arXiv subjects
Publications and source records attributed to Yu. S. Kalashnikova.
The large distance behaviour of the adiabatic hybrid potentials is studied in the framework of the QCD string model. The calculated spectra are shown to be the result of interplay between potential-type longitudinal and string-type transverse vibrations.
Strong mesonic decays are studied in the framework of the 't Hooft model for the two-dimensional QCD in the axial gauge. Special attention is payed to the processes with pions in the final state involved and the low energy theorems have been checked including the "Adler zero". It is demonstrated explicitly that in the chiral limit any three-meson decay amplitude with at least one pion vertex vanishes identically for any values of the external momenta. Ward identities for the dressed vector and axial-vector currents vertices are identified and their relationship to the pionic vertex are discussed.
Bosonization of the two-dimensional QCD in the large N_C limit is performed in the framework of Hamiltonian approach in the Coulomb gauge. The generalized Bogoliubov transformation is applied to diagonalize the Hamiltonian in the bosonic sector of the theory, and the composite operators creating/annihilating bosons are obtained in terms of dressed quark operators. The bound state equation is reconstructed as a result of the generalized Bogoliubov transformation, and the form of its massless solution, chiral pion, is found explicitly. Chiral properties of the theory are discussed.
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the procedure of gauge fixing turns out rather dangerous and may lead to a quantum anomaly in the operator algebra. We discuss additional classical symmetries as an essential element for tracing out this anomaly. The two cases of a spinning and a spinless particles in the external electromagnetic field are discussed to illustrate the situation.
The system of light quark and heavy antiquark source is studied in 1+1 QCD in the large N_C limit. The situation is demonstrated to be the two dimensional analogue of the problem in 3+1 QCD corresponding to the essentially nonlocal case of zero vacuum correlation length, which does not allow perturbative treatment. The modified Fock-Schwinger gauge condition is employed to derive the effective Dirac-type equation for the spectrum, which is proved to be equivalent to the 't Hooft equation in the limit of one heavy mass. The chiral condensate is shown to appear naturally in the given approach and to coincide with the convenient value.
The canonical description of the straight-line string is given in the einbein field formalism. The system is quantized and Regge spectrum is reproduced. The covariant analogue of the Newton-Wigner coordinate is found, and peculiarities of the gauge fixing in τ-reparametrization group are discussed.
Propagation of the heavy quark in the field of a static antiquark source is studied in the framework of effective Dirac equation. The model of QCD vacuum is described by bilocal gluonic correlators. In the heavy quark limit the effective interaction is reduced to the potential one with 5/6 Lorentz scalar and 1/6 Lorentz vector linear confinement, while spin-orbit term is in agreement with Eichten-Feinberg-Gromes results. New spin-independent corrections to the leading confining regime are identified, which arise due to the nonlocality of the interaction in time direction and quark Zitterbewegung.
The canonical description is presented for the string with pointlike masses at the ends in 1+1 dimensions in two different gauges: in the proper time gauge and in the light cone one. The classical canonical transformation is written out explicitly, which relates physical variables in both gauges, and equivalence of two classical theories is demonstrated in such a way. Both theories are quantized, and it is shown that quantum theories are not unitary equivalent. It happens due to the fact that the canonical transformation depends on interaction. The quantum Poincare algebra proves to be closed in both cases, so that the requirement of Poincare covariance is not able to distinguish between two versions of the theory.
The models for hybrid mesons are discussed, in which the gluonic excitations manifest themselves as the vibrations of the quark- antiquark QCD string. The predictions for the spectra, decays and mixing with hadronic channels are presented.
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some arguments are involved in the favour of Lorents covariant gauge fixing conditions.
The QCD-motivated constituent string model is extended to consider the baryon. The system of three quarks propagating in the confining background field is studied in the Wilson loop approach, and the effective action is obtained. The resulting Lagrangian at large interquark distances corresponds to the Mercedes Benz string configuration. Assuming the quarks to be heavy enough to allow the adiabatic separation of quark and string junction motion and using the hyperspherical expansion for the quark subsystem we write out and solve the classical equation of motion for the junction. We quantize the motion of the junction and demonstrate that the account of these modes leads to the effective "swelling" of the baryon in comparison with the standard potential picture. We discuss the effects of the finite gluonic correlation length which do not affect the excited states but appear to be substantial for the baryonic ground state, reducing the "swelling" considerably and leaving room to the short range Coulomb force in the three quark system.
Theoretical arguments are given in favour of existence of gluonic degrees of freedom at the constituent level. Models for hybrid mesons are discussed, and the predictions are compared with the data on meson spectroscopy in the light quark sector. It is demonstrated that the $q\bar q g$ content might be responsible for the properties of some recently found mesonic states.
The model for hybrid excitations of the QCD string with quarks is presented starting from the perturbation theory in the nonperturbative background. The propagation of a system containing $q \bar q$-pair and gluon is considered. The simplified version of the Hamiltonian, including both long-range nonperturbative interaction and Coulomb force, is derived. The masses of the lowest $q \bar q g$ hybrids are evaluated, and numerical results for the spectra are listed.
We extend the model for QCD string with quarks to consider the Mercedes Benz string configuration describing the three-quark baryon. Under the assumption of adiabatic separation of quark and string junction motion we formulate and solve the classical equation of motion for the junction.We dare to quantize the motion of the junction, and discuss the impact of these modes on the baryon spectra.
The notion of constituent gluon is introduced as a gluon propagating in the vacuum background field. The Hamiltonian approach for a system containing such gluon and a $q\bar{q}g$ pair is formulated, and the masses of lowest $q\bar{q}g$ hybrids are estimated.
The model for constituent glue is presented starting from the perturbation theory in nonperturbative QCD vacuum. Green function is constructed for a system containing qqbar pair and gluon propagating in the vacuum background field, and Hamiltonian approach to the problem is formulated. The masses of lowest qqbarg hybrids with light quarks are evaluated, and implication of results for the spectroscopy of exotic states is discussed.
The average of two Wilson loops is expressed in terms of gauge invariant field strength correlators. Assuming the existence of finite correlation length $T_g$ and taking into account the absence of a fixed direction in colour space, we generalize the area law asymptotics for the case of the average of two Wilson loops embedded into the same plane. The results are presented in terms of averaged single Wilson loop operators in irreducible representations which correspond to the geometry of the contours. A special reduction of our results (obtained for arbitrary dimensionality of space-time) to the case of two-dimensional SU(N) theory is performed and the connection to the results existing in literature is established.