arXiv subjects
Publications and source records attributed to M. N. Sergeenko.
Inclusive processes at high energies are studied in a non-perturbative approach in QCD using a modified Quark-Gluon String Model. Theoretical and experimental aspects of diffraction dissociation are discussed. In the calculations of cross sections, the parameters of complex nonlinear trajectories of Pomeranchuk and Reggeons are used. Particular attention is paid to elastic and inelastic processes at LHC energies.
Relativistic bound state problem in hadron physics is studied. Mesons and their resonance excitations in the framework of Relativistic Quantum Mechanics (RQM) are investigated. Two-particle wave equation for the Lorentz scalar QCD inspired funnel-type potential with the coordinate dependent strong coupling $α_§(r)$ is derived. The concept of distance dependent particle mass is developed. Two exact asymptotic expressions for the system's squared mass are obtained and used to derive the meson interpolating complex-mass formula. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Practical applications of the model are given.
One of the interesting fundamental phenomenon which was observed in the last decades is the discovery of anyons, relativistic spinning particles in $2+1$ dimensions. In contrast to three-dimensional space, indistinguishable quantum particles in two-dimensional space can, in general, have anomalous statistics [1-4]. These quasiparticles carry not only a charge $q$ also the magnetic flux $Φ_0$.
Quarkonium resonances in the complex-mass scale are studied. Relativistic quark potential model is used to describe the quark-antiquark system. The complex-mass formula is obtained from two exact asymptotic solutions for the QCD motivated potential with the distance-dependent value of the strong coupling in QCD. The centered masses and total widths of some meson resonances are calculated. A possible origin of the ``dark matter'' and the ``Missing Mass''is discussed.
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass formula. The centered masses and total widths of the $ρ$-family resonances are calculated.
Bound state of two massive constituent gluons is studied in the potential approach. Relativistic quasi-classical wave equation with the QCD-inspired scalar potential is solved by the quasi-classical method in the complex plane. Glueball masses are calculated with the help of the universal mass formula. The hadron Regge trajectories are given by the complex non-linear function in the whole region of the invariant variable $t$. The Chew-Frautschi plot of the leading glueball trajectory, $α_P(t)$, has the properties of the t-channel Pomeron, which is dual to the glueball states in the s channel. The imaginary part of the Pomeron is also calculated.
Glueballs are considered to be bound states of constituent gluons. Relativistic wave equation for two massive gluons interacting by the funnel-type potential is analyzed. Using two exact asymptotic solutions of the equation, we derive an interpolating mass formula and calculate glueball masses in agreement with the lattice data. We obtain the complex non-linear Pomeron trajectory, $α_P(t)$, in the whole region of $t$. The real part of the trajectory corresponds to the soft Pomeron, parameters of which are found from the fit of recent HERA data.
Transverse momentum spectra of charmed and beauty mesons produced in proton-proton and proton-antiproton collisions at high energies are analyzed within the modified quark-gluon string model (QGSM) including the internal motion of quarks in colliding hadrons. It is shown that this approach can describe rather satisfactorily the experimental data at not large values of the transverse momentum where the NLO QCD calculation has a big uncertainty. We also show that using both the QGSM and the NLO QCD one can describe these data in a wide region of transverse momenta and give some predictions for the future LHC experiments.
Pomeron is modeled as a system of two interacting by the Cornell potential massive gluons. In bound state region, a relativistic wave equation for the potential is analized. Two exact asymptotic solutions of the equation are used to derive an interpolating mass formula for gluonium states and the Pomeron trajectory in the whole region. The trajectory obtained is linear at large timelike $t$ and flattens off at -1 in the scattering region at large $-t$. Parameters of the trajectory are found from the fit of recent HERA data for $α_P(t)$.
The eigenvalue problem in quantum mechanics is reduced to quantization of the classical action of the physical system. State function of the system, $ψ_0(ϕ)$, is written in the form of superposition of two plane waves in the phase space. Quantization condition is derived from the basic requirements of continuity and finiteness for $ψ_0(ϕ)$ in the whole region.
Solution of the Schrödinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, $A_n\cos(k_nx+δ_n)$, and are the asymptote of the exact solution.
The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $ψ(x)=Ae^{iϕ(x)}+ Be^{-iϕ(x)}$, where $ϕ(x)=\frac 1\hbar W(x)$ and $W(x)$ is the reduced classical action of the physical system, result in the asymptote of the exact solution and general quantization condition for $W(x)$, which yields the exact eigenvalues of the system.
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the classical Hamilton-Jacobi equation. Each one-dimensional equation obtained after separation is solved by the conventional WKB method. Quasiclassical solution of the angular equation results in the integral of motion $\vec M^2=(l+\frac 12)^2\hbar^2$ and the existence of nontrivial solution for the angular quantum number $l=0$. Generalization of the WKB method for multi-turning-point problems is given. Exact eigenvalues for solvable and some "insoluble" spherically symmetric potentials are obtained. Quasiclassical eigenfunctions are written in terms of elementary functions in the form of a standing wave.
A model potential for two-particle relativistic systems is investigated in the framework of Poincare-invariant quantum mechanics (or relativistic Hamiltonian dynamics). The potential considered allows to reduce the main integro-differential equation of Poincare-invariant quantum mechanics to the equation analogous to the radial equation and have analytical solution for relativistic bound system. We discuss the possible choice of the parameters of potential and apply our model to the description of light meson Regge trajectories.
Quasiclassical solution of the three-dimensional Schredinger's equation is given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is shown, which corresponds to the quantum fluctuations of the angular momentum and contributes to the energy of the ground state.
The properties of relativistic particles in the quasiclassical region are investigated. The relativistic semiclassical wave equation appropriate in the quasiclassical region is derived. It is shown that the leading-order WKB quantization rule is the appropriate method to solve the equation obtained.
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials.
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in the regions of the classical turning points. The band structure of several periodic potentials is computed using our semiclassical quantization condition.