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)
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 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.