Search for lensing signatures from the latest fast radio burst observations and constraints on the abundance of primordial black holes

The possibility that primordial black holes (PBHs) form a part of dark matter has been considered for a long time but poorly constrained over a wide mass range. However, a renewed special interest of PBHs in the $1-100~M_{\odot}$ (or stellar mass range) was triggered by the discovery of the merger events of black-hole binaries by the LIGO-Virgo gravitational observatories. Fast radio bursts (FRBs) are bright radio transients with millisecond duration and almost all of them are at cosmological distances. Lensing effect of these bursts has been proposed as one of the cleanest probes for constraining the presence of PBHs in the stellar mass window. In this paper, we first apply the normalised cross-correlation algorithm to search and identify candidates of lensed FRBs in the latest public FRB observations, i.e. $593$ FRBs which mainly consist of the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, and then derive constraints on the abundance of PBHs from the null search result of lensing signature. For a monochromatic mass distribution, we find that the fraction of dark matter made up of PBHs could be constrained to $\leq10\%$ for $\geq150~M_{\odot}$. In addition, we derive constraints on PBHs with a log-normal mass function which is a natural prediction of some popular inflation models and often investigated with gravitational wave detections. We find that, in this mass distribution scenario, the constraint from currently public FRB observations is relatively weaker than the one from gravitational wave detections. It is foreseen that upcoming complementary multi-messenger observations will yield considerable constraints on the possibilities of PBHs in this intriguing mass window.