International Journal of Modern Physics A

Nucleus–nucleus collisions at very high energy are believed to create the conditions for the existence of a new state of matter, the so-called quark–gluon plasma. This possibility depends on the magnitude of the energy density really achieved during the collisions. Estimates of the energy density are model dependent and have been attempted according to various approaches: fire-ball model and Bjorken model. The understanding of the transverse energy flow measurements and of the stopping power helps to define a proper way to estimate the energy density beyond naive approaches. A space- and time-averaged energy density is shown to be a more reliable probe for the QGP search than is a naive estimate of the maximum energy density. The computation is performed within the framework of hydrodynamics. The data considered in this paper were obtained by experiments performed to study nucleus–nucleus collisions at the CERN Super Proton Synchrotron (CERN-SPS). The incident nuclei were accelerated at energies of 60 and 200 GeV/nucleon.

A simple scheme of unified description of different physical phenomena by using the Langevin type equations is reviewed. Within this approach much attention is being paid to the study of Brownian and quantum motions. Stochastic equations with a white noise term give all characteristics of the Brownian motion. Some generalization of the Langevin type equations allows us to obtain nonlinear equations of particles' motion, which are formally equivalent to the Schrödinger equation. Thus, we establish Nelson's stochastic mechanics on the basis of the Langevin equation.

Production cross-sections of color-sextet quarks at hadron colliders are estimated in various energies and the results are compared with cross-sections of the conventional top quark productions. Particular attentions are paid for a model recently proposed in Ref. 2 in order to explain the dynamical mechanism of the electroweak symmetry breaking. The model may be tested at SSC and LHC if the sextet quarks dominantly decay semileptonically through effective fourfermion interactions, or if the sextet quarks have long enough lifetime to reach the detectors.

We present, based upon quantum electrodynamics in Robertson–Walker flat universes, a thorough analysis of the creation of mutually interacting electron–positron pairs and photons from vacuum. Therefore we discuss at least qualitatively all processes contributing to the number densities of created particles up to the second order in the coupling constant.

For two particular expansion laws with Minkowskian in respectively in and out regions, we obtain exact solutions to the Dirac equation and investigate in detail the process of simultaneous creation of electron–positron pairs and photons and the related attenuation effect for fermionic particles. This is done for electrons and positrons which have nonrelativistic momenta at Compton time in rapidly expanding universes.

The results are compared with the zeroth-order creation of electron–positron pairs. Despite being smaller by a factor of roughly , the interacting-particle creation is important mainly as a source of photons even in conformally flat universes.

Recent works devoted to investigating the role of electric polarizability of nuclei in elastic and nucleosynthesis reactions are critically and constructively reviewed, in order to formulate some problems of the low-energy potential scattering theory. Possible methods for solving these problems are outlined. One of the problems, a correct definition of the range of action of the polarization potential, is discussed in detail. An intuitively clear conception of this radius — the lower bound of the distance range, where the polarization potential may be replaced by identical zero — is used as a starting point. The fact that this bound should be defined in each concrete case is demonstrated by the results obtained by exploration of the pp reaction and the S-wave π^±d-elastic collisions. Also discussed are numerical and analytical methods for finding the action radius depending on the studied function, the accuracy required for its evaluation, the scattering energy and the sign of the Coulomb potential.

Multi-instanton effect in the standard electroweak model for baryon and lepton number violation is discussed. Instanton interaction is shown to play a major role in the TeV range. First, the validity of the treatment of the interaction is explicitly checked in the quantum-mechanical case. Then interactions induced by both bosons and fermons are examined in the SU(2) Yang–Mills–Higgs model. They are shown to lead to an effective theory which is manifestly unitary. This results in an estimate that the relevant cross section saturates the unitary bound at the TeV scale, indicating the possibility of detecting baryon- and lepton-number-violating phenomena.

We consider a class of four-fermi theories in 2 + 1 dimensions minimally coupled to electromagnetism. The low energy effective Lagrangian is derived in the Coulomb phase using a duality transformation. It is shown that the photon field (which is a Goldstone boson following from spontaneous breakdown of the magnetic flux symmetry) plays the same role as any other Goldstone boson, namely that of one of the coordinates on the order parameter manifold. Treating this Lagrangian as a quantum theory, we find that it shows the same phase structure as the original theory, giving thereby the description of the same phases and excitations in the dual language.

