Predictions for the isospin-violating decays of *

Abstract In this study, we investigate the isospin-violating decays of , which may provide additional information for the determination of the properties of , the first orbital excitation states of the meson. By assuming a dual relation between the U (1) anomaly soft-gluon coupling for and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four P -wave states. We observe that the partial decay width of is approximately three orders of magnitude larger than that for . This indicates that can be established in the decay channel as a single state. Meanwhile, the two axial-vector states can be possibly identified in with comparable strengths. Although these isospin-violating decays are observed to be small, the theoretical predictions should be useful for guiding future experimental efforts.