Improvement of the follow-up observations of IceCube neutrinos by CTA LST

A decade has passed since high-energy astrophysical neutrinos have been discovered by IceCube, however the corresponding sources have not been fully identified yet. The reported coincidence of the high-energy IceCube-170922A with the gamma-ray blazar TXS 0506+056 is not enough to claim that blazars are the dominant high-energy neutrino emitters in the Universe. In fact, recently IceCube announced a second correlation with NGC 1068, a nearby Seyfert galaxy, which is significantly different from a gamma-emitting blazars. The hunt for counterparts of the IceCube neutrinos using gamma-ray telescopes started in 2012. Nonetheless, these efforts will continue with the next-generation gamma-ray telescopes, such as the CTA Large Size Telescopes (LSTs) and other telescopes, by means of an improved and revised observation strategy. These new observations will allow us to detect enough sources in order to elucidate the mystery of the neutrino emitters. In this contribution, we introduces the efforts made thus far in the search for gamma-ray counterpart of high-energy IceCube events using the current generation IACTs, focusing on alerts made of multiple neutrinos events, and present an idea to improve in the observational strategies with the CTA LSTs that will become operational in the coming decade. We will discuss how to reduce the bias to gamma-ray emitters in order to search for possible neutrino counterparts.