The LHC experiments make use of a Tier-organized distributed system for the storage and analysis of recorded and simulated data, called the Worldwide LHC Computing Grid (WLCG) [50]. The WLCG consists of over 170 centres distributed across 41 countries. The Tier-0 is located at the main CERN site at Meyrin in Switzerland. The data recorded by the experiments are directly transferred to Tier-0 enabling a fast transfer of data through the enormous storage resources provided by the Tier-0. The main processing of the data is carried out in the distributed Tier-1 centres. These centres are spread out all over the world and connected via high-speed networks. The Tier-1 centres additionally provide a backup for the data stored at the Tier-0 centres. The over 160 Tier-2 centres provide a platform for data analysis performed by scientists all over the world.
Chapter 3
Analysis objects
In high energy physics, when particles collide together it is necessary to reconstruct the image of the collision for real data as well as for simulated data. In the second case, simulations involve all the physics phenomena that take place, from the proton-proton collision to the interaction of the produced particles with the materials. The Monte Carlo (MC) simulation mechanism is presented in Section 3.1. Final states of hadronic topologies, like the one studied in this work, typically involve jets, showers of hadrons produced by the strong interaction. In Section 3.2, a description of jets is provided. The identification of jets originating from bottom quarks is referred to as b-tagging and
presented in Section 3.3. Jets can be also boosted when the pT of the particle originating
the jet is quite large. This implies that particles are clustered inside a cone with a proper radius parameter according to a specific algorithm which is presented in Section 3.4. Finally, it is not easy to identify jets and recognizing which particle originates them. Multivariate analysis techniques have been employed to perform this job, as well as to discriminate signal events from background ones. In Section 3.5, some of the most important multivariate analysis techniques which will be adopted in the following chapter are reported. Finally, the standard HEP tagger used by CMS is described in Section 3.6.
3.1 Monte Carlo Simulation
The structure of a proton-proton collision at the LHC needs to be reproduced by the MC event generators using the existing knowledge of SM and guesses on BSM. The understanding of the final state particles in proton-proton collisions is a very challenging problem. The simulation of a proton-proton collision by MC event generators consist of the following steps:
1. Hard process. It is defined by the collision of two beam constituents at a high momentum scale and consists of the most energetic final states. It is denoted as the central red blob in Fig. 3.1. This process involves large invariant momentum transfers and it is the first step of any simulation through MC event generators. The implementation is not straightforward since it involves non-perturbative cal- culations. According to the asymptotic freedom of QCD, hadrons interact weakly
at high energies corresponding to a smaller coupling constant, ↵S, so that the con-
stituents of the hadron can be regarded as free particles. Whereas, at low energies
the interaction becomes stronger as the ↵S becomes larger and partons confine into
hadrons. The high-energetic interactions, also called short-distance interactions, can be calculated perturbatively while in case of low-energy, long-distance, inter-
42 CHAPTER 3. ANALYSIS OBJECTS
Figure 3.1: Representation of a pp collision at LHC.
actions this is not possible due to the large value of ↵S. Therefore the so-called
factorisation theorem brings a solution to this problem by resolving the short dis- tance parton cross section from the long distance interactions. Accounting for the factorisation theorem for partons a and b, from hadrons 1 and 2, scattering to c and
dpartons, the following equation can be written
d h1h2!cd = Z 1 0 dx1 Z 1 0 dx2 X a,b fa/h1(x1, µ 2 F)fb/h2(x2, µ 2 F)dˆab!cd(µ2R, µ2F) (3.1)
where fa/hi(xi, µ
2
F)is the parton distribution function (PDF) which gives the prob-
ability of finding a parton of flavour a with momentum fraction xiof the hadron hi
at the energy scale µF. The parameter µF is the factorisation scale, which charac-
terises the hard scattering and can be thought as the scale that separates the long-
and short-distance interactions, while µR is the renormalisation scale, which is a
scale used to fix the divergences of loop diagrams. The PDFs can not be obtained via perturbative QCD calculations, so they are computed by fitting the data from several experiments and many different processes. This is possible due to the fact that the PDFs are process-independent meaning that they are universal. They can be measured in one process and can be applied to other processes. Their evolu- tion to any scale can be calculated by DGLAP evolution functions once they are measured in one scale. The hard interaction differential cross section for a and b
scattering to c and d is denoted by dˆab!cd(µ2
R, µ2F). This term contains only hard
emissions above the factorisation scale µF and can be calculated by perturbative
QCD.
2. Parton shower. The simulation of the proton-proton collision is followed by the parton shower. The partons carrying a colour charge can emit gluons (QCD radia- tion) and can also interact with each other emitting further gluons. This process is called parton shower, denoted by the red spiral tree structure surrounding the hard interaction. It evolves until the partons lose energy due to gluon emission and they go into the hadronisation phase.
3.2. JETS 43