How Does the ss¯ Pair Affect the Partial Width Γ2 in Gluon Decays?

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VikasRajG
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TL;DR
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:

feynmanbjks.png
feynmareal.png

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