arXiv subjects
Publications and source records attributed to A. N. Sissakian.
We investigate the structure of some first terms of Watson series representing the amplitude of lepton-pair production in the ion collisions. It is shown that infrared instabilities of individual terms trend to cancel each other providing the infrared stability of whole amplitude.
It is shown that the amplitudes of electron-ion scattering and $e^+e^-$ pair production in the Coulomb field of two colliding ions are sxpressed in the terms of electron scattering amplitudes in the fields of the individual ions via the Watson expansion. We have obtained the compact expressions for these amplitudes valid in the high energy limit and discuss the crossing symmetry relations among the considered processes.
The semi-inclusive deep inelastic scattering (SIDIS) process is considered. A theoretical procedure is proposed allowing the direct extraction from the SIDIS data of the first moments of the polarized valence distributions and of the first moment difference of the light sea quark polarized distributions in the next to leading QCD order. The validity of the procedure is confirmed by the respective simulations.
It is shown that the processes of electron(positron) scattering and $e^+e^-$ pair production in the Coulomb fields of two relativistic ions, can be expressed through the amplitudes of lepton scattering off the ion Coulomb field via Watson expansion. We obtained the compact expressions for these amplitudes valid in the high energy limit and discuss the crossing symmetry relations among the considered processes.
The semi-inclusive deep inelastic scattering (SIDIS) process is considered. It is proposed a theoretical procedure allowing the direct extraction from the SIDIS data of the first moments of the polarized valence distributions and of the first moment difference of the light sea quark polarized distributions in the next to leading (NLO) QCD order. The validity of the procedure is confirmed by the respective simulations.
The dynamical quantum effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied. It is shown that while the Neumann BC lead to the usual scalar field mass generation, the Dirichlet BC give rise to the dynamical mechanism of spontaneous symmetry breaking. Due to the later, there arises the possibility of the respective phase transition from the normal phase to the spontaneously broken one. In particular, at the critical value of the combined evolution parameter the usual massless scalar QED transforms to the Higgs model.
The scalar field theory and the scalar electrodynamics quantized in the flat gap are considered. The dynamical effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied. It is shown that while the Neumann BC lead to the usual scalar field mass generation, the Dirichlet BC give rise to the dynamical mechanism of spontaneous symmetry breaking. Due to the later, there arises the possibility of the new type phase transition from the normal to spontaneously broken phase. The decreasing in the characteristic size of the quantization region (the gap size here) and increasing in the temperature compete with each other, tending to transport the system in the spontaneously broken and in the normal phase, respectively. The system evolves with a combined parameter, simultaneously reflecting the change in temperature and in the size. As a result, at the critical value of this parameter there occurs the phase transition from the normal phase to the spontaneously broken one. In particular, the usual massless scalar electrodynamics transforms to the Higgs model.
The results of SIDIS experiments concerning the first moments of the polarized quark distributions are considered. The possible reasons of the deviation from the fundamental restrictions such as the Bjorken sum rule and the ways to properly improve the analysis of measured SIDIS asymmetries are discussed. The possibility of broken polarized sea scenario is analysed.
Based on the two Higgs doublet model, we study the effect of Higgs-boson exchange on the (super)heavy quarkonium \bar QQ, which induces a strong attractive force between a (super)heavy quark Q and an antiquark \bar Q. An interesting application is the decay of (super)heavy quarkonia \bar QQ into a Higgs boson associated with gauge bosons. The criterion for making the \bar QQ bound state is studied. We also show that non-perturbative effects due to gluonic field fluctuations are rather small in such a heavy quark sector. Possible enhancement for productions and decays of \bar QQ bound states made from the fourth generation quark Q is discussed for \bar p p (at the Tevatron) and pp (at the LHC) collisions.
In this note we establish a relation between two exactly-solvable problems on circle, namely singular Coulomb and singular oscillator systems.
It is shown that the evaluation of the expectation value (EV) of topological charge density over $θ$-vacuum is reduced to investigation of the Chern-Simons term EV. An equation for this quantity is established and solved. EV of the topological charge density at an arbitrary $θ$ occurs equal to zero and, as a consequence, topological susceptibility of both QCD and pure Yang-Mills vacua defined in a Wick sense is equal to zero, whereas when defined in a Dyson sense it differs from zero by the quantity proportional to the respective condensate of the chromomagnetic field. Thus, the usual Witten-Veneziano formula for the $η^{'}$ meson mass is modified.
In connection with the semi-inclusive polarized DIS, it is proposed to consider the first Melin moments $Δq$ of the polarized quark and antiquark densities, instead of the respective variables $δq(x)$, local in Bjorken x themselves. This gives rise to a very essential simplification of the next to leading order (NLO) QCD and, besides, allows one to use the respective QCD sum rules. An expression for $Δ\bar{u}-Δ\bar{d}$ in NLO is obtained which is just a simple combination of the directly measured asymmetries and of the quantities taken from the unpolarized data.
The Schrödinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the spherical and cylindrical bases of the oscillator are calculated. It is shown that the relevant coefficients are expressed through the generalised hypergeometric functions $_4F_3$ of the unit argument or $6_j$ Racah symbols extended over their indices to the region of real values. Limiting transitions to a free motion and flat space are considered in detail. Elliptic bases of the oscillator are constructed in the form of expansion over the spherical and cylindrical bases. The corresponding expansion coefficients are shown to obey the three-term recurrence relations.
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases (transition matrix), and vice-versa, are found in terms of the SU(2) Clebsch--Gordan coefficients analytically continued to real values of their arguments. The diagram method, which allow one to construct a transition matrix for arbitrary dimension, is developed.
Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern--Simons term. It occurs that the chiral anomaly doesn't depend on density and temperature. Chern-Simons term appearance in even dimensions is studied under two types of constraints: chiral and usual charges conservation. In odd dimensions, by using different methods it is shown that $μ^2 = m^2$ is the crucial point for Chern--Simons at zero temperature. So when $μ^2 < m^2$ $μ$--influence disappears and we get the usual Chern-Simons term. On the other hand, when $μ^2 > m^2$ the Chern-Simons term vanishes because of non--zero density of background fermions. The connection between parity anomalous Chern-Simons in odd dimension and chiral anomaly in even dimension is established at arbitrary density and temperature. These results hold in any dimension as in abelian, so as in nonabelian cases.
The bound system composed of the Yang monopole coupled to a particle of the isospin by the SU(2) and Coulomb interaction is considered. The generalized Runge--Lenz vector and the SO(6) group of hidden symmetry are established. It is also shown that the group of hidden symmetry make it possible to calculate the spectrum of the system by a pure algebraic method.
This article deals with a nonrelativistic quantum mechanical study of a charge-dyon system with the SU(2)--monopole in five dimensions. The Schrödinger equation for this system is separable in the hyperspherical and parabolic coordinates. The problem of interbasis expansion of the wave functions is completely solved. The coefficients for the expansion of the parabolic basis in terms of the hyperspherical basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2).
In this report, in the framework of an analytical approach and with help of the generalized version of the Hurwitz transformation the five-dimensional SU(2)--monopole model is constructed from the eight-dimensional quantum oscillator. The SU(2)--monopole fields, the Clebsh-Gordan expansion stimulated by the space-gauge coupling, the hyperangle and the radial parts of the total wave function, the energy spectrum of the charge-monopole bound system and the corresponding degeneracy are calculated.