Effective Lagrangian with two color-singlet gluon fields

An effective Lagrangian with scalar and pseudoscalar ''matter'' fields as well as scalar and pseudoscalar (gauge-invariant) color-singlet gluon fields is constructed. It is a representation of quantum chromodynamics in that it has the same symmetry structure as that theory. The present model is a generalization of a one- (pseudoscalar) gluon-field effective Lagrangian which compactly summarizes the results of the 1/N/sub c/ approximation, gives a simple picture for the ''U(1) problem,'' and essentially reduces to a type of generalized sigma model. The new feature here is that, in addition to the chiral-anomaly equation, the trace-anomaly equation is automatically fulfilled. This gives a framework for discussion of the properties of a 0+ color-singlet gluon field. The model may be formulated either so that this field is eliminated by a constraint equation or so that it is associated with a physical particle. Probably, experiment is the best way at present of deciding between the two possibilities. A number of possibilities for further generalization of the effective Lagrangian, including a hint of a possible connection with the ''confinement'' problem, are mentioned