Theoretical analysis and sensitivity study for the NA62 experiment of the decay of the K meson into two pions and a pseudoscalar particle

The axion is widely thought to be among the best-motivated additions to the SM, providing a solution to the strong CP problem and being a possible DM candidate. In this thesis, we give a review of its properties — re-deriving some of them in the framework of CHPT — and of the most common experimental techniques used in axion searches. Afterwards, we focus our attention on a specific family of models, dubbed axiflavon. Combining the QCD axion with a Froggatt–Nielsen flavon, they provide a solution to the flavour model, on top of being QCD axion models. For general axion models, the discovery potential of flavour physics experiments is in general not competitive with respect to astrophysical probes; the opposite is true for axiflavon models. Indeed, for the vectorial coupling of axiflavon to quarks, the Kaon factory NA62 can probe the DM window, a unique feat among particle physics experiments. However, an experimental effort to measure the corresponding axial-vector coupling at current experiments is, to date, lacking. Motivated by this, the second and main part of this thesis is dedicated to the estimation of the sensitivity the NA62 experiment can have for the $K^+ \to \pi^+ \pi^0 a$ decay, with a being any stable pseudoscalar. This is done using MC simulations, employing also a newly-written MC event generator, and the data from the 2017B data-taking period, corresponding to ≈ $8 \times 10^8 K^+$ decays in the fiducial volume. Our statistical analysis, which employs the CLs method, yields an estimate of the BR sensitivity of O($10^{−7}$) in the mass range [0, 200] MeV/$c^2$ . This should be taken as a preliminary result, with areas of possible improvement already under examination in the NA62 collaboration. Nonetheless, it shows a sizeable margin of improvement (roughly 2 orders of magnitude) from current limits.