PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Chapter 1
Introduction
1.1 Standard Model of Particle Physics
The standard model of particle physics, established by Glashow-Weinberg-Salam [1,2]
in the 1960’s has been extremely successful in decscribing the microscopic nature of the
elementary particles. The model is based on the gauge group SU(3) C × SU(2) L × U(1) Y
andsuccessfully unifies theelectromagnetic andweak interaction of nature. The fermionic
particle contents of the standard model and their transformation properties under the
standard ( model ) gauge group are the following,
uL
Q L = ≡ (3,2, 1
d ), u 3 R ≡ (3,1, 4), d 3 R ≡ (3,1,− 2),
3 L
and ( )
νL
L = ≡ (1,2,−1), e
e R ≡ (1,1,−2).
L
In the standard model there are 12 gauge bosons and three family of fermions. The gauge
fields of the standard model are the gauge bosons Wµ, i B µ and the gluons G a µ, where µ,ν
are the Lorentz indices, i = 1,2,3 is the SU(2) gauge index and a = 1,..8 is the SU(3)
color index. The gauge field Lagrangian of the standard model is,
L = − 1 4
∑
i=1,2,3
W i µν Wiµν − 1 4 B µνB µν − 1 4
∑
a=1,...8
G a µν Gaµν , (1.1)
where the SU(2) L
, SU(3) C
and U(1) Y
field strengths W i µν , Ga µν and B µν are respectively
the following,
W i µν = ∂ µ W i ν −∂ νW i µ +gǫijk W j µ Wk ν ,
G a µν = ∂ µ G a ν −∂ νG a µ +g sf abc G b µ Gc ν ,
B µν = ∂ µ B ν −∂ ν B µ . (1.2)
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