# ABC toy theory Feynman rules

1. Nov 23, 2008

### Someone1987

1. The problem statement, all variables and given/known data
In an ABC toy theory, the only allowed vertex is one that couples A, B and C. Thus there are no AAA, ABB, ACC...ect vertices allowed. My question is suppose a diagram has na external A lines, nb external B lines, and nc external C lines. Develop a simple criterion for determining whether it is an allowed reaction.

2. Relevant equations

3. The attempt at a solution
I'm just a little unsure of what the question wants. Does it want a mathematical formula or just a statement in plain english. I don't see a way of developing a mathematical formula that can encompass all the possible diagrams (decays and scattering) one can draw. The best criterion I can think of is that each identical external line must be attached to separate vertices. Another way of saying this is that no vertex can have two A's, two B,'s or two C's attached to it. Although this is correct, it doesn't seem like its the best criterion one can develop. I'd appreciate any additional insights anyone can provide. Thanks.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 23, 2008

### Avodyne

Either a formula or a statement in plain English is probably acceptable.

Here's a way to think about it: let i_a, i_b, and i_c be the number of internal lines of each type. Can you find a relation between n_a, i_a, and the number of vertices v?