Quantum chiral field theory of $0^{-+}$ glueball

A chiral field theory of $0^{-+}$ glueball is presented. The coupling between the quark operator and the $0^{-+}$ glueball field is revealed from the U(1) anomaly. The Lagrangian of this theory is constructed by adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons. Quantitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.