Study of the decay $B^+ \rightarrow K^+\pi^0$ at LHCb

This analysis investigates the capability of LHCb to study the decay mode $B^+ \rightarrow K^+\pi^0$. This serves as a prototype analysis for decay channels with similar topologies, such as the $B^0 \rightarrow K^0\pi^0$, the $\Lambda_b \rightarrow \Lambda^0\gamma$, and the $B^0 \rightarrow K^0\pi^0\gamma$ decays, which involve photons in the final state and lack a reconstructed decay vertex. There is significant interest in these channels due to their sensitivity to effects of physics beyond the standard model. The proton-proton collision data set collected in 2011-2012, corresponding to $3.0~\text{fb}^{-1}$ of integrated luminosity, is studied. An analysis strategy is developed to mitigate the effects of low trigger efficiency and large combinatorial background leading to the reconstruction of $72\pm26$ signal events with a statistical significance of $3.7\sigma.$ Based on the findings of this study, a dedicated software trigger is being developed for use in the next data-taking period scheduled for later this year, when the LHC centre-of-mass energy will be increased.