Wing Sheung Chan

30 The Large Hadron Collider and the ATLAS detector triplets, each of which is a system of three quadrupole magnets, are placed on each sides of the four collision points. Their purpose is to tighten the beams as much as possible before crossing the beams in order to maximise the chance of collision. There are currently eight different experiments at the LHC: ALICE, ATLAS, CMS, LHCb, LHCf, MOEDAL, TOTEM, and the recently approved FASER. ALICE, ATLAS, CMS and LHCb are the four main experiments. Each of these experiments have their detector constructed in one of the underground caverns at the four collision points. ATLAS and CMS are the two general-purpose detectors at the LHC. They are the experiments that discovered the Higgs boson in 2012 using pp collision data from the first operational run (Run 1) of the LHC. ALICE and LHCb are more specialised detectors. ALICE is designed for studying strong interactions in quark-gluon plasma, while LHCb is specialised in measuring CP violation of b -hadrons. The remaining four experiments are considerably smaller experiments, both in terms of the physical size of their detectors and the size of the collaborations. The data analysed in this thesis were collected by the ATLAS detector, which will be described in more details later in Section 2.2. 2.1.3. Luminosity and pile-up For any given process, the expected number of events occurred at the LHC N is the product of the integrated luminosity L and the interaction cross section σ for that process: N = Lσ. (2.2) The integrated luminosity can be understood as the expected number of “encounters” between particles in the colliding beams, while the interaction cross section is a measure of the probability that a certain process will occur during an encounter. The integrated luminosity is the time-integrated value of the instantaneous luminosity L : L = Z L d t. (2.3) The instantaneous luminosity can be interpreted as the rate of particle encounters, and can be approximated by L = f r n b N 2 p γ 4 πε n β ∗ F ( θ c , σ x , σ z ) , (2.4) where f r is the LHC revolution frequency, n b is the number of bunches in each beam, N p is the number of particles per bunch, γ is the relativistic Lorentz factor, ε n is the normalised transverse emittance, β ∗ is the amplitude function at the interaction point, and F is the geometric reduction factor, which is a function of the crossing angle θ c and the beam cross-sectional sizes σ x and σ z . During Run 2, the LHC has delivered pp collisions to ATLAS for a total integrated luminosity of 156 fb − 1 , of which 147 fb − 1 were recorded by ATLAS, and of which 139 fb − 1 were good for physics analyses. The integrated luminosities over time throughout Run 2 are shown in Figure 2.2a.