Quark confinement, rising trajectories, and asymptotic behavior of form factors

Abstract

Several long-range force models of quark confinement are considered, with particular emphasis on gluon exchange analogous to linear and harmonic potentials. First, the nonrelativistic case is discussed and the connection between the rise of the Regge trajectories and the power of the potential is derived. Then semirelativistic and relativistic equations are considered. It is shown that in each case the rising trajectories result from large quark-gluon coupling constants. It is also shown that an asymptotic power decrease of bound-state form factors follows only if the interaction contains an additional Coulomb- or Yukawa-type part, and only in the spacelike or the timelike domain. The significance of infrared cutoffs is examined, violations of unitarity are pointed out, and the behavior in the static limit is discussed.