Production of Chern-Simons bosons in decays of mesons

We consider the effective interaction of quarks with a new GeV-scale vector particle that couples to electroweak gauge bosons by the so-called effective Chern-Simons interaction. We call this particle the Chern-Simons (CS) boson. We construct effective Lagrangian of the CS boson interaction with quarks of two different flavors. This interaction is given by a divergent loop diagram, however, it turns out that the divergent part is equal to zero as a consequence of the CKM matrix unitarity in the SM. Therefore, we are able to predict effective interaction of the CS boson with quarks of different flavors without introducing new unknown parameters to the model, using only parameters of the initial effective Lagrangian. Our results show, that the effective interaction of the CS boson with down-type quarks is sufficiently stronger compared with up-type quarks. Based on our results, we give a prediction for the production of CS bosons in mesons decays.