International Journal of Modern Physics A

The four detectors ALEPH, DELPHI, L3 and OPAL have collected ≈550,000 Z⁰ decays during the LEP run in 1990. We have made model-independent simultaneous fits to the LEP data to determine the Z⁰ parameters. The mass and widths of Z⁰ are M_z=91.177± 0.006±0.02(LEP) GeV, Γ_z=2.481±0.010 GeV, Γ_had=1.734±0.010 GeV and Γ_lept=83.0 ± 0.4 MeV. The number of ν families is determined to be N_ν=3.01±0.05. Simultaneous fits are performed within the Standard Model framework to the LEP data and constraining the value of sin² θ_w from the colliders we get the following values for top mass, electroweak mixing angle sin² θ_w and the radiative correction , sin² θ_w=0.230±0.004 and ∆r=0.056±0.011.

New results in applications of the analytical perturbative approach to the description of particle distributions in QCD jets are presented. We study inclusive energy spectra of partons from QCD cascades truncated at different values of the cutoff parameter Q₀, which can be used to model the energy distributions of massive hadrons in the framework of the local parton-hadron duality hypothesis. Results of straightforward numerical calculations of parton distributions which solve the MLLA evolution equations are compared to approximate formulas representing the spectra in terms of a few analytically calculated shape parameters.

From the peripheral collisions of a ³²S beam at 200A GeV in nuclear emulsion, He tracks among the projectile fragments are identified and are followed for their interactions. The multiplicity distributions and their fluctuations in pseudorapidity intervals of the shower particles produced with ~500 He interactions in emulsions are compared with ³²S and ¹⁶O beams at 200A GeV and ¹⁶O at 60A GeV interactions. It is primarily the geometry of the nuclear collisions that determines the shape of different distributions.

Making use of a vector-dominance model for the nucleon electromagnetic form factors, we investigate the consequences for the calculation of the inclusive electromagnetic response (in the quasielastic domain) of recent suggestions that mesonic mass parameters are modified in a nuclear medium.

A systematic discussion of the probability of eta and K_L bound-state decays— and (l=e, μ)—within a three-dimensional reduction to the two-body quantum field theory is presented. The bound-state vertex function depends on the relative momentum of constituent-like particles. A structure-transition form factor is defined by a confinement-type quark-antiquark wave function. The phenomenology of this kind of decays is analyzed.

Generalized models are considered with exponential interactions and in the presence of a background charge vector. In order for the action to be renormalizable, the vectors involved in the exponential interactions should form a geometrical figure. Along renormalization-group flows, the shape of the figure changes, but not its topology. The β functions describing the figure distortion are obtained in general. When the corresponding geometrical figure is a triangle, the model is investigated in detail. This “triangle model” has nine running coupling parameters, among which three parameters describe the shape of the triangle. From the nine β functions of the model, the fixed points are found and their stability is determined. By using the exact results for the fixed points and their stability, the general structure of the renormalization-group flows is discussed.

We extend the recently invented method of calculating massive Feynman integrals, namely the differential equations method, to vertex-type diagrams. As an example, for calculations of one-and two-loop diagrams we show that by analogy with propagator-type diagrams this method is a simple procedure for evaluating the result without calculating D-space integrals (for dimensional regularization).

The positive total energy test is applied to the Poincaré Gauge Theory of gravity. Both the asymptotically flat and asymptotically constant negative curvature case are considered. The test shows that in either case, the theory with generic values for the parameters is not viable.

Using a mechanism similar to that employed by Freedman and Townsend in four dimensions, we discuss a variety of two- and three-dimensional gauge theories. The simplest of these models is equivalent to the nonlinear sigma model; another corresponds to a massive vector theory. In three dimensions, there exists a gauge invariance associated with the auxiliary vector ϕ_μ^a; when we quantize, this is accommodated using both the Batalin-Vilkovisky configuration space formalism and the Batalin-Fradkin-Vilkovisky configuration space formalism. Explicit one-loop calculations in the simplest two-dimensional model are carried out. The regularization used is a variant of operator regularization, allowing one to remain in two dimensions, hence circumventing problems associated with definition of the antisymmetric tensor ε_μν. This model is renormalizable, with renormalization mixing the scalar field ϕ^a and the transverse component of the vector field V_μ^a.

A model for the 17 keV Dirac neutrino is considered in the framework of the SU(2)×U(1) theory. No right-handed neutrinos are introduced. The Dirac mass for the neutrino arises from the L_e+L_τ–L_μ invariant couplings of the left-handed neutrinos to an SU(2) triplet. An SU(2) singlet field is introduced to suppress the Majoron coupling to the Z. This makes the model consistent with the LEP results on the invisible Z width. The singlet vacuum expectation value ω is constrained to be ≤O(80 MeV) from cosmological considerations. For, ω≈80 MeV, the 17 keV neutrino is shown to provide the bulk of the dark matter.

A possible reheating mechanism in inflationary universe models is studied in some detail. Results are presented of numerical investigations of particle creation and corresponding reheating within a self-coupled scalar field model. By using the method of Hamiltonian diagonalization attention is devoted to the time development of the process and its parameter dependence. The effect of particle production is found to depend strongly on the anharmonicity of the potential around its minimum and on the amplitude of the oscillations of the scalar background field.

A way to estimate photino contamination in neutrino flux from supernovas is suggested. By comparing the experimental and theoretically expected ratios of forward peaked events in the direction of the neutrino source and isotropic events, one can set a limit on selectron mass. As an example, the data from SN 1987A are used to set a limit on selectron mass. Assuming a hypothetical form of matter density variation of the supernova, the limits are obtained by varying the strength of Photino interactions.

Quantum electrodynamics in an expanding Robertson-Walker universe with the line element ds²=dt² – a²(t)(dx²+dy²+dz²) (radiation-dominated universe) is considered. The differential probability of bremsstrahlung of an electron in the external gravitational field and the differential probability of an electron-positron pair and photon creation from the vacuum are calculated by using the perturbative S-matrix formalism. The behavior of these probabilities in different kinematic regions is investigated. The total probabilities are shown to be finite. In conclusion, the total probability of a pair and photon creation from vacuum W_e is compared with the total probability of pair production due to an expansion of the universe W₀. The comparison shows that W_e=1.9·10⁻²W₀ at about the Compton time of an electron.

A geometric shape is a rigid shape in n-dimensional Euclidean space. These shapes commonly occur in the Born-Oppenheimer approximation in molecular physics, and collective models of nuclei. Abelian and non-Abelian generalizations of the vacuum angle of gauge theories are realized in the quantum theory of shapes. In this paper, such generalizations are presented in the language of modern quantum physics and it is shown that parity, , and time reversal, , are violated in certain of these quantum theories. However, the combined symmetry of parity composed with time reversal generally remains a good symmetry, just as in gauge theories. The exceptions are the quantum theories of staggered conformations which can violate only . The mechanism responsible for the loss of these symmetries is a generalization of the vacuum angle mechanism for the same effect. An important result of the present analysis is the demonstration that geometric shapes, molecules in the Born-Oppenheimer approximation, and nuclei in the collective model description furnish concrete systems which upon quantization discriminate between left- and right-handed coordinates even though this distinction is entirely absent in their classical descriptions.