Sensitivity Study in the Search for $B^{\pm}\to K^{\pm}a$ (displaced $a\to\gamma\gamma$) Decays at Belle II

In a set of simple extensions of the Standard Model, Axion Like Particles (ALPs) arise as pseudo Nambu-Goldstone bosons of theories with a spontaneously broken Peccei-Quinn symmetry that is anomalous under the Standard Model gauge symmetry. Due to constraints in flavour-changing current  (FCNC) processes, involving the coupling of ALPs directly to Standard Model fermions and gluons, direct couplings of ALPs to the electroweak gauge bosons are particularly interesting. As a result of a coupling to $W$ bosons, ALPs can emerge in FCNC $b\to s$ transitions. Depending on the ALP mass and the coupling strength to photons a possible experimental signature is $B^{\pm}\to K^{\pm}a, a\to\gamma\gamma$ with long lived ALP decays. This thesis performs a sensitivity study in the search for the $B^{\pm}\to K^{\pm}a, a\to\gamma\gamma$ signature based on Belle II simulation samples corresponding to an integrated luminosity of 100\,fb$^{-1}$. The sensitivity study includes an optimised candidate selection and signal yield scans of the invariant di-photon mass distribution in the range of $0.175\,\text{GeV/c}^2$ to $4.600\,\text{GeV/c}^2$ for eight different ALP lifetimes between $0\,\text{cm}$ and $50\,\text{cm}$. Resulting expected limits are comparable to a similar search for $B^{\pm}\to K^{\pm}a, a\to\gamma\gamma$ on data collected by the BABAR experiment.