Hao-Hao Chen, Wen-Tao Xu, Xin-Yu Liang, Ming-Xuan Lu, Can-Min Deng

The physical origin of fast radio bursts (FRBs) remains an unsolved mystery in astrophysics, with the magnetar central engine model as the leading framework. Systematically searching for physical associations between FRBs and the energetic astrophysical transients (ATs) that form magnetars provides a critical test of this scenario, and key clues to FRB progenitors. We perform a systematic search for FRB-AT associations using a sample of 3765 unique FRBs, combining the second CHIME/FRB catalog with 124 additional localized FRBs with measured redshifts. We develop a 3D Bayesian inference framework that jointly incorporates angular separation, positional uncertainty, and redshift constraints to quantify the association probability of candidate pairs. Through spatial cross-matching, we identify 14 FRB-optical transient and 15 FRB-gamma-ray burst (GRB) candidate pairs. Our framework recovers the previously reported high-significance association between FRB 20180916B and AT 2020hur, with an association probability of 0.9998. For the proposed candidate FRB 20190309A and short GRB 060502B, our analysis yields an association probability of 0.83, which is insufficient to claim statistically significant association. No new statistically significant FRB-AT associations are found for all remaining candidates. Our work demonstrates that small angular separation alone is insufficient to confirm FRB-AT associations, and high-precision FRB localization is essential for definitive identification.