Blazar -- IceCube neutrino association revisited

The reported association of high-energy neutrino event IceCube-170922A and blazar TXS 0506+056 has sparkled discussion about blazars as sources of cosmic neutrinos. In this paper, we use publicly released IceCube data and blazar locations from Roma-BzCat to test spacial correlation between neutrino events and blazar locations. We also scrutinize the correlation between $\gamma$-ray flux and neutrino flux of blazars by applying a temporal filter onto the data based on Fermi monitored source list. We find no compelling evidence to prove blazars as the main source of cosmic neutrinos, as known before the detected IceCube-170922A / TXS 0506+056 association. While we do not rule out the association between IceCube-170922A and TXS 0506+056, the significance level we obtained is not high enough to claim a strong association. If such an association is real, a special physical condition is desired to allow a small fraction of blazars to become bright neutrino sources.