Were recently reported MHz events planet mass primordial black hole mergers?

Abstract: A bulk acoustic wave cavity as high frequency gravitational wave antenna has recently detected two rare events at $5.5$MHz. Assuming that the detected events are due to gravitational waves, their characteristic strain amplitude lies at about $h_c\approx 2.5 \times 10^{-16}$. While a cosmological signal is out of the picture due to the large energy carried by the high frequency waves, the signal could be due to the merging of two planet mass primordial black holes ($\approx 4\times 10^{-4} M_\odot$) inside the Oort cloud at roughly $0.025$ pc ($5300$ AU) away. In this short note, we show that the probability of one such event to occur within this volume per year is around $1:10^{24}$, if such Saturn-like mass primordial black holes are $1\%$ of the dark matter. Thus, the detected signal is very unlikely to be due the merger of planet mass primordial black holes. Nevertheless, the stochastic background of saturn mass primordial black holes binaries might be seen by next generation gravitational wave detectors, such as DECIGO and BBO.