J/Ѱ Interaction with Light Mesons in QCD-Improved Cornell Model for Tetraquarks

Abstract

We have calculated the cross-sections for the processes ρJ/ψ → D0 ¯ D0, ρJ/ψ → D0 ¯ D0∗ or D0∗ ¯ D0, ρJ/ψ → D0∗ ¯ D0∗, D0 ¯ D0 → ρJ/ψ, D0∗ ¯ D0 or D0 ¯ D0∗ → ρJ/ψ and D0∗ ¯ D0∗ → ρJ/ψ using a QCD-motivated improvement to the usual sum of pairwise interaction model. This improvement is modelled in the literature by a gluonic field overlap factor f multiply ing off-diagonal elements of normalization, kinetic energy and potential energy matrices in the basis composed of different q¯ q clusterings of a two quarks two antiquarks system. We study the effect of this f factor in these meson-meson scatterings. Gaussian form of f i.e. (exp(−bskf∑i<j r2 ij)) is taken for computational convenience. The chosen value of the parameter kf is originated from numerical lattice QCD simulation. For a comparison, we also calculated the cross sections for f = 1 meaning the sum of pair-wise model limit. The Res onating group method has been used to make a maximum use of the wave function of a single cluster of a quark anti-quark pair. Kinetic energy and overlap matrices have been treated on the model of the potential matrix in the gluonic basis. Here quadratic wave functions are taken by fitting the parameters in such a way that we get maximum overlap of meson quadratic and Cornell wave functions. In order to decouple the coupled integral equations resulting from the resonatinggroup method, Bornapproximationis used. In this thesisthe quadratic aswell as the Cornell potential are used for pairwise interaction in the Hamiltonian of the four quark system. With the Cornell potential we incorporated the spin and flavour dependence in the total wave function of the four quark system. In this thesis a comparison of the cross sections obtained by using the quadratic potential and the Cornell potential is made. In this study we have found v that the Cornell potential gives lesser cross-sections as compared to the quadratic potential. We present the graphs which represent the justification of the difference of the cross sections ob tainedbytwodifferentpotentials. Inthisjustificationtheintegralkernelissplittedintotwoparts (i- potential part and ii- kinetic energy plus constant part). The results of these terms are plotted where it is observed that these terms try to cancel out each others effect to give the lesser hij factor which decreases the T matrix elements and hence the cross sections. This cancelation effect is large when Cornell potential is used. We then introduced the Gaussian form of f in the off diagonal parts of the kinetic energy, potential energy and the overlap matrices in the colour basis. There is a significant suppression in the cross sections obtained when f is introduced as compared to the cross sections obtained from simple sum of two body approach.