Strategy for real-time search of neutrino counterparts of Gravitational Wave events during the O4 run of the VIRGO/LIGO/KAGRA observatory with the KM3NeT/ARCA neutrino telescope

The strength of multi-messenger astronomy allows us to deeply investigate the Universe: by combining diverse observations, such as photons, gravitational waves, and high-energy particles, it is possible to increase the significance of a detection. Due to their unique physical properties, neutrinos are ideal probes to study high-energy astrophysical phenomena and the most extreme and energetic astrophysical environments. This thesis is developed within the KM3NeT experiment, which is a major upcoming facility in the field of neutrino astronomy. It is currently being built in the Mediterranean Sea and it is composed of two detectors: ORCA and ARCA. Along with searching for neutrinos accumulated over a long livetime from several sources (offline searches), KM3NeT is part of a global multi-messenger program that involves receiving and sending real-time alerts. If an interesting event occurs, a short message is automatically sent to the GCN, SNEWS or the AMON network, which triggers several other telescopes. In the KM3NeT Online Framework, different online pipelines are optimized based on the specific event to follow up. The aim of this thesis is the definition of the event selection for KM3NeT/ARCA in the real-time pipeline whose goal is to search for neutrinos in coincidence with the emission of gravitational waves (GWs). In order to reduce the expected background and the amount of data to process, an event selection is required. Only well-reconstructed events are kept, and they are used to discriminate signal from background. The strategy of the follow-up is based on an ON/OFF analysis technique that looks for a space and time correlation between neutrino events and GW alerts coming from the LIGO/VIRGO/KAGRA O4 observing run, that started on May 24th, 2023. The event selection has been first validated (offline) by analyzing GW events coming from the O3 observing run. The results of the study have then been implemented in the online pipeline.