Measurements of the $\pi^0 \rightarrow e^+ e^- \gamma$ decay with application of Deep Learning techniques

<!--HTML-->We present the measurement of the transition form factor of the $\pi^0$ that we performed analyzing the Run1 data, collected by the NA62 experiment during the year 2017-2018. It accounts for the largest worldwide sample of $\pi^0$ Dalitz decays with $8.7 \times 10^6$ events, allowing to reduce the statistical uncertainty by a factor $\sim1.8$ with respect to the previous measurement. While the statistical uncertainty is dominated by the statistics in the available MC sample, the largest uncertainty to the final result arises from the systematics due to the trigger emulation in the MC sample. Our result is<br><br>$a \pm \delta a_{stat} \pm \delta a_{sys} = (3.56 \pm 0.29 \pm 1.35) \times 10^{−2}$. <br><br>We also discuss the measurement of the $\pi^0$ Dalitz branching ratio which is on hold due to the need of data processing at the experiment level. We also report some studies of a new data-analysis technique based on Deep Learning methods which were performed while considering different approaches for the measurement, to investigate the possibility of fully performing an event selection using reconstructed quantities while minimizing any human input on the properties of the events being searched for. A byproduct of this work is a new fine calibration method for the energy clusters of the electromagnetic calorimeter, now the default method used in the official data- processing of the NA62 experiment. We show how our method reached similar performances with respect to previous ones, without introducing any biases and with the significant advantage of requiring much less computational power and time. As this work has been developed during the NA62 experiment shut-down, before the restarting of the new data-taking period in 2021, as an additional byproduct of the investigation of Deep-Learning techniques in high-energy physics, we also studied the possibility of a new algorithm for the L1 software trigger, implementing Deep Learning techniques to perform an unbiased particle identification exploiting the information coming from the NA62 Rich Cherenkov Counter. While the results of this study did not reach the efficiency levels required for its actual implementation in the experiment before the start of the new data-taking period, they represent an important basis for futures studies.