(p.664) Appendix E Feynman Rules Of The Standard Electroweak Model
(p.664) Appendix E Feynman Rules Of The Standard Electroweak Model
The Feynman rules allow one to calculate the transition amplitude A of a given process. In the following, we summarize the Feynman rules of the Standard Electroweak Model in the unitary gauge, for the calculation of tree diagrams. This is sufficient for the topics discussed in the book. The calculation of higher order diagrams with loops is much more complicated (see, for example, Refs. [25, 634, 314, 917, 720, 721]). In section E.4 we give general formulas suitable for the calculation of the crosssection or decay rate of a process from its amplitude.
The Feynman rules for the calculation of the treelevel amplitude A of a given process are as follows:

1. Draw all connected tree diagrams which contribute to the process under consideration by using the external lines in section E.1, the internal lines in section E.2 and the vertices in section E.2.

2. For each external line, write down the corresponding quantity in section E.1.

3. For each internal line, write down the corresponding propagator in section E.2.

4. For each vertex, write down the corresponding quantity in section E.3.

5. Enforce energy–momentum conservation in each vertex.

6. Assign a relative factor –1 to diagrams which differ only by an interchange of two external lines (the overall sign is irrelevant).
E.1 External lines
p is the particle momentum, r is the spin index for fermions and α is the spin index for spinone bosons.
E.3 Vertices
The coefficient q _{f} is the charge of the fermion f in units of the elementary charge e: q _{ν} = 0, q _{e} = q _{µ} = q _{τ} = –1, q _{u} = q _{c} = q _{t} = 2/3, q _{d} = q _{s} = q _{b} = –1/3. The coefficients${g}_{V}^{f}$and${g}_{A}^{f}$are given in Table 3.6 (page 78). From eqn (3.42) we have gsinϑ_{w} = e.
E.4 Crosssections and decay rates
The differential crosssection of a process with two particles a, b in the initial state and N _{f} particles in the final state is given by
The crosssection of a process of the type
The decay width of a particle with mass m in a final state with N _{f} particles is given by