Calculation of partial width of decays where gluons decaying to a quark-antiquark pair are involved

[VikasRajG]

TL;DR Summary

How to calculate/estimate partial decay width of a decay when gluons decaying to a quark-antiquark pair are involved?

How do we normally calculate the partial width Γi for a decay involving gluons.Consider the following example:

in the first example, I know that one can estimate the partial width Γ1 using CKM matrix elements to get "Γ1 is directly proportional to V2cb V2cs
."Now, for the second diagram it is essentially the same but with an additive gluon going to ss¯¯¯

. Ofcourse, the partial width now changes to look like:
"Γ2 is directly proportional to V2cb V2cd
."BUT,this doesn't tell anything on how the gluon changes things. So what I want to know is, how exactly does the ss¯¯¯

pair changing the Γ2
!!!????If there are any sources/articles for this, it would be really helpful as I haven't found much regarding these 3 body decays!

 

[Vanadium 50]

What are you looking for exactly? Someone to calculate the matrix element for you?

 

[VikasRajG]

Have you even read the whole thing?
I know how to calculate the CKM matrix element, I am asking how to consider the gluon to ssbar contribution in decay width!

 

[Vanadium 50]

Have you even read the whole thing?

In am not your servant. Don't treat me like one.

You put a propagator in for the gluon, and T matrices at each colored vertex.

 

[VikasRajG]

Thank You!
Sorry for that, I was just a bit frustrated.