• lepton flavor violation
• Belle II
• tau decays

The measurement of the tau to lepton gamma decay, where the lepton can be a muon or an electron, is of great interest for high-energy physics. In the Standard Model, where charged lepton flavour is conserved, this decay is heavily suppressed and can only occur at loop level with very low probabilities. However, several new physics models predict scenarios where this decay is more likely to occur, with probabilities up to 10^(-10). A positive detection of a signal would represent indisputable evidence of physics beyond the Standard Model, but also improving the experimental limit of this measurement is important to constrain a wide class of possible Standard Model extensions.

The current best measurements for tau to mu gamma and tau to e gamma have been reported by the Belle and BaBar collaborations, with upper limits of 4.2 and 3.3 times 10^(-8), respectively. Both experiments used data coming from electron-positron collisions at the $\Upsilon(4S)$ resonance energy in the center of mass system.

Belle II, the successor experiment of Belle, collected so far about 4 times 10^8 tau-pairs, corresponding to more than 10^10 tau-pairs. With this amount of data, it will be possible to greatly improve the sensitivity to the tau to lepton gamma search.

In this thesis, I developed the selection criteria for a measurement of the tau to lepton gamma decay, using tau^+tau^- events. The Belle II analysis searches for an event in which one of the two tau's (signal) decays as tau to lepton gamma, while the other one (tag) decays generically, according to the known SM processes. The previous measurement of the tau to lepton gamma at Belle adopted a one-prong tag approach, in which an event is identified through the tau decays in one charged particle. Instead, I will focus on events identified by tag tau decaying in three charged particles (referred to as three-prong tag mode). The three-prong topology is more constrained than the one-prong one, allowing an efficient selection with low background.
The three-prong tag can be combined with the existing one-prong selection, increasing the statistical power of the analysis at a given luminosity. This work shows the potential, related to more inclusive approaches, to increase the sensitivity of the data at Belle II.