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We specify an angular motion on geodesics to reduce the problem to the case of radial motion elaborated in previous chapters. An appropriate value of entropy for a charged and rotating black hole is obtained by calculating the partition function on thermal geodesics confined under horizons. The quantum aggregation is classified in a similar way to the Reissner--Nordstrom black hole., Comment: 6 pages, 1 eps-figure, iopart class, acknowledgement extended

The entropy of charged black hole is calculated by using the partition function evaluated at radial geodesics confined under horizons. We establish two quantum phase states inside the black hole and a transition between them., Comment: 10 pages, 6 eps-figures, iopart class, acknowledgement extended

Causal radial geodesics with a positive interval in the Schwarzschild metric include a subset of trajectories completely confined under a horizon, which compose a thermal statistical ensemble with the Hawking-Gibbons temperature. The Bekenstein--Hawking entropy is given by an action at corresponding geodesics of particles with a summed mass equal to that of black hole in the limit of large mass., Comment: 16 pages, 12 eps-figures, iopart class, tought experiment (p.7) added

This report is the result of the collaboration and research effort of the Quarkonium Working Group over the last three years. It provides a comprehensive overview of the state of the art in heavy-quarkonium theory and experiment, covering quarkonium spectroscopy, decay, and production, the determination of QCD parameters from quarkonium observables, quarkonia in media, and the effects on quarkonia of physics beyond the Standard Model. An introduction to common theoretical and experimental tools is included. Future opportunities for research in quarkonium physics are also discussed., Comment: xviii + 487 pages, 260 figures. The full text is also available at the Quarkonium Working Group web page: http://www.qwg.to.infn.it

We argue for black holes do not represent a strict consequence of general relativity., Comment: Eq.(5) gives the strict inequality for a velocity of massive particle. It is not correct because the observer on the horizon of black hole is light-like, hence, the corresponding relative velocity reaches the unit limit. Second, the trajectory satisfies the Hamilton-Jacobi equation, that means that the massive particle is always on the mass-shell. The conclusion (page 6) is erroneous

An effective action of ghost condensate with higher derivatives creates a source of gravity and mimics a dark matter in spiral galaxies. We present a spherically symmetric static solution of Einstein--Hilbert equations with the ghost condensate at large distances, where flat rotation curves are reproduced in leading order over small ratio of two energy scales characterizing constant temporal and spatial derivatives of ghost field: mu_*^2 and mu_\star^2, respectively, with a hierarchy mu_\star\ll \mu_*. We assume that a mechanism of hierarchy is provided by a global monopole in the center of galaxy. An estimate based on the solution and observed velocities of rotations in the asymptotic region of flatness, gives mu_* ~ 10^{19} GeV and the monopole scale in a GUT range mu_\star ~ 10^{16} GeV, while a velocity of rotation v_0 is determined by the ratio: sqrt{2} v_0^2= mu_\star^2/mu_*^2. A critical acceleration is introduced and naturally evaluated of the order of Hubble rate, that represents the Milgrom's acceleration., Comment: 4 pages, RevTeX4 file, references and clarifying footnotes added

We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the time component about the Planck mass m_{Pl} and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocity of rotation v_0 is determined by the hierarchy of scales: \sqrt{2} v_0^2= M/m_{Pl}, and M\sim 10^{12} GeV. A natural estimate of Milgrom's acceleration about the Hubble rate is obtained., Comment: 17 pages, iopart style, misprint removed

We derive generic equations for a vector field driving the evolution of flat homogeneous isotropic universe and give a comparison with a scalar filed dynamics in the cosmology. Two exact solutions are shown as examples, which can serve to describe an inflation and a slow falling down of dynamical ``cosmological constant'' like it is given by the scalar quintessence. An attractive feature of vector field description is a generation of ``induced mass'' proportional to a Hubble constant, which results in a dynamical suppression of actual cosmological constant during the evolution., Comment: 14 pages, LaTeX file, iopart class, discussion extended, reference added

We summarize theoretical predictions on the decays of B_c meson., Comment: 18 pages, revtex4 style, 7 eps-figures

