Hiroto Masaoka, Tetsuya Hashimoto, Shotaro Yamasaski, Yuhei Iwata, Tomoki Wada, Tomotsugu Goto, Shintaro Yoshiura, Kazuaki Hashiyama, Mareki Honma, Takuya Akahori, Kohei Kurahara

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 $p=0.076$ ($1.43σ$), consistent with a chance coincidence. Within our statistical framework, a detectable physical association would require a time offset shorter than $\sim256$~s at $3σ$ or $\sim63$~ms at $5σ$. Using a population-level stacking analysis, we derive 90\% upper limits on the neutrino-to-radio luminosity ratio of FRBs, $ξ\lesssim 10^{8}-10^{11}$ for neutrino power-law spectral indices $γ=1.0-3.0$. 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.