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.
Highlights
The discoveries of the gravitational waves at frequencies f > 10 Hz by LIGO and Virgo collaboration via a binary black hole merger and a binary neutron star inspiral have been hailed as a major milestone of gravitational wave astronomy [1,2,3,4]
The gravitational wave is expected to be an exquisite tool to study astronomical objects such as black holes and neutron stars, and to probe viable extension of general relativity as well as what lies Beyond the Standard Model (BSM) of elementary particles
The recent analyses of the 12.5-year pulsar timing array data at frequencies f ∼ 1/yr by NANOGrav Collaboration [5] in search for a stochastic gravitational wave background [6,7,8] are of particular importance and are encouraging enough for us to speculate much about BSM: cosmic strings or super-massive black holes as possible sources of the gravitational wave, first order phase transitions in the dark sector, new scenarios of leptogenesis induced by gravitational backgrounds and so on so forth
Summary
The discoveries of the gravitational waves at frequencies f > 10 Hz by LIGO and Virgo collaboration via a binary black hole merger and a binary neutron star inspiral have been hailed as a major milestone of gravitational wave astronomy [1,2,3,4]. In search for new avenues of BSM with the help of stochastic gravitational waves, it would sometimes happen that one has to deal with gravitational interactions of heavy unknown particles, in particular, on the quantum level In such a case we are necessarily forced to pay attention to heavy particle mass effects on physical observables. After submitting the present paper for publication, we learned that the process (1) had once been computed in the ’t Hooft-Feynman gauge and in the unitary gauge by Degrassi et al [25] and was investigated by Coriano et al [26, 27] for a different purpose from ours Their elaborate calculations, are not quite suitable for our use since they put external quarks on the mass shell, while we would like to make the non-decoupling phenomena manifest by studying off-shell effective interactions in the large top quark mass limit. Various definitions of Feynman parameters’ integrations are collected in Appendix A and some combinations thereof are defined in Appendix B
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