This paper has been withdrawn by the author, due an error in Eq.(4.4), wherein a term of cosmological constant added into a theory of gravitation by Ref.[8], in which such the term is truly forbidden., Comment: This paper has been withdrawn

We calculate the contribution of local gluon condensate into the quadratic theta-term of vacuum energy and discuss its application to the study of axion mass., Comment: 3 pages, ReVTeX4,1 eps-figure, short explanations added

We calculate the leptonic constant for the ground pseudoscalar state of B_c meson in the framework of QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in the nonrelativistic QCD as matched with the full QCD., Comment: 6 pages, RevTeX4 file, 3 eps-figures, several references and remarks added

On the base of an exact solution for the static spherically symmetric Einstein equations with the quintessential dark matter, we explain the asymptotic behavior of rotation curves in spiral galaxies. The parameter of the quintessence state, i.e. the ratio of its pressure to the density is tending to -1/3. We present an opportunity to imitate the relevant quintessence by appropriate scalar fields in the space-time with extra 2 dimensions., Comment: 11 pages, LaTeX file, 4 eps-figures, references added

The model-independent method based on the triangle ideology is implemented to extract the CKM-matrix angle gamma in the decays of doubly heavy long-lived meson B_c. We analyze a color structure of diagrams and conditions to reconstruct two reference-triangles by tagging the flavor and CP eigenstates of D^0 meson in the fixed exclusive channels. The characteristic branching ratios are evaluated in the framework of QCD sum rules., Comment: 11 pages, RevTeX4 file, 4 eps-figures

In the framework of the constituent quark model the exclusive pair production of the charmed mesons in the photon-photon interaction is calculated. The comparison of these predictions with the ones of the heavy quark effective theory is performed. It is shown, that the light valence quark of D-meson plays the essential role not only in the hadronization process, but also in the production of the heavy c-quark. Moreover, it is shown, that because of the strong interaction between the initial photon field and the light quark charge the similar situation is kept even in the limit (m_{Q}\to \infty), whence it is concluded, that the application of the heavy quark effective theory in the case of the photon-photon interaction is not valid because it does not take into account one of the dominant mechanisms of the heavy meson production., Comment: 15 pages, 6 figures

We discuss the motivations and perspectives for the studies of the mesons of the (bc) family at LHCb. The description of production and decays at LHC energies is given in details. The event yields, detection efficiencies, and background conditions for several Bc decay modes at LHCb are estimated., Comment: 20 pages, 5 eps-figures

The model-independent method based on the triangle ideology is implemented to extract the CKM-matrix angle gamma in the decays of doubly heavy baryons containing the charmed and beauty quarks. We analyze a color structure of diagrams and conditions for reconstructing two reference-triangles by tagging the flavor and CP eigenstates of neutral D mesons in the fixed exclusive channels. The characteristic branching ratios are evaluated in the framework of a potential model setting a parametric dependence on the hadronic matrix elements for the decay rates., Comment: 15 pages, LaTeX file, 8 eps-figures, title changed, typos corrected

We formulate a general scheme to improve the truncated perturbative expansion in alpha_s by means of the renormalization group in QCD for the single-scale quantities. The procedure is used for the evaluation of hadronic decay rates of tau-lepton and eta_c-charmonium. The scale dependence of result for eta_c is studied in the scheme of fixed value for the MS-bar mass of charmed quark., Comment: 10 pages, LaTeX file, 2 eps-figyres, referense added

We summarize theoretical calculations of B_c decays and lifetime in the framework of QCD sum rules and compare the results with the estimates by the methods of Operator Product Expansion in the inverse heavy quark masses as well as of potential quark models. The agreement of estimates in the various approaches is discussed. The features of B_c decay modes are considered., Comment: 15 pages, ReVTeX4, 6 eps-figures, interference contribution and cc-bar(2S) yield corrected

