisting of a point material particle and a field described by the nonlinear Klein-Gordon equation has been considered. The particle produces an inhomogeneity of the field...