Measurement of NA62(CERN) sensitivity towards the search of $\pi^{0}\rightarrow3\gamma$ and $\pi^{0}\rightarrow4\gamma$ decays

The aim of the paper is measurement of NA62 experiment sensitivity towards the search for forbidden in Standard Model decay $\pi^{0}\rightarrow3\gamma$, that violates C-invariance principle, and allowed in Standard Model decay $\pi^{0}\rightarrow4\gamma$. Current upper limit on the probability of $\pi^{0}\rightarrow3\gamma$ ($\pi^{0}\rightarrow4\gamma$) decay is $3.1\times10^{-8}$ ($2\times10^{-8}$) with $90\%$ confidence level. In the paper $K^{+}\rightarrow\pi^{+}\pi^{0}$ decays are used as a source of $\pi^{0}$. The idea of selection of events with 3 products or 4 products after $\pi^{0}$ decay in NA62 detector was developed. NA62 detector and all physical processes were modelled with Monte Carlo method using Geant4. Single event sensitivity towards $\pi^{0}\rightarrow3\gamma$ ($\pi^{0}\rightarrow4\gamma$) decay without background events consideration is $\mathcal{O}(10^{-9})$, which is 1 order better than current upper limits. Consideration of background events for each decay leads to decline of sensitivity to the level of current limits.