Understanding Feynman Rules for ABC Theory

[ercagpince]

[SOLVED] feynman rules

Hi , It is a simple question from the book of david j .griffiths :"introduction to elementary particles" (6.11)

Homework Statement

(a) Is A--->B+B a possible process in the ABC theory (feynman rules for a toy theory)
(b)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 .

Homework Equations

The Attempt at a Solution

(a)I presume that if A is heavier than both B particles it should be a legitimate process .
I am not sure whether there is any extra information needed for this question.
(b)It is related to (a) , so I am certainly missing something .

 

[Avodyne]

You need to tell us what the theory is. There may be conservation laws. For example, in phi^4 theory, particle number is conserved modulo two, so if you start with an even (odd) number of particles, you always end with an even (odd) number.

 

[ercagpince]

There are a bunch of feynman rules for this ABC theory but none of them is relevant with the possibility of a certain decay or scattering process . At least it is not indicated in the book .

 

[Avodyne]

The relevant parts are the types of lines that are connected by each vertex.

 

[ercagpince]

I don't get it , there is no specific particle for the process (a) .
What then does determine the possibility of it ?

 

[Mr.Brown]

you just have to take into account all the conservation laws don´t you ?
But that´s no simple criterion at all ?

 

[Avodyne]

I don't get it , there is no specific particle for the process (a). What then does determine the possibility of it ?

Suppose, for example, the only interaction in the lagrangian was A^2 B^2. Then the process A->BB could not occur. If there was an interaction of the form A B^2, then it would occur.

The interaction terms in the lagrangian determine the types of vertices you can have in Feynman diagrams, so it would be equivalent to know what all the allowed vertices are. Which is why I asked for that info.

 

[ercagpince]

I see ,
Thank you .