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

CHAPTER 1: The Standard Model of Particle Physics 9the strong interactions. The quarks are triplets under the gauge transformations ofthe SU(3) c symmetry group and the eight gauge boson, G a , which are introducedaccordingly are the massless gluons, the intermediate bosons of the strong interactions.The covariant derivative which contains the information of the strong interaction isthen expressed asD µ = ∂ µ + ig Y Y B µ + ig Wτ i2 W i µ + ig Sλ a2 Ga µ,where the g S , being another free parameter of the model, is the strong coupling constantand λ a are the Gelman matrices which are the generators of the color SU(3) cgroup.The Higgs mechanism and the Yukawa interactions are as before and the SU(3) c remainsunbroken after the electroweak symmety breaking.1.2 Top Quark Sector of the Standard Model1.2.1 Indirect Evidence for the Existence of the Top QuarkBefore its discovery in 1995, the top quark was predicted by the Standard Model. Inorder to obtain a renormalisable gauge theory, the anomalies arrising from the so-calledtriangle diagrams of which an example can be found in Figure 1.1, should cancel. Sinceeach triangle is proportional to c f A Q2 f , where Q f is the charge of fermion and c f Ais theaxial coupling of the weak neutral current, the total anomaly can be obtained byN∑=i=1( 12 × (0)2 − 1 2 × (−1)2 + 1 2 × 3 × (+2 3 )2 − 1 2 × 3 × (−1 3 )2 ),where N denotes an equal number of lepton and quark doublets. Therefore in order tohave a vanishing anomaly, it was required that the quark generations come in pairs tocompensate the divergencies from the fermion loops.Figure 1.1: The triangle diagram containing a fermion loop which produces divergencesin the quantum field theory.Another indirect evidence for the existence of the third generation of quarks, hencethe top quark as one of the components, was to provide a natural way to suppress