Searching for Charged Lepton Flavour Violation at LHCb and Long-Lived Particles with CODEX-b

The CODEX-b detector is an RPC-based experiment proposed to search for long-lived particles that may be produced in $pp$ collisions at the LHC. The first comprehensive investigation on the impact of misalignments of CODEX-b are presented alongside reports of hardware quality assurance tests of the readout electronics for this detector. The mechanical precision $(<5\,\text{mm})$ when constructing the RPC modules will be more than sufficient to ensure track reconstruction is unaffected by misalignments. The first major quality control process for the evaluation of CODEX-b's RPC readout boards and its results are also presented, with more than 95% of the 440 tested boards validated for installation. The first experimental upper limits of the branching fraction of the rare decay, $\Lambda_b^0 \rightarrow \Lambda e^\mp\mu^\pm$, are presented based on analysis of data taken by the LHCb experiment between 2011 and 2018 (Run 1 & 2), corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$. Although the dataset remains blinded, estimated upper limits of the branching fraction of $\Lambda _b ^0 \rightarrow \Lambda e^\mp\mu^\pm$ assuming no signal is present were obtained using a background-only proxy dataset derived from the data sidebands. This is evaluated for two scenarios, one with higher efficiency and one with lower background contributions (including a $\Lambda^+_c$ decay veto), leading to results of \begin{align*} \cal{B} (\Lambda^0_b\rightarrow e^\mp\mu^\pm)_{\text{std }}\lesssim2.09\times10^{-7} \text{ @ 95% CL},\\ \cal{B}(\Lambda^0_b\rightarrow e^\mp\mu^\pm)_{\text{veto}}\lesssim6.45\times10^{-8} \text{ @ 95% CL}, \end{align*} respectively. These limits are comparable to that from a theoretical analysis of a proposed model-independent limit.