To What Extent is Gluon Confinement an Empirical Fact?

Experimental verifications of confinement in hadron physics have established the absence of charges with a fraction of the electron’s charge by studying the energy deposited in ionization tracks at high energies, and performing Millikan experiments with charged droplets at rest. These experiments test only the absence of particles with fractional charge in the asymptotic spectrum, and thus “Quark” Confinement. However what theory suggests is that Color is confined, that is, all asymptotic particles are color singlets. Since QCD is a non-Abelian theory, the gluon force carriers (indirectly revealed in hadron jets) are colored. We empirically examine what can be said about gluon confinement based on the lack of detection of appropriate events, aiming at an upper bound for high-energy free-gluon production.     

Relativistic Hamiltonian dynamics

A manifestly covariant relativistic hamiltonian dynamics is presented for a closed system of N particles in mutual interaction. The “no-interaction theorem” is overcome by use of relativistic center-of-mass variables instead of individual particle variables. The theory permits canonical quantization.     

On the superconvergence of meson-nucleon invariant scattering amplitudes

Using two models, i.e. perturbation theory with the usual PS-PS Hamiltonian and a “relativistic” version of the Lee model with the same type of interaction, it has been tried to clarify the question if there are superconvergent amplitudes in the (π, K) meson-nucleon forward scattering. Does the impressive validity of the well-known sum rule for theB ⁽⁺⁾ amplitude makes a serious support of the assumed superconvergence (becauseB describes the spin-flip scattering)? Indications, obtained from perturbation theory, including all Feynman diagrams up to the sixth order in the coupling constant and from the Lee model, where all allowed diagrams can be summed up, do not support the superconvergence assumption. Therefore the impressive prediction of theB ⁽⁺⁾ amplitude sum rule seems to be accidental.     

Relativistic approaches to investigation of few-nucleon systems

Theoretical approaches used in investigation of relativistic effects in high energy lepton and hadron collisions with few-nucleon systems are analyzed. The Bethe-Salpeter formalism for describing interacting systems of two spinor particles both in the continuum and bound state is described in detail. Special attention is paid to partial expansions, taking into account the analytic properties of Bethe-Salpeter amplitudes and unitary transformations correlating different representations of partial amplitudes. Mathematical methods of numerical solution of equations are considered. Results of calculation of relativistic corrections and effects of interaction in the final state in particular reactions with participation of the deuteron, namely, in elastic pD backward scattering and in reactions of deuteron break-up with production of correlated pairs, are presented.     

Persistent threshold effects characterizing dimuon and hadron distributions due to charmed particle production by neutrinos

If massive charmed particles are being produced in current νN scattering experiments, their semi-leptonic decay leads to dimuon states. The production and decay of such particles in this process is examined in a parton model which has been modified to realistically incorporate the threshold due to the large mass of the charmed particle.The model then predicts threshold scaling violations which are unexpectedly large, and persist out to several hundred GeV in neutrino energy. These effects are particularly striking in the distributions of the charmed particle and its decay products, whose naive-scaling violations are so extreme as to be better described in terms of new anomalous scaling “laws”.The resultant dimuon and hadron distributions are qualitatively consistent with all trends observed in the recent dimuon experiments. Comparative tests between charm and other mechanisms for dimuon production are proposed. An important feature of these tests is their reliance on the persistent threshold effects predicted above. The present data on the muonic energy asymmetry β as a function of incoming neutrino energy is in agreement with the anomalous scaling predicted in the above model.     

Practical relativistic three-particle theory with arbitrary particle interactions

Relativistic three-particle equations are established by the rules of Blankenbecler and Sugar, which put the intermediate particles on the mass shell. By use of the Wightman-Gåding momenta we preserve the correct cluster properties, time-reversal invariance and avoid a spurious s = 0 singularity. A reduction to effective multichannel two-particle equations which is not restricted to separble potentials is discussed. Our approach admits the systematical application of perturbation theory to relativistic composite particle scattering problems.     

Bemerkungen zum Kleinschen Paradoxon

The problem of stationary energy eigenstates of relativistic spin 1/2-particles in external potentials exceeding twice the particles rest mass (Klein's paradox) is investigated, neglecting the interaction of the particles with the radiation field. This corresponds to theH ₀ of the “bound state interaction representation” in quantum electrodynamics. For simplicity, explicit calculations are based on a one dimensional square well potential. In potentials of this type which vanish at infinity and which do not become critically singular at the origin there always exists a stationary ground state of fixed total charge. Though this state, naturally, cannot be attributed to a sharp number of particles, no real paradox occurs.     

Finite energy sum rules for π-N backward scattering

Finite energy sum rules for the A and S,π-N scattering amplitudes are saturated in the region ?0.4 GeV²< u <0 with a number of s andt channel resonances. It turns out that one needs a rather large π—π s wave contribution, to get agreement with the high energy Regge pole analysis, which explains the dip structure in π⁺p scattering atu ₀=?0.15 GeV² by a zero in theN _α contribution. The coupling of theN _α trajectory seems to be much stronger than the coupling of theN _γ andΔ _δ trajectories.     

相对论粒子的散射与低速粒子的散射

研究了相对论粒子间散射的规律,推导了相对论粒子间散射的洛伦兹因子公式.结果发现:如果两个粒子的静止质量相同,则粒子在高速时的碰撞规律和低速时的碰撞规律相同,即两个正碰粒子互换速度;如果两个粒子的静止质量不同,则粒子在高速时的碰撞规律和低速时的碰撞规律不同,高速正碰时重粒子将损失大部分能量,轻粒子的速度将接近光速,而不等于重粒子速度的2倍.     

