2 research outputs found
Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation
A rigorous three-dimensional relativistic equation satisfied by two-gluon
bound states is derived from the QCD with massive gluons. With the gluon fields
and the quark fields being expanded in terms of the gluon multipole fields and
the spherical Dirac spinors respectively, the equation is well established in
the angular momentum representation and hence is much convenient for solving
the problem of two-gluon glueball spectra. In particular, the interaction
kernel in the equation is exactly derived and given a closed expression which
includes all the interactions taking place in the two-gluon glueballs. The
kernel contains only a few types of Green's functions and commutators.
Therefore, it is not only easily calculated by the perturbation method, but
also provides a suitable basis for nonperturbative investigations
Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of the glueball spectrum
In the preceding paper, a rigorous three-dimensional relativistic equation
for two-gluon bound states was derived from the QCD with massive gluons and
represented in the angular momentum representation. In order to apply this
equation to calculate the glueball spectrum, in this paper, the equation is
recast in an equivalent three-dimensional relativistic equation satisfied by
the two-gluon positive energy state amplitude. The interaction Hamiltonian in
the equation is exactly derived and expressed as a perturbative series. The
first term in the series describes the one-gluon exchange interaction which
includes fully the retardation effect in it. This term plus the linear
confining potential are chosen to be the interaction Hamiltonian and employed
in the practical calculation. With the integrals containing three and four
spherical Bessel functions in the QCD vertices being analytically calculated,
the interaction Hamiltonian is given an explicit expression in the angular
momentum representation. Numerically solving the relativistic equation with
taking the contributions arising from the retardation effect and the
longitudinal mode of gluon fields into account, a set of masses for the
and glueball states are
obtained and are in fairly good agreement with the predictions given by the
lattice simulatio