Decay Topology

A decay chain is a simple tree, from top particle to final particles. So the decay chain can be describing as Node (Decay) and Line (Particle)

Topology identity: The combination of final particles

For example, the combination of decay chain A->RC,R->BD and A->ZB,R->CD is

{A: [B, C, D], R: [B, D], B: [B], C: [C], D: [D]}

and

{A: [B, C, D], Z: [C, D], B: [B], C: [C], D: [D]}

The item R and Z is not same, so there are two different topology.

{{A: [B, C, D], B: [B], C: [C], D: [D]}}

is the direct A->BCD decay.

From particles to enumerate all possible decay chain topology:

From a basic line, inserting lines to create a full graph.

from a line: A -> B,

insert a line (node0 -> C) and a node (node0):

1. A -> node0, node0 -> B, node0 -> C

insert a line :

1. A -> node0, node0 -> B, node0 -> node1, node1 -> C, node1 -> D

2. A -> node1, node1 -> node0, node0 -> B, node0 -> C, node1 -> D

3. A -> node0, node0 -> node1, node1 -> B, node0 -> C, node1 -> D

there are the three possible decay chains of A -> B,C,D

1. A -> R+B, R -> C+D

2. A -> R+D, R -> B+C

3. A -> R+C, R -> B+D

the process is unique for different final particles

Each inserting process delete a line and add three new line, So for decay process has \(n\) final particles, there are \((2n-3)!!\) possible decay topology.