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.