Critical velocities c/3c/\sqrt 3 and c/2c/\sqrt 2 in general theory of relativity

We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the outside motion there exists a critical value of coordinate velocity ${\rm v}_c = c/\sqrt 3$: particles with ${\rm v} < {\rm v}_c$ are accelerated by the field, like Newtonian apples, particles with ${\rm v} > {\rm v}_c$ are decelerated like photons. Particles moving inside a body with constant density have no critical velocity; they are always accelerated. We consider also the motion of a ball inside a tower, when it is thrown from the top (bottom) of the tower and after classically bouncing at the bottom (top) comes back to the original point. The total time of flight is the same in these two cases if the initial proper velocity $v_0$ is equal to $c/\sqrt 2$.Comment: 13 page

Do Present LEP Data Provide Evidence for Electroweak Corrections?

The Born approximation, based on $\bar\alpha \equiv\alpha (m_Z)$ instead of $\alpha$, reproduces all electroweak precision measurements within their $(1\sigma)$ accuracy. The low upper limits for the genuinely electroweak corrections constitute one of the major achievements of LEP. The astonishing smallness of these corrections results from the cancellation of a large positive contribution from the heavy top quark and large negative contributions from all other virtual particles. It is precisely the non-observation of electroweak radiative corrections that places stringent upper and lower limits on the top mass.Comment: 12 pages, preprint CERN-TH.6943/9

Theory of Z boson decays

The precision data on Z boson decays from LEP-I and SLC colliders are compared with the predictions based on the Minimal Standard Theory. The Born approximation of the theory is based on three most accurately known observables: G_mu -- the four fermion coupling constant of muon decay, m_Z -- the mass of the Z boson, and alpha(m_Z) -- the value of the running fine structure constant at the scale of m_Z. The electroweak loop corrections are expressed, in addition, in terms of the masses of higgs, m_H, of the top and bottom quarks, m_t and m_b, and of the strong interaction constant alpha_s(m_Z). The main emphasis of the review is focused on the one-electroweak-loop approximation. Two electroweak loops have been calculated in the literature only partly. Possible manifestations of new physics are briefly discussed.Comment: 80 pages, 16 figures, accepted in Reports on Progress in Physic

Electroweak radiative corrections in Z boson decays

Contribution to A.D.Sakharov memorial volume. A detailed review of the electroweak radiative corrections to the Z-boson decays in the framework of the Minimal Standard Modelm (MSM) is presented. After a short historical introduction we describe the optimal parametrization of the MSM, especially of the Born approximation, and derive expressions for the one-loop electroweak corrections. Finally a global fit of all relevant experimental data is performed, resulting in fitted values of the top-quark mass, m_t, and strong coupling constant /alpha_s. Allowed range for the value of the Higgs mass, m_H, is discussed. Various details of calculations are described in 16 appendices.Comment: 98 pages,21 EPS and PS figures,uses epsf.sty, separate file with the tared, compressed and uuencoded figures is awailable at http://wwwtheor.itep.ru/~vysotsky/figures.u

Do neutrino oscillations allow an extra phenomenological parameter?

The quantity $\xi$ introduced recently in the phenomenological description of neutrino oscillations is in fact not a free parameter, but a fixed number.Comment: 2 pages, LaTeX 2e style articl

Precision measurements, extra generations and heavy neutrino

The existence of extra chiral generations with all fermions heavier than $M_Z$ is strongly disfavored by the precision electroweak data. The exclusion of one additional generation of heavy fermions in SUSY extension of Standard Model is less forbidden if chargino and neutralino have low degenerate masses with $\Delta m \simeq 1$ GeV. However the data are fitted nicely even by a few extra generations, if one allows neutral leptons to have masses close to 50 GeV. Such heavy neutrino can be searched in the reaction $e^+ e^- \to N\bar{N}\gamma$ at LEP-200 with total final luminosity of $2600 pb^{-1}$.Comment: 5 pages, 6 figures, Proceedings ICHEP2000 Osaka conferenc

On the search for 50 GeV neutrinos

Using the computer code CompHEP we estimate the number of events and the background, at LEP II and TESLA, for the reaction $e^+ e^- \to N\bar{N}\gamma$, where $N$ is a hypothetical Dirac neutrino with mass of the order of 50 GeV.Comment: Standard LaTeX, 9 pages, 2 tables, 3 figure