Constraints on the Physical Association between ICECAT1 Neutrinos and Fast Radio Bursts Using the Second CHIME/FRB Catalogue

We present a search for neutrino counterparts to fast radio bursts (FRBs) using temporal and spatial cross-matching between the Second CHIME/FRB catalogue and the IceCube high-energy alert-track catalogue ICECAT1. Because current FRB–neutrino models do not provide a unique consensus on emission ordering, our primary significance test adopts a two-sided, order-agnostic temporal hypothesis. The analysis accounts for declination-dependent CHIME/FRB exposure and the look-elsewhere effect across multiple trials. No statistically significant FRB–neutrino association is found. The most significant pair is FRB,20190630C–IC,190629A, with a post-trial probability of $p=0.076$ ($1.43\sigma$), consistent with a chance coincidence. Within our statistical framework, a detectable physical association would require a time offset shorter than $\sim 256$~s at $3\sigma$ or $\sim 63$~ms at $5\sigma$. Using a population-level stacking analysis, we derive 90% upper limits on the neutrino-to-radio luminosity ratio of FRBs, $\xi \lesssim {10}^8-{10}^{11}$ for neutrino power-law spectral indices $\gamma =1.0-3.0$. These limits improve upon previous constraints by approximately two orders of magnitude and represent the most stringent bounds from FRB–neutrino coincidence searches to date. Although the current limits remain above the predictions of most magnetar-based models, they begin to constrain scenarios involving exceptionally efficient hadronic energy dissipation.