We present new static spherically-symmetric exact solutions of Einstein equations with the quintessential matter surrounding a black hole charged or not as well as for the case without the black hole. A condition of additivity and linearity in the energy-momentum tensor is introduced, which allows one to get correct limits to the known solutions for the electromagnetic static field implying the relativistic relation between the energy density and pressure, as well as for the extraordinary case of cosmological constant, i.e. de Sitter space. We classify the horizons, which evidently reveal themselves in the static coordinates, and derive the Gibbons-Hawking temperatures. An example of quintessence with the state parameter w=-2/3 is discussed in detail., Comment: 11 pages, LaTeX file, 1 eps-figure, discussion and references added

We speculate on a possible interpretation of events selected by the SELEX collaboration and stress an insufficient evidence for the observation of doubly charmed baryon., Comment: 3 pages, ReVTeX4 file

We show that the Einstein-Hilbert action for the gravitational field can be obtained as a linear low-energy approximation for the dynamical massless fields in the theory with the lagrangian quadratic in the gauge field strength-tensor of spin connection under the spontaneous breaking of symmetry with a vacuum state described by an ansatz for nontrivial background strength-tension., Comment: 4 pages, LaTeX file, minor corrections to strict claims

We evaluate the masses of baryons composed of two heavy quarks and a strange quark with account for spin-dependent splittings in the framework of potential model with the KKO potential motivated by QCD with a three-loop beta-function for the effective charge consistent with both the perturbative limit at short distances and linear confinement term at long distances between the quarks. The factorization of dynamics is supposed and explored in the nonrelativistic Schroedinger equation for the motion in the system of two heavy quarks constituting the doubly heavy diquark and the strange quark interaction with the diquark. The limits of approach, its justification and uncertainties are discussed. Excited quasistable states are classified by the quantum numbers of heavy diquark composed by the heavy quarks of the same flavor., Comment: 14 pages, revtex4-file, 3 eps-figures, 5 tables, typos corrected

In the framework of scalar-vector dominance we calculate the hadronic matrix elements of scalar and tensor effective quark currents induced by virtual leptoquark interactions. Combined bounds on the product of couplings and leptoquark masses are obtained from experimental data., Comment: 19 pages, 15 eps-figures, discusion on the lepton polarization added

This report provides a comprehensive overview of the prospects for B physics at the Tevatron. The work was carried out during a series of workshops starting in September 1999. There were four working groups: 1) CP Violation, 2) Rare and Semileptonic Decays, 3) Mixing and Lifetimes, 4) Production, Fragmentation and Spectroscopy. The report also includes introductory chapters on theoretical and experimental tools emphasizing aspects of B physics specific to hadron colliders, as well as overviews of the CDF, D0, and BTeV detectors, and a Summary., Comment: 583 pages. Further information on the workshops, including transparencies, can be found at the workshop's homepage: http://www-theory.lbl.gov/Brun2/. The report is also available in 2-up http://www-theory.lbl.gov/Brun2/report/report2.ps.gz or chapter-by-chapter http://www-theory.lbl.gov/Brun2/report/

The factorization of hard and soft contributions into the hadronic decays of B_c meson at large recoils is explored in order to evaluate the decay rates into the S, P and D-wave charmonia associated with rho and pi. The constraints of approach applicability and uncertainties of numerical estimates are discussed. The mode with the J/psi in the final state is evaluated taking into account the cascade radiative electromagnetic decays of excited P-wave states, that enlarges the branching ratio by 20-25%., Comment: 13 pages, LaTeX axodraw-style, 1 figure, 2 tables

The cross section of the $D^*$-meson diffractive photoproduction at the HERA collider has been calculated in the framework of perturbatively motivated model for the different kinematic regions. The camparison between the different Pomeron models has been performed., Comment: 9 pages, 3 figures

We present a review of general picture in the sector of electroweak symmetry breaking with the CP-violation in the heavy quark interactions., Comment: 15 pages, 11 eps figures, a talk given at XXIV International Workshop on Fundamental Problems of High Energy Physics and Field Theory, Protvino, 2001

