Effective theory analysis for vector-like quark model
Takuya Morozumi (Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan, Core of Research for the Energetic Universe, Hiroshima University, Higashi-Hiroshima 739-8526, Japan); Yusuke Shimizu (Core of Research for the Energetic Universe, Hiroshima University, Higashi-Hiroshima 739-8526, Japan); Shunya Takahashi (Core of Research for the Energetic Universe, Hiroshima University, Higashi-Hiroshima 739-8526, Japan); Hiroyuki Umeeda (Graduate School of Science and Engineering, Shimane University, Matsue 690-8504, Japan)
We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor-changing neutral currents (FCNCs) arise at tree level and the unitarity of the Cabibbo–Kobayashi–Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from transitions, especially and processes. In order to analyze these processes we derive an effective Lagrangian that is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for . It includes the effects of the SM quarks and the violation of CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on , , , and CKM matrix elements, as well as theoretical uncertainties. We find that the constraint from is more stringent than that from ]. We also obtain a bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of the transition. Using the CKM elements that satisfy the above constraints, we show how the unitarity is violated on the complex plane.
