Measurement of the photon polarisation in $B^+ \to K^+ \pi^- \pi^+ \gamma$ decays at LHCb

All physical processes can be described, at a fundamental level, through interactions of elementary particles. The Standard Model of particle physics (SM) describes three of the four known fundamental forces and all of the known elementary particles. The accuracy of the predictions made using this theory has been experimentally established over a wide range of processes. Physicists endeavour to extend the SM to cover those phenomena, observed or hypothesised, that are currently beyond its scope. To develop these extensions, it is useful to identify processes involving SM particles where SM predictions differ from what is measured in nature.

The fact that flavour-changing neutral currents (FCNC) processes are forbidden at tree level in the SM makes them a promising laboratory for precision measurements that can show effects of physics beyond the SM: New Physics (NP) at energy scales higher than those of an FCNC process can nevertheless indirectly affect it to a potentially measurable extent. This work realises one such precision measurement. It concerns the polarisation of the photon in $b \to s \gamma$ transitions. Due to the chiral nature of the weak interaction, which is the only SM interaction that mediates FCNC processes, the photon is almost entirely left-handed in decays that proceed through a $b \to s \gamma$ transition. NP with a chiral structure that is different from that of the weak interaction could enhance the right-handed component of the photon. The photon polarisation in $b \to s \gamma$ transitions is experimentally constrained through measurements of the inclusive branching fraction $B \to X_s \gamma$ and other measurements of radiative decays of $b$ hadrons, as well as from $B^0 \to K^{*0} e^+ e^-$ decays at low $q^2$. It has been directly measured in $\Lambda_b \to \Lambda \gamma$ decays. The experimental results are consistent with SM predictions. A measurement of the up-down asymmetry in $B^+ \to K^+ \pi^- \pi^+ \gamma$ decays has shown that the photon in these decays is polarised, but the value of the polarisation parameter $\lambda_\gamma$ could not be extracted from this measurement. In this work, an amplitude analysis of $B^+ \to K^+ \pi^- \pi^+ \gamma$ decays recorded at the LHCb experiment during Run 1 and Run 2 of the LHC is performed, and a model of the $B^+ \to K^+ \pi^- \pi^+ \gamma$ decay, including the value of $\lambda_\gamma$, is defined. This measurement further constrains the photon polarisation in $b \to s \gamma$ transitions and thus contributes to the identification of promising avenues for extending the SM.

The reconstruction of charged particle momenta at LHCb requires a precise knowledge of the magnetic field that bends the particles' trajectories. A new map of the magnetic field of the LHCb dipole was developed for use in Run 3 of the LHC. This map and its development is also discussed in this work.