Search for long-lived supersymmetric particles using fuzzy displaced vertices in pp collision at $\sqrt{s}$ = 13 TeV with the LHC-ATLAS detector

The Standard Model (SM) accurately predicts most of the experimental results from particle physics. However, there are several problems that the SM cannot explain, such as the existence of dark matter and the fine tuning problem of the Higgs boson mass. Many theories beyond the SM are proposed to solve such problems. One of the most famous and comprehensive models is the Supersymmetry (SUSY). Among many SUSY models, this thesis focuses on a model called bino-wino co-annihilation scenario, which is motivated by dark matter relic density. In this model, the second lightest neutralino $\tilde{\chi}_{2}^0$ can have a decay length measurable by the collider experiments. This thesis presents the search for the pair production of the second lightest neutoralino $\tilde{\chi}_{2}^0$ and the lightest chargino $\tilde{\chi}_{1}^{\pm}$ in such model using 137 fb$^{-1}$ of proton-proton ($pp$) collision at $\sqrt{s} = 13$ TeV collected by the LHC-ATLAS detector. The target process: \begin{align*} pp \rightarrow \tilde{\chi}_{2}^0 + \tilde{\chi}_{1}^{\pm}, ~\tilde{\chi}_{1}^{\pm} \rightarrow \tilde{\chi}_{1}^0 + W^{*} (\rightarrow ff'), ~\tilde{\chi}_{2}^0 \rightarrow \tilde{\chi}_{1}^0 + h^{*}(\rightarrow b\bar{b}) \end{align*} is searched using an unconventional signature. Suppose $\tilde{\chi}_{2}^0$ has a lifetime of an order of $\mathcal{O}(10^{-2})$-$\mathcal{O}(1)$ ns. In this case, it makes a secondary vertex away from the $pp$ collision point with high track multiplicity and invariant mass. Such a signature called the displaced vertex (DV) helps identify the heavy neutral long-lived particle (LLP), which is not included in the SM. The standard method for reconstructing DVs used in ATLAS cannot efficiently reconstruct them when the LLP decay includes $b$-quarks. A new method for DV reconstruction has been developed to solve this fatal drawback to this search. Using this new algorithm, the efficiency with which signal events have DVs with high track multiplicity and an invariant mass increased by a factor of 2–6. The first analysis using DVs reconstructed by the new method was performed. The signal region (SR) was required to have a missing transverse momentum larger than 150 GeV and at least one DV reconstructed by the new method with five or more tracks and an invariant mass larger than 10 GeV. The SM processes may have DVs that pass the selections for the SR by experimental effects. The number of background events in the SR was estimated by a new estimation method using the correlations between the DV and the other variables. After validating the validity of the estimation, the data in the SR were unblinded. Three events were observed, while the estimated number of background events was $0.81 \pm 0.49$. The upper limits were set based on the results. The $\tilde{\chi}_{2}^0$ mass up to 650 GeV is excluded at 95% confidence level for the case when $\tilde{\chi}_{2}^0$ lifetime is 0.03 ns, and the mass splitting between $\tilde{\chi}_{2}^0$ and $\tilde{\chi}_{1}^0$ is 50 GeV. This search gives the first exclusion limit in the LHC experiments for the target model.