The Bethe–Salpeter equations for the n-particle irreducible Green functions in quantum field theory are derived. Their kernels are expressed in terms of the functional Legendre transforms, and n-particle irreducibility of the perturbation theory graphs for the kernel of the n-particle equation is proved. The method for obtaining the Faddeev–Yakubovski equations in quantum field theory is demonstrated for the three-particle case.

A recently proposed, new construction of the Standard Model based on the graded Lie algebra SU(2|1) is analyzed in some depth. The essential ingredient is an algebraic superconnection which incorporates both the gauge fields and the Higgs fields and whose curvature automatically leads to a spontaneously broken realization of the theory. The mechanism of hiding the original algebraic structure is unorthodox and is due to the specific, "noncommutative" realization of SU(2|1). The model is characterized by a constant background supercurvature which is invariant under arbitrary, constant SU(2|1) gauge transformations. This background field whose effect is analogous to the action of a constant magnetic field on a spherical atom, is traced back to the differential in the space of (super)matrices by means of which the supercurvature is constructed. The same background field is responsible for the fact that the ground state has no more than the U(1)_e.m. symmetry of electromagnetism, the SU(2)_L × U(1) symmetry of the Standard Model being recovered only after "backshifting" the Higgs fields. Thus, the Higgs mechanism receives a new and geometrical interpretation.

We use the Faddeev–Popov method to calculate explicitly the path integral propagator for a relativistic spinless charged particle in the presence of a constant magnetic field. We obtain the conservation laws in the path integral approach. We also establish the equivalence between the Faddeev–Popov method and the Fock–Schwinger proper time approach. Finally, after proposing a suitable regularization prescription for the non-relativistic problem, we obtain the Landau levels directly from the path integral result.

A simple independent-quark model based on the Dirac equation with an equally mixed scalar–vector linear confining potential model is used to obtain a fit for the electromagnetic properties — like the magnetic moments, charge radii and axial-vector coupling-constant ratios — of octet baryons, taking into account the appropriate center-of-mass corrections. This fit is extended to include the quark-core contributions to the nucleon electromagnetic form factors , , and the axial-vector form factor G_A(q²). The respective root-mean-square radii associated with and G_A(q²) come out as and . The possibility of restoring in this model the chiral symmetry in the usual way is discussed and the pion-nucleon coupling constant is found as g_πNN = 13.72 as compared to (g_πNN)_exp ≃ 13.

To have a consistent picture, a simultaneous analysis for the K → ππ isospin amplitudes A₀ and A₂, the ΔI = 1/2 rule, CP-violating ε′/ε, and and mixings within the standard model is made by employing the recent reanalyzed values of the parameters and relating the penguin matrix elements involved in the K → ππ decays to the known matrix elements of the ΔI = 1/2 operator (Q₂ − Q₁) and ΔI = 3/2 operator (Q₂ + 2Q₁). The allowed values for all the relevant quantities are calculated in detail. A general bound for top quark mass m_t, CP phase δ and ε′/ε is found: for δ in the second quadrant, 84GeV ≤ m_t ≤ 250GeV, δ ≤ 173° and 1 × 10⁻⁴ < ε′/ε ≤ 1 × 10⁻²; for δ in the first quadrant, 126GeV ≤ m_t ≤ 664GeV, δ ≥ 11º and 1 × 10⁻³ < ε′/ε ≤ 1 × 10⁻² as m_t ≤ 260GeV. Taking the plausible central values of the parameters — |V_cb| = 0.041, |V_ub|/|V_cb| = 0.12, B_K = 0.75, , x_B = 0.70, m_s = (100 ~ 125)MeV and Λ_QCD = (200 ~ 300)MeV — as a "standard" set, we then obtain from the simultaneous analysis a consistent prediction: A₀ = (3.24 ± 0.70) × 10⁻⁷, A₂ = (0.145 ± 0.007) × 10⁻⁷, ω = A₂/A₀ = 0.046 ± 0.007 and m_t ≃ 142GeV, δ ≃ 152°, ε′/ε ≃ (2.5 ± 1.0) × 10⁻³. The possible implications for the experiments are also discussed.