Color Confinement and Massive Gluon in Superfield Formalism

Abstract

In connection with the question of confinement of massive ghost in quadratic gravity (QG), color confinement in quantum chromodynamics (QCD) has been reconsidered in the superfield formalism. It is shown that when a bound state in the BRST transformation of the gluon field exists, the gluon becomes massive and is confined. It is also shown that the asymptotic field of the gluon field obeys the field equation for not the conventional massive Klein-Gordon field but the massive dipole field. In case of quark confinement, it is shown that the quark field satisfies the massive spinor dipole equation in the confinement phase, which might suggest a physical picture such that a pair of quark and anti-quark constitutes a bound state and is confined into a meson. These facts encourage us to conjecture that the similar phenomenon could take place in confinement of massive ghost, which violates the unitarity of the physical S-matrix, and might provide us with a resolution to the unitarity problem in QG.