Understanding the impact of non-local contributions to $ \bar{B}^{0} \rightarrow \bar{K}^{ *0}μ^{+}μ^{-} $transitions

The impact of the non-local contributions to $ \bar{B}^{0} \rightarrow \bar{K}^{ *0}\mu^{+}\mu^{-} $ decays has been assessed through creating a framework suitable to perform a five dimensional, unbinned, maximum likelihood fit to the data collected by the LHCb experiment. Both $\bar{B}^{0}$ and $B^{0}$ decays are treated equally in this analysis, thus providing a sample rich in $ \bar{B}^{0}$$({B}^{0}) $ $\rightarrow $$\bar{K}^{ *0}$$(K^{ *0})$$\mu^{+}\mu^{-} $ candidates. The data analysed corresponds to the full Run 1 dataset which equates to an integrated luminosity of 3 fb$^{−1}$, and the 2016 dataset from Run 2 that amounts to an integrated luminosity of 1.67 fb$^{−1}$. The model considers all possible hadronic contributions that contribute to $\bar{B}^{0} \rightarrow \bar{K}^{ *0}\mu^{+}\mu^{-} $ decays, in the invariant dilepton mass squared (q2) region of 1.0 < $q^2$ < 18.0 GeV$^2/c^4$. No previous analyses have been published that determine the impact of the non-local contributions in $\bar{B}^{0} \rightarrow \bar{K}^{ *0}\mu^{+}\mu^{-} $ decays. Therefore, for the first time, the analysis presented in this thesis tries to understand these contributions. Recent results published from LHCb reveal anomalous results seen in $b \rightarrow s\ell^+\ell^−$ transitions. Possible explanations include New Physics, at the TeV scale, or hadronic resonances interfering with the penguin component and causing a sizeable effect that appears like New Physics. This analysis through a fit to the data will determine the latter, demonstrating how the effects seen could be due to our lack of understanding of the non-local contributions.