Quarkonium decay into photon plus graviton: a golden channel to discriminate General Relativity from Massive Gravity?

TL;DR

This paper investigates the potential of quarkonium decays into photon plus graviton as a way to distinguish between General Relativity and Massive Gravity, analyzing decay rates within effective field theory and their experimental detectability.

Contribution

It provides a comparative analysis of decay rates in GR and Massive Gravity, highlighting the impact of the graviton mass and the vDVZ discontinuity on observable decay channels.

Findings

Decay rates are extremely suppressed and overshadowed by Standard Model backgrounds.

Massive Gravity predicts decay rates that differ significantly from GR in the massless limit.

The study discusses the implications of the vDVZ discontinuity for gravitational theories.

Abstract

After the recent historical discovery of gravitational wave, it is curious to speculate upon the detection prospect of the quantum graviton in the terrestrial accelerator-based experiment. We carefully investigate the "golden" channels, $J/\psi(\Upsilon)\to\gamma+\text{graviton}$, which can be pursued at \textsf{BESIII} and \textsf{Belle 2} experiments, by searching for single-photon plus missing energy events. Within the effective field theory (EFT) framework of General Relativity (GR) together with Nonrelativistic QCD (NRQCD), we are capable of making solid predictions for the corresponding decay rates. It is found that these extremely suppressed decays are completely swamped by the Standard Model background events $J/\psi (\Upsilon)\to \gamma+\nu\bar{\nu}$. Meanwhile, we also study these rare decay processes in the context of massive gravity, and find the respective decay rates in the limit of vanishing graviton mass drastically differ from their counterparts in GR. Counterintuitive as the failure of smoothly recovering GR results may look, our finding is reminiscent of the van Dam-Veltman-Zakharov (vDVZ) discontinuity widely known in classical gravity, which can be traced to the finite contribution of the helicity-zero graviton in the massless limit. Nevertheless, at this stage we are not certain about the fate of the discontinuity encountered in this work, whether it is merely a pathology or not. If it could be endowed with some physical significance, the future observation of these rare decay channels, would, in principle, shed important light on the nature of gravitation, whether the graviton is strictly massless, or bears a very small but nonzero mass.