Two-dimensional algebro-geometric difference operators

A generalized inverse problem for a two-dimensional difference operator is introduced. A new construction of the algebro-geometric difference operators of two types first considered by I.M.Krichever and S.P.Novikov is proposedComment: 11 pages; added references, enlarged introduction, rewritten abstrac

Lattice Gauge Theory Sum Rule for the Shear Channel

An exact expression is derived for the $(\omega,p)=0$ thermal correlator of shear stress in SU($N_c$) lattice gauge theory. I remove a logarithmic divergence by taking a suitable linear combination of the shear correlator and the correlator of the energy density. The operator product expansion shows that the same linear combination has a finite limit when $\omega\to\infty$. It follows that the vacuum-subtracted shear spectral function vanishes at large frequencies at least as fast as $\alpha_s^2(\omega)$ and obeys a sum rule. The trace anomaly makes a potential contribution to the spectral sum rule which remains to be fully calculated, but which I estimate to be numerically small for $T\gtrsim 3T_c$. By contrast with the bulk channel, the shear channel spectral density is then overall enhanced as compared to the spectral density in vacuo.Comment: 11 pages, no figure

Topological Phenomena in the Real Periodic Sine-Gordon Theory

The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the consequences of this property. In particular this description allows to calculate the topological charge of solutions (the averaging of the $x$-derivative of the potential) and to show that the averaging of other standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure

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

Diagrammatic calculation of energy spectrum of quantum impurity in degenerate Bose-Einstein condensate

In this paper we considered a quantum particle moving through delute Bose-Einstein condensate at zero temperature. In our formulation the impurity particle interacts with the gas of uncoupled Bogoliubov's excitations. We constructed the perturbation theory for the Green's function of the impurity particle with respect to the impurity-condensate interaction employing the coherent-state path integral approach. The perturbative expansion for the Green's function is resumed into the expansion for its poles with the help of the diagrammatic technique developed in this work. The dispersion relation for the impurity clothed by condensate excitations is obtained and effective mass is evaluated beyond the Golden rule approximation

Mass of the higgs versus fourth generation masses

The predicted value of the higgs mass $m_H$ is analyzed assuming the existence of the fourth generation of leptons ($N, E$) and quarks ($U, D$). The steep and flat directions are found in the five-dimensional parameter space: $m_H$, $m_U$, $m_D$, $m_N$, $m_E$. The LEPTOP fit of the precision electroweak data is compatible (in particular) with $m_H \sim 300$ GeV, $m_N \sim 50$ GeV, $m_E \sim 100$ GeV, $m_U +m_D \sim 500$ GeV, and $|m_U -m_D| \sim 75$ GeV. The quality of fits drastically improves when the data on b- and c-quark asymmetries and new NuTeV data on deep inelastic scattering are ignored.Comment: 8 pages, 4 figure

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

Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page