q q Systems in QCD-Based Models and Scalar Mesons

Abstract

The dynamical effects of gluon field overlap factor ’f’ between different q q ̄ clusterings of a qq q ̄ q ̄ system has been seen in the scattering process of two mesons. The form of ’f’ (exp(−kS min )) used in the first part of the work was selected from a comparison of different forms of ’f’ with two-colour numerical lattice simulations in the pure gluonic theory. The four quark potential matrix model being used is known to fit well a large number of data points for lattice simulations of different geometries of a four-quark system. In the first part of the work we study the coupling of a tetraquark system to an exchanged meson- meson channel. We have used the formalism of resonating group method, treated kinetic energy and overlap matrices on model of the potential matrix. We have taken advantage of few approximations e.g. we have used quadratic confinement instead of linear plus coulombic for pair wise interactions. Furthermore in the first part of the study we have also used the Born approximation and taken the constituent quark masses to be equal. There we find that when we used the minimal area based form of ’f’ in the off diagonal elements of potential energy, kinetic energy and overlap matrices in the gluonic basis in the model of four-quark system, we get a (scattering) angle dependence of T-matrix elements and phase shifts. Its partial wave analysis reveals that along with S-wave there is a presence of D-wave and higher angular momentum components in the T-matrix elements. In addition to the obvious implications of this result for the meson-meson scattering, this new feature indicates the possibility of orbital excitations influencing properties of meson- meson molecules through a polarization potential. In the 2nd part of the work another form of ’f’ (exp(−b s k f i<j 2 )) is used that is chosen only for computational convenience, r ij though the value used for the parameter in the exponent has its origin in numerical lattice simulations. There we have calculated the cross sections and phase shifts for the scattering xixii process of D o D o∗ −→ ωJ/ψ when f (Gaussian form) is used in the off-diagonal elements of potential energy, kinetic energy and normalization matrices of model of q 2 q 2 systems in the gluonic cluster basis. These cross sections can be potentially compared with actual experiments. Furthermore we have checked X(3872) to be recognized as a possible bound state of D o D o∗ system. Thus we have extended in the dynamical study of the f-model the spin-flavor independent formalism to the realistic systems, which are scalar mesons. By including the spin and flavor, we have addressed actual meson-meson systems. o These include D o D which is a scalar meson. But, considering current topics in meson spectroscopy, we have calculated dynamical predictions for a D o D important component of the much-addressed X(3872) meson.