We consider the dynamics of tensor and scalar gravitational fields in the Relativistic Theory of Gravitation with the Minkowskian vacuum metric and generalize the formulation to the massless graviton. The potential of scalar field is determined in the presence of cosmological term under clear physical motivations. We find cosmological inflationary solutions and analyze conditions providing the transition to the regime of hot expanding universe., Comment: 23 pages, 3 eps-figures, title extended, arguements added, evolution eqs. unchanged, derivation and treatment of dimensional parameter improved

We consider a general scheme for calculating the leptonic constant of heavy quarkonium QQ-bar in the framework of nonrelativistic quantum chromodynamics, NRQCD, operating as the effective theory of nonrelativistic heavy quarks. We explore the approach of static potential in QCD, which takes into account both the evolution of effective charge in the three-loop approximation and the linearly raising potential term, which provides the quark confinement. The leptonic constants of bb-bar and cc-bar systems are evaluated by making use of two-loop anomalous dimension for the current of nonrelativistic quarks, where the factor for the normalization of matrix element is introduced in order to preserve the renormalization group invariance of estimates., Comment: 18 pages, 6 eps-figures, discussion and references added, vNRQCD analysis considered

We construct a Lagrangian of Weyl spinors and gauge fields, which is invariant under the action of equivalent local transformations on the spinor algebra representations. A model of vacuum with a nontrivial gauge strength-tensor setting a scale and spontaneously breaking the gauge symmetry is suggested, so that the leading approximation at low energies is described by the Einstein--Hilbert Lagrangian of gravity. We consider a mechanism for the cancellation of cosmological constant due to a symmetry between the vacuum strength tensor and the tensor dual to it. The appearance of nonzero masses for the non-graviton degrees of freedom for the gauge field is shown. The generalization to the Dirac spinors is considered, and a group of additional gauge symmetry is determined. We argue for a necessary introduction of supersymmetry., Comment: 24 pages, LaTeX file, 1 eps-figure, reference added, subsection 3.5.2 and section 5. little modified

We consider general physical characteristics of doubly heavy baryons: the spectroscopy in the framework of potential approach and sum rules of QCD, mechanisms of production in various interactions on the basis of fragmentation model with account of preasymptotic corrections caused by higher twists over the transverse momentum of baryon, inclusive decays and lifetimes in the operator product expansion over the inverse powers of heavy quark masses as well as the exclusive decays in the sum rules of QCD. We generalize the methods developed in the effective theory of heavy quarks towards the description of systems with two heavy quarks and a single light quark. The calculations are presented for the masses, decay widths and yields of baryons with two heavy quarks in the running and planned experimental facilities. We discuss the prospects of search for the baryons and possibilities of experimental observation. The most bright physical effects concerning these baryons as well as their position in the system for the theoretical description of heavy quark dynamics are considered., Comment: review, LaTeX file, 32 postscript figures

In the framework of three-point QCD sum rules, the form factors for the semileptonic decays of B_c^+ -> B_s(B_s^*) l \nu are calculated with account for the Coulomb-like alpha_s/v-corrections in the heavy quarkonium. The generalized relations due to the spin symmetry of HQET/NRQCD for the form factors are derived at the recoil momentum close to zero. The nonleptonic decays are studied using the assumption on the factorization. The B_c meson lifetime is estimated by summing up the dominating exclusive modes in the c -> s transition combining the current calculations with the previous analysis of b -> c decays in the sum rules of QCD and NRQCD., Comment: 7 pages, JHEP class, 5 eps-figures, Talk given at the Vth International Workshop "HEAVY QUARK PHYSICS" April 6-8, 2000, Dubna, Russia

Following the procedure and motivations developed by Richardson, Buchmuller and Tye, we derive the potential of static quarks consistent with both the three-loop running of QCD coupling constant under the two-loop perturbative matching of V and MS-bar schemes and the confinement regime at long distances. Implications for the heavy quark masses as well as the quarkonium spectra and leptonic widths are discussed., Comment: 33 pages, ReVTeX file, 8 eps-figures, 6 tables; references and Comments added, version to appear in Physical Review D

