Angular analysis of the $B^0 → \pi^+\pi^- \mu^+\mu^-$ decay mode at LHCb

Flavour changing neutral current processes, such as the $b \rightarrow dl^{+}l^{-}$ quark transitions, occur only at loop level within the Standard Model (SM), making them highly sensitive probes for potential New Physics (NP) contributions. This thesis presents work on the first angular analysis of the $b \rightarrow \pi^{+}\pi^{-}\mu^{+}\mu^{-}$ decay mode, where muon pairs do not originate from a resonance. The analysis utilises the datasets collected by the LHCb experiment during the years 2011-2012 and 2015-2018, in proton-proton collisions at the Large Hadron Collider. The combined dataset corresponds to an integrated luminosity of $9 fb^{-1}$. The angular observables $F_{L}$, $S_{3}$, $A_{6}$, and $A_{9}$ are measured within two distinct bins of dimuon invariant mass squared ($q^{2}$) and within the dipion range of $0.62-0.92$GeV. Results are kept blind in this work pending review within the LHCb collaboration. Consistency checks using the $B^{0} \rightarrow J/\psi\pi^{+}\pi^{-}$ and $B^{0} \rightarrow \psi(2S)\pi^{+}\pi^{-}$ decay modes show agreement with existing published results, supporting the robustness of the analysis.