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

CHAPTER 1: The Standard Model of Particle Physics 7charge of fermions is recovered. As an example, only the first generation of the leptonsis considered. The Lagrange equation can be expanded as(¯ψνe,L ¯ψ)e,L γµ[τ 3 ] ( )− g Y Y B µ − g W2 W µ3 ψ νe,L+ψ ¯ψ[e,R γ µ − g Y Y B µ]ψ e,R ,e,Lwhere only the part responsible to re-produce the electromagnetic interaction is kept.The two gauge bosons B µ and Wµ 3 are combined to make the new physics gauge bosonsA µ and Z µ , according to( ) ( ) ( )Aµ cosθW sin θ=W BµZ µ − sin θ W cos θ W Wµ3 ,where θ W is the Weinberg mixing angle. Therefore the Lagrangian expression is simplifiedand given by(¯ψνe,L ¯ψ)e,L γ µ A µ[−g Y cosθ W Y − 1 ( ) 1 0 ] (2 g ψνe,LW sin θ W0 −1With the assumption of e = g Y cosθ W = g W sin θ W and assigning( )ψνe,LY = − 1 ( ) ( ) 1 0 ψνe,L,ψ e,L 2 0 1 ψ e,LandY ψ e,R = −1ψ e,R ,the Lagrangian expression would be simplified to+eA µ[¯ψe,L γ µ ψ e,L + ¯ψ e,R γ µ ψ e,R]= +eA µ ¯ψe γ µ ψ e .ψ e,L)+ ¯ψ e,R γ µ A µ[−g Y cosθ W YTherefore, the electromagnetic interaction term with the right electric charge is recoveredgiven that a correct value for the hypercharge quantum number is chosen.The problem which arises is that the observed weak bosons are massive while an explicitmass term cannot be introduced into the Lagrangian as it spoils the gauge symmetry.The Higgs mechanism [9–11], which is described in detail in the following, is responsiblefor giving mass to the particles in the Standard Model.Electro-weak Symmetry BreakingSince the observed weak bosons are massive, the electroweak symmetry must be broken.The formalism of symmetry breaking is introduced with the use of the Higgsmechanism. A new doublet containing scalar fields is introduced as( ) h1φ =h 2whose hypercharge quantum number is chosen to be + 1 . The corresponding Lagrangian2term which describes the dynamic of the scalar field φ is written asL Higgs = D µ φ † D µ φ − V (φ),]ψ e,R .