In the framework of two-point sum rules of NRQCD, the masses and couplings of doubly heavy baryons to the corresponding quark currents are evaluated with account of coulomb-like corrections in the system of doubly heavy diquark as well as the contribution of nonperturbative terms determined by the quark, gluon, mixed condensates and the product of gluon and quark condensates. The introduction of nonzero light quark mass destroys the factorization of baryon and diquark correlators even at the perturbative level and provides the better convergency of sum rules. We estimate the difference M_Omega - M_Xi = 100+/- 10 MeV. The ratio of baryonic constants |Z_Omega|^2/|Z_Xi|^2 is equal to 1.3+/-0.2 indicating the violation of SU(3) flavor symmetry for the doubly heavy baryons., Comment: 18 pages, ReVTeX file, 7 eps-figures, references added

In the framework of three-point QCD sum rules, the form factors for the semileptonic decays of B_c --> B_s(B_s^*) l \nu are calculated with account for the Coulomb-like alpha_s/v-corrections in the heavy quarkonium. The generalized relations due to the spin symmetry of HQET/NRQCD for the form factors are derived at the recoil momentum close to zero. The nonleptonic decays are studied using the assumption on the factorization. The B_c meson lifetime is estimated by summing up the dominating exclusive modes in the c --> s transition combining the current calculations with the previous analysis of b --> c decays in the sum rules of QCD and NRQCD., Comment: 31 pages, LaTeX file, 15 eps-figures, 4 tables, more figures, a discussion and an explanation of results are added

Introducing a source for a bi-local composite operator motivated by the perturbative expansion in gauge couplings, we calculate its effective potential in the renormalization group of Standard Model with no involvement of technicolor. The potential indicates the breaking of electroweak symmetry below a scale M due to a nonzero vacuum expectation value of neutral component for the SU(2)-doublet operator. At virtualities below a cut off \Lambda we introduce the local higgs approximation for the effective fields of sources coupled to the composite operators. The value of \Lambda\approx 600 GeV is fixed by the measured masses of gauge vector bosons. The exploration of equations for infrared fixed points of calculated Yukawa constants allows us to evaluate the masses of heaviest fermion generation with a good accuracy, so that m_t(m_t) = 165\pm 4 GeV, m_b(m_b) = 4.18\pm 0.38 GeV and m_\tau(m_\tau) = 1.78\pm 0.27 GeV. After a finite renormalization of effective fields for the sources of composite operators, the parameters of effective Higgs field potential are calculated at the scale of matching with the local theory \Lambda. The fixed point for the Yukawa constant of t quark and the matching condition for the null effective potential at M drive the M value to the GUT scale. The equation for the infrared fixed point of quartic self-action allows us to get estimates for two almost degenerate scalar particles with m_H= 306\pm 5 GeV, while third scalar coupled with the tau lepton is more heavy: m_{H_\tau} = 552\pm 9 GeV. Some phenomenological implications of the offered approach describing the effective scalar field, and a problem on three fermion generations are discussed., Comment: 24 pages, LaTeX file, 10 eps-figures, minor clarifications added

The masses of baryons containing two heavy quarks and their couplings to the corresponding quark currents are evaluated in the framework of NRQCD sum rules. The coulomb-like corrections in the system of doubly heavy diquark are taken into account, and the contribution of nonperturbative terms coming from the quark, gluon and mixed condensates as well as the product of quark and gluon condensates, is analyzed. The higher condensates destroy the factorization of baryon and diquark correlators and provide the convergency of sum rule method. As a result the accuracy of estimates is improved., Comment: 17 pages, LATEX file and 6 eps-figures

The fragmentation function of vector particle into possible bound S-wave states with a heavy antiquark is calculated in the leading order of perturbative QCD for the high energy processes at large transverse momenta with the different behaviour of anomalous chromomagnetic moment. One-loop equations are derived for the evolution of fragmentation function moments, which is caused by the emission of hard gluons by the vector particle. The integrated probabilities of fragmentation are given. The distribution of bound state over the transverse momentum with respect to the axis of fragmentation is calculated in the scaling limit., Comment: 10 pages, Latex file + 4 ps-figures

