Search for neutrino emission from blazar \(γ\)-ray flares accounting for possible neutrino time delays

We report the results of the search for the high-energy neutrino emission associated with blazar flares, accounting for a possible lag of neutrinos with respect to the electromagnetic emission, either due to the slowness of the proton energy losses in \(pγ\) collisions and/or proton acceleration. We perform two tests, cross-matching neutrinos with energies \(E_ν \gtrsim 100\) TeV from the public catalogue of neutrino alerts IceCat-1 with active galactic nuclei from two source samples based on 1) the MOJAVE database and 2) the CGRaBS catalogue, and utilising Fermi-LAT light curves from the public light curve repository. We scan over a wide range of values of the jet-frame time delay \(t^{\prime}_{\mathrm{delay}}\) between the neutrino arrival and the time of the prior major \(γ\)-ray flare and find a pre-trial \(\sim 2σ\) correlation at \(t^{\prime}_{\mathrm{delay}} \sim 10^{3}\) d, which is consistent (\(p_{\mathrm{post-trial}} \sim 0.1\)) with expectations under the null hypothesis after trial correction.