Wing Sheung Chan

6 The Standard Model and lepton flavour violation amplitude is the sum over e iS for every possible path. The principle of least action only applies as a limiting case, in which the classical results can be reproduced. 1.2.2. Elementary particles and their interactions The complete Standard Model Lagrangian (before electroweak symmetry breaking) can be expressed as L SM = − 1 4 G α µν G µν α − 1 4 W µν · W µν − 1 4 B µν B µν + i ¯ ψγ µ ∂ µ ψ − 1 2 ¯ ψ q γ µ g s λ α G α µ ψ q − ¯Ψ L γ µ g T · W µ + 1 2 g 0 Y B µ Ψ L − 1 2 ¯ ψ R γ µ ( g 0 Y B µ ) ψ R + 1 2 i∂ µ − 1 2 g T · W µ − 1 2 g 0 Y B µ φ 2 − V ( φ ) + 1 2 y ¯Ψ L φψ R + h.c. , (1.9) where G are the gluon gauge fields, W are the weak isospin gauge fields, B is the weak hypercharge gauge field, ψ (R /q ) are the (right-handed/quark) fermion fields, Ψ L are the left-handed doublet fermion fields, φ is the Higgs field, g s is the strong coupling, g is the weak isospin coupling, g 0 is the weak hypercharge coupling, y is the Yukawa coupling, T is the weak isospin operator, Y is the weak hypercharge operator, γ are the Dirac matrices, λ are the Gell-Mann matrices, V is the Higgs potential, and h.c. stands for hermitian conjugate of the previous terms. The above equation elegantly encapsulates all elementary particles and their interactions known to date. However, it is admittedly obscure and far from easy to understand at first glance. In this and the upcoming sections, we shall try to break down this cryptic