We investigate a connection between a renormalon ambiguity of heavy quark mass and the gluon condensate contribution into the quark dispersion law related with a virtuality defining a displacement of the heavy quark from the perturbative mass-shell, which happens inside a hadron., Comment: 6 pages, RevTeX4, 1 eps-figure, improved edition

We estimate the differential and total cross sections for both the photoproduction of vector D*-meson and its yield in deep inelastic scattering at the HERA collider in the framework of model motivated by perturbative calculations in QCD. The offered model allows us to take into account higher twists over the transverse momentum of meson at p_T ~ m_c and to correctly approach the dominance of $c$-quark fragmentation at p_T >> m_c. We consider a possibility for the hadronization of color-octet c q-bar state into the meson. The combined contribution by the singlet and octet-color terms results in a good agreement with the experimental data for both the photoproduction and the production in deep inelastic scattering., Comment: 27 pages, ReVTeX, 8 eps-figures, explanations added, results unchanged

The semileptonic B_c-meson decays into the heavy quarkonia J/\psi (\eta_c) and a pair of leptons are investigated in the framework of three-point sum rules of QCD and NRQCD. Calculations of analytical expressions for the spectral densities of QCD and NRQCD correlators with account for the Coulomb-like \alpha_s/v terms are presented. The generalized relations due to the spin symmetry of NRQCD for the form factors of B_c\to J/\psi (\eta_c)l\nu_l transitions with l denoting one of the leptons e, \mu or \tau, are derived at the recoil momentum close to zero. This allows one to express all NRQCD form factors through a single universal quantity, an analogue of Isgur-Wise function at the maximal invariant mass of lepton pair. The gluon condensate corrections to three-point functions are calculated both in full QCD in the Borel transform scheme and in NRQCD in the moment scheme. This enlarges the parameteric stability region of sum rule method, that makes the results of the approach to be more reliable. Numerical estimates of widths for the transitions of B_c\to J/\psi (\eta_c)l\nu_l are presented., Comment: 37 pages, Latex file, 10 figures, 15 epsf-insertions, revised version to appear in Nucl.Phys.B

In the framework of the model motivated by perturbative calculations in the fourth $O(\alpha^3_s\alpha)$-order, the estimates for the $\gamma p$ cross-section of the $D^*$-meson production in the ZEUS experiment are performed. We factorize the hadronization of $(c\bar q)$-state hardly produced in perturbative QCD, which allows us to take into account the higher twist terms in the powers of $1/p_T$ at $p_T\sim m_c$ and to correctly reproduce the c-quark fragmentation dominant at high $p_T\gg m_c$ to the given order of $\alpha_s$. We find a good agreement with the experimental data on the photoproduction, if the color-octet $(c\bar q)$-state is taken into account, which yields $ \approx 0.33-0.49 GeV^3$., Comment: 10 pages, LATEX file, 5 ps-figures, short corrections added

Estimates of lifetimes and partial branching ratios for the baryons $\Xi_{bc}^{+}$ and $\Xi_{bc}^{0}$ are presented using the inverse heavy quark mass expansion technique carried out in the Operator Product Expansion approach. We take into account both the perturbative QCD corrections to the spectator contributions and, depending on the quark contents of hadrons, the Pauli interference and weak scattering effects between the constituents, using a potential model for the evaluation of the non-perturbative parameters., Comment: 15 pages, LATEX file, 2 eps-figures

The characteristic scale of neutral current, provided by an extension of Standard Model with a local group over the right-handed fermions, determines the smallness of neutrino masses of Dirac kind. The experimental observation of neutrino oscillations imposes the stringent limit on the $Z^\prime$ physics appearance at low energies., Comment: 10 pages, eps-figure

Spectra of masses are calculated for the families of doubly heavy baryons in the framework of nonrelativistic quark model with the QCD potential by Buchmuller--Tye. We suppose the quark-diquark structure for the wave functions and take into account the spin-dependent splittings. The physical reasons causing the existence of quazi-stable excited states in the subsystem of heavy diquark are considered for the heavy quarks of identical flavors., Comment: 24 pages, revtex, 4 figures, 9 tables, revised version to appear in Physical Review D