Measurement of the Jet Energy Scale in the CMS experiment ... - IIHE

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48 CHAPTER 4: Reconstructing and Selecting Physics EventThe first step which is the core of the generation procedure is to produce thehard scattering process which is a result of the interaction of two high-energy partonsarising from the two colliding protons. The next step is to consider the possibility ofbranching of a parton to other partons or radiation of a gluon resulting in a cascadeof partons referred to as parton showering. After producing a list of partons carryingcolor-charges, due to the quark confinement principle, they hadronize and combinein such a way to make colorless hadrons. The produced hadrons that are not stableparticles, decay subsequently in the last step of the event generation procedure. Thefinal particles interact with the detector material and can be reconstructed as describedin Chapter 3.Some of these generation steps such as the hard scattering can be described fromfirst principles, while for others like the hadronization stage require phenomenologicalmodels to be modeled. The different generation steps are discussed in more detail inthe following sections.4.1.1 Hard Scattering EventIn a proton-proton collision, along with so many soft elastic interactions, hard inelasticscattering occurs which can include any new physics such as Higgs bosons or hints forsuper-symmetric phenomena. In order to describe the physics at high-energy hadroncolliders, the knowledge of Quantum Chromodynamics (QCD) is needed [80]. Accordingto the parton model, a proton is not an elementary particle and comprises quarksand gluons, generally called partons. When two protons collide heads on, actually thecollision happens between their constituents. Partons within the proton are describedby the parton distribution functions (pdfs) which are represented as a function of themomentum fraction carried by the parton inside the proton and also with the Q 2 energyscale at which the proton is probed. At high center of mass energies where the strongcoupling constant α s is small, perturbative calculations are feasible and the collisionbetween the two incoming protons can be described accordingly. A hard scatteringprocesses is schematically depicted in Figure 4.2.Figure 4.2: A typical hard scattering process in proton-proton collision.For the hard scattering interactions, the factorization theorem which predicts thecharacteristics of the event, is used. As a result, the total hadronic cross section can
CHAPTER 4: Reconstructing and Selecting Physics Event 49be obtained asσ p+p→X =∫ 10∫ 1dx 1 dx 2 f1(x p 1 , Q 2 )f2(x p 2 , Q 2 )σ 1+2→X .0Hence the evaluation of the total rate for a hard scattering interaction, reduces to thecalculation of the sub-process cross section σ 1+2→X by identifying the leading-orderpartonic processes that contribute to 1 + 2 → X. For example, for the top quark pairproduction the Feynman diagrams contributing to the final state X = t¯t at leadingorder of perturbation theory are shown in Figure 4.3.Figure 4.3: Leading order Feynman diagrams for the production of top quark pair viaquark-antiquark annihilation and gluon-gluon fusion.The distribution of the various pdfs, extracted from deep-inelastic scattering data,are provided by different collaborations such as CTEQ [81] and can be found in Figure4.4. They are obtained at Q = 100GeV which is about the order of the energyneeded to produce a pair of heavy particles like top quark. It is seen that for highcenter of mass energies corresponding to small distances, gluons are more energeticcomparing to the other quarks. Therefore it can be deduced that at the LHC the productionof t¯t via gluon-gluon fusion is the dominant process compared to the Tevatronwhere quark-antiquark annihilation is the main channel for top pair production.4.1.2 Parton-Parton Interaction and Event GenerationAccording to the factorization theorem described in the previous section, the calculationof the partonic sub-process cross section σ 1+2→X which is then convoluted with theappropriate pdfs is the major task in evaluating the cross section of the hard scatteringevent. The partonic cross section can be further factorized as followsdσ 1+2→X = 1 F × |M|2 × dcosθdφ,where M is the invariant amplitude of the interaction which depends on the phasespace variables such as θ or φ and F is proportional to the center of mass energydsquared. The differential cross section σ dcosθdφ 1+2→X(θ, φ) provides the probabilitydensity functions which are then fed into a generator to generate events accordingly.Monte Carlo techniques are used in order to generate events randomly according to
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SummaryJets appear in the final sta
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