Search for long-lived supersymmetric particles using displaced vertices and multiple jets in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

The Standard Model (SM) of particle physics describes all fundamental forces of electromagnetic, weak, and strong interactions, except for gravity in the universe. The behaviour of elementary particles predicted by the SM is in good agreement with the results of the experiments obtained so far. However, there are some problems that cannot be solved by the SM alone; the Higgs boson mass 125 GeV cannot be naturally derived and the dark matter cannot be formed from the particles in the SM. Supersymmetry (SUSY) could solve these problems. Also, SUSY possibly unifies the electroweak and strong interactions at a high energy scale. SUSY particles have been searched for up to $O(1)$ TeV at the Large Hadron Collider (LHC), but no SUSY particles have been found. A large parameter space for SUSY particles, which provides all above benefits, has been excluded. Therefore, I focused on the SUSY model, which solves the mass problem of the Higgs boson at least. I focused on the $R$-parity violating model. In this model, the lightest SUSY particles can decay to the SM particles. The coupling constants between SM and SUSY particles are predicted to be small due to proton decay constraints. Since regions with very small coupling constant have already been searched for in other analyses at the ATLAS experiment, this thesis focuses on the case where the coupling constant is $O(10^{-4})$-$O(10^{-3})$. This case does not allow SUSY particles to form dark matter candidates, but the other two benefits can be kept. This thesis presents a search for long-lived SUSY particles in events with displaced vertices and multiple jets using the 139 $\rm fb^{-1}$ of $pp$ collision data collected at $\sqrt{s}$ = 13 TeV by the ATLAS detector at the LHC. Two signal processes are searched for, which are $pp \rightarrow \tilde{g}\tilde{g}$, $\tilde{g} \rightarrow qq\tilde{\chi}_{1}^{0}(\rightarrow qqq)$ and $pp \rightarrow \tilde{\chi}_{1}^{0}\tilde{\chi}_{1}^{\pm}, \tilde{\chi}_{1} \rightarrow qqq$. The lightest electrowikinos $\tilde{\chi}_{1}$ have a long lifetime due to the small $R$-parity violating coupling. I focus on the models characterized by multiple jets and the decay vertex of the long-lived electrowikino being $O(1)$-$O(100)$ mm away from the interaction point, which is called displaced vertex. We established the analysis method using dedicated techniques to reconstruct the tracks derived from the long-lived electrowikino decay and the decay vertex of the electrowikino. A signal region (SR) is defined for each signal process. In SRs, at least one displaced vertex and multiple high momentum jets are required. The displaced vertex must be reconstructed from five or more tracks and the invariant mass calculated from the four-momenta of these tracks, obtained by assuming the pion mass for each track, must be larger than 10 GeV. The dominant background events are due to accidental reconstruction of displaced vertices by some sources. I established a new background estimation method and achieved accurate estimation. The new method estimates the background events inclusively using the relation between the number of accidentally reconstructed displaced vertices and the number of jets. The number of observed events did not significantly exceed the background estimations in each SR. At 95% confidence level, the neutralino mass up to 1.58 TeV for lifetime of 0.1 ns is excluded. This analysis allows the search for the models in which the lightest electrowikino with lifetimes of 0.01 - 1 ns decays into light-flavour quarks, which has not been searched for to date.