Open flavour charmed mesons in a quantum chromodynamics potential model

We modify the mesonic wave function by using a short distance scale r ₀ in analogy with hydrogen atom and estimate the values of masses and decay constants of the open flavour charm mesons D, D _s and B _c within the framework of a QCD potential model. We also calculate leptonic decay widths of these mesons to study branching ratios and lifetime. The results are in good agreement with experimental and other theoretical values.     

Root mean square radii of heavy flavoured mesons in a quantum chromodynamics potential model

We report the results of root mean square (r.m.s.) radii of heavy flavoured mesons in a QCD model with the potential V(r)=?(4α_s/3r) + br + c. As the potential is not analytically solvable, we first obtain the results in the absence of confinement and Coulomb terms respectively. Confinement and Coulomb effects are then introduced successively in the approach using the Dalgarno’s method of perturbation. We explicitly consider the following two quantum mechanical aspects in the analysis: (a) The scale factor c in the potential should not effect the wave function of the system even while applying the perturbation theory. (b) Choice of perturbative piece of the Hamiltonian (confinement or linear) should determine the effective radial separation between the quarks and antiquarks. The results are then compared with the available theoretical values of r.m.s. radii.     

A model of unified quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T (4) × [SU (3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ’effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of ef f ective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

Gluon and quark jets in a recursive model motivated by quantum chromodynamics

We compute observable quantities like the multiplicity and momentum distributions of hadrons in gluon and quark jets in the framework of a recursive cascade model, which is strongly motivated by the fundamental interactions of QCD. Fragmentation occurs via 3 types of breakups: quark → meson+ quark, gluon→meson+gluon, gluon→quark+ antiquark. In our model gluon jets are softer than quark jets. The ratio of gluon jet to quark jet multiplicity is found to be 2 asymptotically, but much less at lower energies. Some phenomenological consequences for λ decay are discussed.     

Scalar quantum chromodynamics in two dimensions and the parton model

We study SU(N) scalar quantum chromodynamics in two space-time dimensions in the large-N limit. This is the model of color gauge fields interacting with scalar quarks. We find that the consensual properties of four-dimensional QCD, i.e. infrared slavery, quark confinement, the charmonium picture, etc. are all realized. Moreover, the current in this model mimics nicely the behavior of the current in four-dimensional QCD, in contrast to the original model of 't Hooft.     

Feynman integral and perturbation theory in quantum tomography

We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.     

A model of uni ed quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T(4)×[SU(3)]_color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same effective Riemann metric tensors' in the geometric-optics (or classical) limit. The emergence of effective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

Color-dielectric properties of a ferromagnetic state in quantum chromodynamics

The response of a color-ferromagnetic state (noticed by Savvidy) to small external perturbations is studied by use of the effective action. An electric instability and the electric Meissner effect combine to reveal the color-confining character of the ferromagnetic state.     

Confinement,chiral symmetry breaking,and the pion in a chromo-dielectric model of quantum chromodynamics

We study a chirally symmetric effective model of quantum chromodynamics, where the long-range parts of the (non-abelian) gluon self-interactions are assumed to give rise to a color-dielectric field. In particular we show how in this model confinement and the Goldstone pion arise naturally and simultaneously from dynamical chiral symmetry breaking. We also provide justification for successful chiral bag models, including for example the cloudy bag model.     

Bounds on the Slope and Curvature of Isgur-Wise Function in a QCD-Inspired Quark Model

The quantum chromodynamics-inspired potential model pursued by us earlier has been recently modified to incorporate an additional factor ‘c’ in the linear cum Coulomb potential. While it felicitates the inclusion of standard confinement parameter b?=?0.183 GeV² unlike in previous work, it still falls short of explaining the Isgur-Wise function for the B mesons without ad hoc adjustment of the strong coupling constant. In this work, we determine the factor ‘c’ from the experimental values of decay constants and masses and show that the reality constraint on ‘c’ yields bounds on the strong coupling constant as well as on slope and curvature of Isgur-Wise function allowing more flexibility to the model.     

Borel summation of perturbation series in quantum mechanics and field theory

The Borel summation of factorial divergent perturbation series is considered. The relation between the asymptotics of the coefficients in the series and the character of the exact function singularity is established. The applicability limits for the improved perturbation theory are obtained. The results are tested on a number of physical problems for which the exact solutions are available.     

Generating the curvature perturbation at the end of inflation in string theory

In brane inflationary scenarios, the cosmological perturbations are supposed to originate from the vacuum fluctuations of the inflaton field corresponding to the position of the brane. We show that a significant, and possibly dominant, contribution to the curvature perturbation is generated at the end of inflation through the vacuum fluctuations of fields, other than the inflaton, which are light during the inflationary trajectory and become heavy at the brane-antibrane annihilation. These fields appear generically in string compactifications where the background geometry has exact or approximate isometries and parametrize the internal angular directions of the brane.     

Summary of working group activities in non-perturbative quantum chromodynamics (lattice gauge theory)

We summarize the activities of the lattice gauge theory section of the working group activities in non-perturbative QCD.     

Stationary perturbation theory in the probability representation of quantum mechanics

In the probability representation of quantum mechanics, the eigenvalue problems in Hilbert space appear as *-genvalue equations. We show the possibility of employing the nondegenerate stationary perturbation method in the probability representation of quantum mechanics. The perturbed eigentomograms and the eigenvalues of energy are shown to be computed ab initio in terms of tomographic symbols of the operators involved.     

Notes on the quantum theory of transition and time-dependent perturbation

It is shown that the introduction of the time-dependent perturbation sharply at an instant, is redundant to obtain the usual expression for the transition rates between states, provided the initial state is an incoherent mixture of the unperturbed states.     

A quantum field theory in momentum space of constant curvature

The model of a polarization operator in the rainbow diagram approximation in momentum space of constant curvature is studied. An integral equation is obtained for the absorptive component of the hadron polarization operator in a stereographic parametrization of the de Sitter space. The solution of the integral equation is found for the case of zero mass of the exchange particle. The sections and mean multiplicity of hadron generation in e⁺e^– annihilation are calculated. The infrared divergences which develop in an exact summation of the class of diagrams considered here manifest themselves as a multiplicative renormalization constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 20–24, September, 1981.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.