Effective Lagrangian with two color-singlet gluon fields

Abstract

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 $\frac{1}{N_c}$ 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 traceanomaly 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.