Topological pomeron andA-universality

The nuclear mass number dependence of inclusive spectra of secondaries with different quantum numbers in the projectile fragmentation region is analysed. We note that in models with topological pomeron, all the particle spectra fall into two main categories. The first one comprises particles which have a common “valence” quark with the projectile, the second one comprises all the other particles built of “sea” quarks. Thus, in the parameterization \(x\frac{{d\sigma }}{{dx}} \propto A^{\alpha (x)} \) the spectra of all “valence” hadrons (p, n, Λ, π^+,0,?,K ⁺, ... in thepA-interaction) atx→1 can be characterized by the single exponent α_υ =α(x?1) which differs slightly from α _s characterizing the spectra of “sea” hadrons ( \(\bar p, \bar \Lambda \) ,K ^?, ... forpA-interactions). This observation is essentially modelindependent and follows only from the topological structure of the pomeron and Gribov's space-time picture of soft hadronic interactions. Deviations from universality due to preasymptotic corrections and coherent particle production processes are estimated.     

Nonlinear Compton scattering of strong laser radiation on channeled particles in a crystal

A version for intense γ-ray radiation based on the multiphoton scattering of strong laser radiation on relativistic particle beam channeled in a crystal is proposed. The incident laser beam and charged particles beam are counter-propagating and the laser radiation is resonant to the energy levels of transversal motion of channeled particles.     

Renormalized Perturbation Expansion in Kinetic Theory

Ladder summation techniques are applied to the recently developed c-number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T-matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell-Boltzmann statistics), the T-matrix introduced coincides with the usual T-matrix of conventional two-body scattering theory in free space. In low-temperature Fermi systems, the T-matrix differs from the reaction matrix of the Brueckner-Goldstone theory because the “healing” property of the two-body wave function does not obtain.     

TheN/D method off the mass shell for the Klein-Gordon equation and the inversion problem

The relativistic analogon of a procedure demonstrating the link between theS-wave off-the-mass- shellN/D equations (variables: the momentum, energy and radial coordinate of a scattered particle) and the Marchenko equations of the inversion problem is presented in the static scattering. For the Klein-Gordon formalism the transition from the former type of the equations to the latter requires: a decomposition of theN/D equation quantities into the components without theE-branch points, a suitable deformation of the integration path in theN/D equations and an assumption on the regular behaviour of the off-the-mass-shellN function discontinuities.     

In-medium relativistic kinetic theory and nucleon-meson systems

Within theσ —ω model of coupled nucleonmeson systems, a generalized relativistic Lennard-Balescu-equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as fluctuation effects. It contains all possible processes due to one-meson exchange and special attention is kept to the off-shell character of the particles. As a new feature of many-particle effects, processes are possible, which can be interpreted as particle creation and annihilation due to in-medium onemeson exchange. In-medium cross sections are obtained from the generalized derivation of collision integrals, which possess complete crossing symmetries.     

Kramers Kronig analysis of the optical properties of small silver particles

In order to complete a preceding paper the dielectric constant? of the particle material of small silver particles with diameters between 210 and 25 Å is computed in the wavelength region 365≦λ≦455 nm from the measured spectra of thesmall particle plasma reasonance absorption. For this purpose a properKramers Kronig relation is derived, and is checked by applying to particles with Drude free electron gas. The results, concerning the silver particles, are that the real part of? changes slightly, whereas the imaginary part is markedly enhanced (up to the ten-fold of the bulk values) if the particle size decreases. This size dependence of? can quantitatively be described with thefree path effect within the accuracy of the measured values. Conversely, thebulk dielectric constant of silver is obtained by applying the free path effect to the measured dielectric constant of the small particles.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

Exact statements about many-particle systems with higher symmetries

A new method of calculating the energy spectrum of a system of A identical Fermi particles with translationally invariant interaction is developed under the assumption that there exists a high symmetry in the 3A-dimensional space of particle coordinates. For a special class of symmetries the many-body problem is split exactly into two sets of equations: one containing only totally symmetric combinations of the particle coordinates which are called “collective variables” and the other equation taking essentially into account the requirements of the Pauli principle and connected symmetry properties. In several cases it is possible to obtain the excitation spectra exactly showing qualitatively new features. They depend on “many-particle quantum numbers” varying independently of each other in an interval which sometimes depends on A. For special high symmetries the collective variables obey equations which are very similar to one-particle equations providing a new explanation of the “Independent-Particle Model” for arbitrary strength and form of the interaction potential. A manifold of unknown up to now excitation spectra of many-particle systems is obtained and discussed.     

Scattering off of an instanton

We consider the scattering of a classical colored particle off an instanton. That is, we investigate Wong's equations (or equivalently, the Kaluza-Klein geodesic equations) for a colorSU(2) particle under the influence of a Euclidean instanton. We solve the equations in the limit in which the instanton becomes singular. Our main result is that particles with head-on trajectories scatter off the instanton with a scattering angle of π/3. This angle is independent of the magnitude of the color charge and velocity of the particle as long as both are nonzero. The plane in which the scattering takes place is determined by the particle's initial position and color charge. We also solve for the geodesics for the corresponding (singular) Kaluza-Klein metric onS ⁷.