Studies On Multiply Heavy Hadron Spectral Density, Charmonium Form Factors And Glueball Mass Spectra

In this thesis, we take the hypergeometric functions as main tools to perform systematic study on the evaluation of the spectral densities of the multiply heavy hadrons like QX, QQ’X and QQQ’X. The evaluation is performed directly in the coordinate space and the spectral density is expressed in terms of hypergeometric functions, which drastically simplifies the QCD sum rules analysis of the newly discovered exotic hadron states and make the spectral density evaluation systematic.We employ the multi-precision finite difference method to extract the Laurent coefficients of the epsilon expansion of a wide variety of epsilon regularized hyper-geometric functions. This elaborate expansion method works for a wide variety of hypergeometric functions, which are needed in the context of dimensional reg-ular ization for Feynman integrals. In addition, there is almost no restriction on the parameters of hypergeometric functions. Based on this new algorithm, we also present a package NumExp, which facilitates the high energy physics calculations.We use the QCD light cone sum rules to study the transition form factors and couplings of two types of charmonium VVP processes D*D*ηc and DD*J/ψ, re-spectively. Transverse relative momentum between two charm quarks are considered and the couplings gηcD*D*and gJ/ψDD*are extracted from the sum rules. So as to make a comparison of the results with the predictions of other theories, we have tried three typical longitudinal distribution amplitudes in the calculation. Then we analyze the possible shapes of the distribution amplitudes of ηc and J/ψ.We perform a tentative study on the mass spectra of two-gluon glueballs in the light-front QCD. The interactions between classical instanton fields and quantum gluon fields are took into consideration. Then we work out the full form of the light-front Hamiltonian. By projecting the glueball states to both sides of the Hamiltonian eigenvalue equation and diagonalizing the eigenvalue matrix, we expect to obtain the mass spectra of some glueball states.