Spontaneous generation of the Nambu --Jona-Lazinio interaction in quantum chromodynamics with two light quarks

In QCD with two light quarks with application of Bogolubov quasi-averages approach a possibility of spontaneous generation of an effective interaction, leading to the Nambu -- Jona-Lazinio model, is studied. Compensation equations for form-factor of the interaction is shown to have the non-trivial solution leading to theory with two parameters: average low-energy value of $\alpha_s$ and dimensional parameter $f_\pi$. All other parameters: the current and the constituent quark masses, the quark condensate, mass of $\pi$ meson, mass of $\sigma$ meson and its width are expressed in terms of the two initial parameters in satisfactory correspondence to experimental phenomenology. The results being obtained allow to state an applicability of the approach in the low-energy hadron physics and promising possibilities of its applications to other problems.Comment: 16 pages, 1 table, 3 figure

Radiative Corrections to Neutrino Deep Inelastic Scattering Revisited

Radiative corrections to neutrino deep inelastic scattering are revisited. One-loop electroweak corrections are re-calculated within the automatic SANC system. Terms with mass singularities are treated including higher order leading logarithmic corrections. Scheme dependence of corrections due to weak interactions is investigated. The results are implemented into the data analysis of the NOMAD experiment. The present theoretical accuracy in description of the process is discussed.Comment: 19 pages, two figures are added, discussion of theoretical uncertainties is extende

Von Neumann's Quantization of General Relativity

Von Neumann's procedure is applied for quantization of General Relativity. We quantize the initial data of dynamical variables at the Planck epoch, where the Hubble parameter coincides with the Planck mass. These initial data are defined via the Fock simplex in the tangent Minkowskian space-time and the Dirac conformal interval. The Einstein cosmological principle is applied for the average of the spatial metric determinant logarithm over the spatial volume of the visible Universe. We derive the splitting of the general coordinate transformations into the diffeomorphisms (as the object of the second N\"other theorem) and the initial data transformations (as objects of the first N\"other theorem). Following von Neumann, we suppose that the vacuum state is a quantum ensemble. The vacuum state is degenerated with respect to quantum numbers of non-vacuum states with the distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functional of the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. We discuss the region of applicability of gravidynamics and its possible predictions for explanation of the modern observational and experimental data.Comment: 14 pages, updated version with extended discussio

Update of the e^+e^-\to\pi^+\pi^- cross section measured by SND detector in the energy region 400<\sqrt{s}<1000 MeV

The corrected cross section of the e^+e^-\to\pi^+\pi^- process measured in the SND experiment at the VEPP-2M e^+e^- collider is presented. The update is necessary due to a flaw in the e^+e^-\to\pi^+\pi^- and e^+e^-\to\mu^+\mu^- Monte Carlo events generators used previously in data analysis.Comment: 10 pages,7 figure

Electroweak Effects in Neutral Current Drell-Yan Processes within SANC System

The complete one-loop electroweak radiative corrections to the neutral current Drell-Yan process $pp \to \ell^+\ell^- X$ are presented for the case of longitudinal polarization of initial particles. The calculations are based on the SANC computer system. The paper contains a brief description of the SANC approach and a discussion of the sources of theoretical uncertainties in electroweak effects

The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.Comment: 22 pages, 6 figure

One-loop chiral amplitudes of Moller scattering process

The high energy amplitudes of the large angles Moller scattering are calculated in frame of chiral basis in Born and 1-loop QED level. Taking into account as well the contribution from emission of soft real photons the compact relations free from infrared divergences are obtained. The expressions for separate chiral amplitudes contribution to the cross section are in agreement with renormalization group predictions.Comment: 15 pages, 3 figure