Heavy particle non-decoupling in flavor-changing gravitational interactions

Abstract

Abstract The flavor-changing gravitational process, d → s + graviton, is evaluated at the one-loop level in the standard electroweak theory with on-shell renormalization. The results that we present in the ’t Hooft–Feynman gauge are valid for on- and off-shell quarks and for all external and internal quark masses. We show that there exist non-decoupling effects of the internal heavy top quark in interactions with gravity. A naive argument taking account of the quark Yukawa coupling suggests that the amplitude of the process d → s + graviton in the large top quark mass limit would possibly acquire an enhancement factor $m_{t}^{2}/M_{W}^{2}$, where mt and MW are the top quark and the W-boson masses, respectively. In practice this leading enhancement is absent in the renormalized amplitude due to cancellation. Thus the non-decoupling of the internal top quark takes place at the ${\cal O}(1)$ level. The flavor-changing two- and three-point functions are shown to satisfy the Ward–Takahashi identity, which is used as a consistency check for the aforementioned cancellation of the ${\cal O}(m_{t}^{2}/M_{W}^{2})$ terms. Among the ${\cal O}(1)$ non-decoupling terms, we sort out those that can be regarded as due to the effective Lagrangian in which quark bilinear forms are coupled to the scalar curvature.