Search for lepton flavour violating $\tau^+\to\mu^+\mu^-\mu^+$ decay at LHCb and study on MCP-PMT detector for future LHCb Upgrade

The physics analysis has been the primary focus of my research activity during the PhD. Within the CERN LHCb collaboration, I've performed an analysis of data collected during the LHC Run2 (2016, 2017 and 2018). The aim of this work is the search for the decay of the $\tau$ lepton into three muons ($\tau^+\to\mu^+\mu^-\mu^+$), a decay that would violate the conservation of charged lepton flavour number (cLFV). The lepton flavour is an accidental symmetry of the Standard Model, and without the oscillations of neutrinos such decay would be prohibited. In the Minimal extended Standard Model the branching ratio $\mathcal{B}(\tau^+\to\mu^+\mu^-\mu^+$) is expected to be $\mathcal{O}(10^{-55}$), well below current and foreseen experimental sensitivity. Theories of physics beyond the Standard Model predict an enhancement of the $\tau^+\to\mu^+\mu^-\mu^+$ decay within present experimental sensitivity $\mathcal{O}(10^{-10})$. This decay has not been observed to date, only upper limits have been established by B-factories (BaBar, Belle) or by hadron collider experiments LHCb. The upper limit improvement implies strengthen of the constraints on exotic theories, while an observation of the decay would be a clear signal of New Physics. The analysis is performed separately for each year, and the data is divided into two subsamples depending on the number of muon candidates triggered by the LHCb muon system. Multivariate models are used to distinguish signal and background to enhance the signal sensitivity, and to define correction for data-simulation agreement. The $D_s^+\to\phi(\mu^+\mu^-)\pi^+$ channel is used as a reference channel to estimate the upper limit on the branching fraction. The expected upper limit is computed with the CLs method and results in \[\mathcal{B}(\tau^+\to\mu^+\mu^-\mu^+)\leq 1.8(2.2)\times10^{-8}\text{ @ 90% (95%) C.L.}\] The original analysis presented in this work is the result of a fruitful collaboration of many people working on the \lhcb experiment at the universities of Milano-Bicocca and Heidelberg. The content of the following chapters is the results of independent efforts of the Author or collaboration among the members of the analysis team. In particular, the studies related to the trigger efficiencies, the methods defined to correct Data-MC differences and the two multivariate classifiers for signal and background discrimination on the main data sample are results of individual work of the Author. The $\tau^+\to\mu^+\mu^-\mu^+$ is an example of a very rare decay, and the analysis involving such decays will benefit from the increment of statistics that will be collected in the current Run3 and in the following Run4 period of data taking at the upgraded LHCb. The High-Luminosity phase of LHCb, starting with Run5 of the LHC, will provide a further boost to the amount of available data. The LHCb detector will need to undergo a second upgrade, to cope with the $\times10$ increase of luminosity. Numerous studies and R&D projects are currently working on the development of technologies for the future detectors of LHCb. A part of my PhD project was devoted to work on a candidate photodetector for the upgraded Ring Imaging Cherenkov (RICH). I've characterized the timing performance of a multianode microchannel plate photomultiplier (MCP-PMT) in single photon regime. For the second upgrade it has been proposed to improve particle identification performance exploiting the use of precise timing information to cope with the increased pileup. MCP-based devices show excellent time resolution, but their use is critical due to saturation at rate above $\sim$100kHz/mm$^2$. The expected rate that the future devices will have to stand is $\sim$10MHz/mm$^2$. The Auratek-Square MCP-PMT produced by Photek is $53\times53$ mm device with $64\times64$ anodes grouped into $8\times8$ pixels. The dependence of the time resolution from the bias voltage and the photon rate was assessed. When operating as single photon counter at low photon rate and with a single pixel illuminated it shows a transit time spread (jitter) of $\sim$100\ps FWHM, saturating at high rate, above $\sim$100kHz/mm$^2$. Lowering the bias voltage between the photocathode and the MCP input or between the MCP slabs can reduce the worsening of the time resolution at high rate. The charge sharing between the neighbouring pixels can degrade the time resolution to $\sim$170 ps FWHM when the entire pixel area is illuminated, and could become a major crosstalk source if not accounted for.