L
Feynman Rules for Tree Graphs in QED
2 → 2 cross section formula
1
dσ =
|M|
2 dLips(s; p 3 , p 4 ).
2 2
4[(p 1 · p 2 ) 2 − m 1 m ] 1/2
2
1 → 2 decay formula
1
2
dΓ =
|M|
2 dLips(m 1 ; p 2 , p 3 ).
2m 1
Note that for two identical particles in the final state an extra factor of
1
2
must be included in these formulae.
The amplitude iM is the invariant matrix element for the process under
consideration, and is given by the Feynman rules of the relevant theory. For
particles with non-zero spin, unpolarized cross sections are formed by averaging over initial spin components and summing over final.
L.1 External particles
Spin1
2
For each fermion or antifermion line entering the graph, include the spinor
u(p, s)
or
v(p, s)
( L . 1 )
and for spin1
2 particles leaving the graph the spinor
¯
u(p
′ , s
′ )
or
¯
v(p
′ , s
′ ).
(L.2)
Photons
For each photon line entering the graph include a polarization vector
∈ μ (k, λ)
( L . 3 )
and for photons leaving the graph the vector
∗
∈ μ (k
′ , λ
′ ).
(L.4)
417
Feynman Rules for Tree Graphs in QED
2 → 2 cross section formula
1
dσ =
|M|
2 dLips(s; p 3 , p 4 ).
2 2
4[(p 1 · p 2 ) 2 − m 1 m ] 1/2
2
1 → 2 decay formula
1
2
dΓ =
|M|
2 dLips(m 1 ; p 2 , p 3 ).
2m 1
Note that for two identical particles in the final state an extra factor of
1
2
must be included in these formulae.
The amplitude iM is the invariant matrix element for the process under
consideration, and is given by the Feynman rules of the relevant theory. For
particles with non-zero spin, unpolarized cross sections are formed by averaging over initial spin components and summing over final.
L.1 External particles
Spin1
2
For each fermion or antifermion line entering the graph, include the spinor
u(p, s)
or
v(p, s)
( L . 1 )
and for spin1
2 particles leaving the graph the spinor
¯
u(p
′ , s
′ )
or
¯
v(p
′ , s
′ ).
(L.2)
Photons
For each photon line entering the graph include a polarization vector
∈ μ (k, λ)
( L . 3 )
and for photons leaving the graph the vector
∗
∈ μ (k
′ , λ
′ ).
(L.4)
417