Q
Feynman Rules for Tree Graphs in QCD and
the Electroweak Theory
Q.1 QCD
Q.1.1 External particles
Quarks
The SU(3) colour degree of freedom is not written explicitly; the spinors have
3 (colour) × 4 (Dirac) components. For each fermion or antifermion line
entering the graph include the spinor
u(p, s)
or
v(p, s)
(Q.1)
and for spin1 particles leaving the graph the spinor
2
′
′
u ¯(p , s
′ )
or
v ¯(p , s
′ ),
(Q.2)
as for QED.
Gluons
Besides the spin-1 polarization vector, external gluons also have a ‘colour
polarization’ vector a
c (c = 1, 2, . . . , 8) specifying the particular colour state
involved. For each gluon line entering the graph include the factor
c
∈ μ (k, λ) a
(Q.3)
and for gluons leaving the graph the factor
∗
c∗
∈ μ (k
′ , λ
′ ) a .
(Q.4)
Q.1.2 Propagators
Quark
i
/ p + m
=
= i
.
(Q.5)
/ p − m
p 2 − m 2
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