Heavy particle non-decoupling in flavor-changing gravitational interactions

TL;DR

This paper investigates flavor-changing gravitational interactions at the quantum level, revealing non-decoupling effects of heavy top quarks and analyzing their implications within the electroweak theory.

Contribution

It demonstrates the non-decoupling of heavy top quarks in flavor-changing gravitational processes and verifies the Ward-Takahashi identity for these interactions.

Findings

Non-decoupling effects of the top quark are present at the O(1) level.

Cancellation of expected mass-enhancement factors occurs in the renormalized amplitude.

Certain non-decoupling terms relate to effective Lagrangians with scalar curvature coupling.

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 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 $m_{t}$ and $M_{W}$ 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 $O(1)$ level. The flavor-changing two- and three-point functions are shown to satisfy the Ward-Takahashi identity, which is used for a consistency-check of the aforementioned cancellation of the $O(m_{t}^{2}/M_{W}^{2})$ terms. Among the $O(1)$ 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.