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

4 CHAPTER 1: The Standard Model of Particle Physics1.1 Elementary Particles and Their Interactions1.1.1 Electroweak TheoryThe fundamental particles, namely quarks and leptons, which are fermions with halfintegerspin are represented by Dirac spinors ψ, that fulfill the Dirac equation 1iγ µ ∂ µ ψ = 0.In the presence of an external electromagnetic field A µ , the fermions couple to thequantum of the field, which is called the photon γ, and their interaction are describedby a Lagrangian term expressed asL inte.m = ∑ f¯ψ f iγ µ D µ ψ f ,where the sum is over all fermions and D µ is the covariant derivative defined as D µ =∂ µ + ieQA µ . In the language of group theory, the dirac spinors are representations ofthe U e.m (1) group since the Lagrangian is invariant under the gauge transformationψ → e ieQ ψ.According to Noethers’s theorem, there is a conservation law that can be associatedto this gauge symmetry. Therefore the electric charge Q, which is expressed in unitsof quantum number e, is constant during the electromagnetic interactions. The Diracspinors associated to the elementary particles and their corresponding charge are listedin Table 1.1.As expressed in Table 1.1, the leptons as well as the quarks appear in three generationswhose constituents are equal in all quantum numbers but differentiated in termsof mass. The most stable particles are the ones listed in the first generation for each ofthe two category of fermions. The elementary particles interact with the electromagneticfield via their charge, hence no interaction vertex is present between the photonand the neutrino in the Standard Model since the neutrinos are neutral fermions.In addition to the electromagnetic interactions which are formulated in a simple Lagrangianterm and can fully describe the interaction of the charged particles, there isanother kind of interaction describing the phenomena like beta decay p → n + e + ν e ,which corresponds to the physics processes containing a neutrino as one of the componentsof the interaction. This kind of interaction, known as the weak interaction,contains a heavy particle as propagator. Because of the rather massive property ofthe propagator of the weak interaction, they are difficult to be produced during aninteraction. Therefore, the weak interactions are rare within the Standard Model.In order to describe the physics of the weak interactions, an appropriate term shouldbe added to the Lagrangian. According to the experimental data, where only lefthandedfermions contribute to the weak interaction, the weak current ¯ψ νe γ µ (1 − γ 5 )ψ e1 The mass term is dropped from the Dirac equation for simplicity.