Self-dual SU(2) invariant Einstein metrics and modular dependence of theta-functions

We simplify Hitchin's description of SU(2)-invariant self-dual Einstein metrics, making use of the tau-function of related four-pole Schlesinger system.Comment: A wrong sign in the formula for W_1 is corrected; we thank Owen Dearricott who pointed out this mistake in the original version of the pape

Z' signal from the LEP2 data

The many-parametric fit of the LEP2 data on e^+e^-\to e^+e^-, \mu^+\mu^-, \tau^+\tau^- processes is performed to estimate signals of the Abelian Z'-boson beyond the standard model. The model-independent relations between the Z' couplings to the standard model particles allow to describe the Z' effects in lepton processes by 4 independent parameters. No signal is found by the complete LEP2 data set, and the 1.3\sigma signal is detected by the fit of the backward bins. The Z' couplings to the vector and axial-vector lepton currents are constrained. The comparisons with the one-parameter fits and with the LEP1 experiments are performed.Comment: 6 pages, 2 figures, RevTeX. The paper was completely rewritten. The errors in the first version were eliminated. The comparison with the LEP1 data is adde

Two-band superconductors: Extended Ginzburg-Landau formalism by a systematic expansion in small deviation from the critical temperature

We derive the extended Ginzburg-Landau (GL) formalism for a clean s-wave two-band superconductor by employing a systematic expansion of the free-energy functional and the corresponding matrix gap equation in powers of the small deviation from the critical temperature tau = 1-T/T_c. The two lowest orders of this expansion produce the equation for T_c and the GL theory. It is shown that in agreement with previous studies, the two-band GL theory maps onto the single-band GL model and thus fails to describe the difference in the spatial profiles of the two band condensates. We prove that except for some very special cases, this difference appears already in the leading correction to the GL theory, which constitutes the extended GL formalism. We derive linear differential equations that determine the leading corrections to the band order parameters and magnetic field, discuss the validity of these equations, and consider examples of an important interplay between the band condensates. Finally, we present numerical results for the thermodynamic critical magnetic field and temperature-dependent band gaps (at zero field), which are in a very good agreement with those obtained from the full BCS approach in a wide temperature range. To this end, we emphasize the advantages of our extended GL theory in comparison with the often used two-component GL-like model based on an unreconstructed two-band generalization of the Gor'kov derivation

Signals of Z' boson in the Bhabha process within the LEP2 data set

The LEP2 data set on the Bhabha process is analyzed with the aim to detect the signals of the heavy virtual Z' gauge bosons. The state interacting with the left-handed standard-model doublets and called the Chiral Z' is investigated. This particle was introduced already as the low-energy state allowed by the renormalizability of the model. The contribution of the Chiral Z' state to the Bhabha process is described by two parameters: the coupling to electrons and the Z-Z' mixing angle. The sign-definite one-parameter observable is proposed to measure the Z' coupling to the electron current. The one-parameter fit of the data shows no signals of the particle. The alternative two-parameter fit of the differential cross-sections is also performed. It also shows no Chiral Z' signals. The comparisons with other fits are discussed.Comment: 15 pages, 4 figures. The paper was completely rewritten on the base of new dat