Diagonalization of the light cone QCD4 mass operator in a ladder quarkonium basis

QCD4 quantized on the light-cone is cast into discretized form by placing the system in a box of finite extent in the x- and transverse directions. In the resulting cutoff theory the quark and gluon field operator expansions are truncated to finite numbers of longitudinal and transverse modes. For a basis of the type {|qq-bar>, |qq-barG>}, corresponding to a light-cone ladder approximation with fermion self-energy insertions, vertex corrections and non-planar effects, the necessary matrix elements for the construction of the normal ordered mass matrix are derived. The lowest eigenvalues of this matrix are found numerically using the Lanczos algorithm. We have studied the behaviour of the ground-state of the system as a function of the coupling constant for various cutoffs and quark masses. In all cases studied the ground state remains below the 2m threshold and eventually becomes tachyonic at some critical coupling, depending on the basis type and quark mass. (author)