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 an 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 the 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 result shows 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. Branching fractions were obtained for the main reactions of the CS production in meson decays. The results obtained will be useful for searching for the long-lived GeV-scale CS boson in intensity frontier experiments.