474 Q. Feynman Rules for Tree Graphs in QCD and the Electroweak Theory
Gluon
(
)
i
k
μ k
ν
δ
ab
=
−g
μν + (1 − ξ)
(Q.6)
k 2
k 2
for a general ξ gauge. Calculations are usually performed in Lorentz or Feynman gauge with ξ = 1 and gluon propagator equal to
μν )δ
ab
(−g
= i
.
(Q.7)
k 2
Here a and b run over the 8 colour indices 1, 2, . . . , 8.
Q.1.3 Vertices
-ig s
λ
2
a γ μ
−g s f abc [g μν (k 1 − k 2 ) λ + g νλ (k 2 − k 3 ) μ + g λμ (k 3 − k 1 ) ν ]
2
−ig s [f abe f cde (g μλ g νρ − g μρ g νλ ) + f ade f bce (g μν g λρ − g μλ g νρ ) +
f ace f dbe (g μρ g νλ − g μν g λρ )]
It is important to remember that the rules given above are only adequate
for tree diagram calculations in QCD (see section 13.3.3).
Q.2 The electroweak theory
For tree graph calculations, it is convenient to use the U gauge Feynman rules
(sections 19.5 and 19.6) in which no unphysical particles appear. These U
gauge rules are given below for the leptons l = (e, μ, τ), ν l = (ν e , ν μ , ν τ ); for