• angular momentum violation
• FCNC.
• kaons
• NA62

The present work presents a feasibility study for the search of the decay $K^+ \rightarrow \pi^+ \gamma$ within the NA62 experiment, the current CERN research program for testing the Standard Model (SM) through the study of rare kaon decays.
The transition is forbidden by angular momentum conservation, but possible in some exotic models. The most recent upper limit on the branching ratio of $2.3 \cdot 10^{-9}$ was established by the BNL E949 collaboration in 2005.
Limits on the analogous decay $K_L\rightarrow \pi^0 \gamma$ were set by the KOTO experiment in Japan at the $10^{-7}$ level.
The aim of this work is to provide a first estimation of the capabilities of the NA62 experiment on this process.

The first chapter gives an introduction to the decay and the past measurements, focusing on the differences between the E979 measurement and NA62.

The NA62 detectors used in this analysis are described in chapter two, explaining the reason of some design choice, related to the main goal of this experiment.

Chapter three describes the selections used to reject most of the backgrounds, which were tested on the MonteCarlo simulation. The definition of a set of cuts selecting a region in which the background is highly-suppressed will be discussed.

Some results on NA62 data collected in 2018 and a new trigger mask that would help in the search of this decay are presented in chapter four.
The final chapter summarizes the results of the work and presents future perspectives.