No abstract

We derive relativistic wave equations for the bound states of two Higgs bosons within the Higgs sector of the minimal standard model. The variational method and the Hamiltonian formalism of QFT are used to obtain the equations using a simple Ihh ) + hhh ) Fock-space ansatz. We present approximate solutions of these equations for a range of Higgs boson masses, and explore the parameter space which corresponds to the existence of two-Higgs-boson bound states.

The Hamiltonian variational method is used to derive relativistic fermion-antifermion (NN) wave equations with interactions mediated by a neutral scalar (or pseudoscalar) ( pi 0) field. A simple mod NN>+ mod NN pi 0>+ mod pi 0 pi 0> Fock-space ansatz is used to derive the coupled integral wave equations. Approximate (numerical) solutions of the equations are presented for a range of values of the masses and coupling constant, for purely bound and decaying (NN to pi 0 pi 0) states. The domain of top-quark and higgs-particle masses for which tt bound states ('toponium') occur due to higgs exchange only is calculated. We find that tt bound states due to higgs exchange can arise for mt>or=401 GeV provided that the higgs particle mass is at least 50 GeV.

The variational method and the Hamiltonian formalism of QCD are used to derive relativistic, momentum space integral equations for a quark–antiquark system with an arbitrary number of gluons present. As a first step, the resulting infinite chain of coupled equations is solved in the nonrelativistic limit by an approximate decoupling method. Comparison with experiment allows us to fix the quark mass and coupling constant, allowing for the calculation of the spectra of massive systems such as charmonium and bottomonium. Studying the results with and without the non-Abelian terms, we find that the presence of the non-Abelian factors yields better agreement with the experimental spectra.