What does decoupling mean when studying fields?

I just started studying field theory and general relativity, and when reading paper titles I often see the word decoupling coming up.

My intuition is that there must be a cross term involving some different fields in the lagrangian so they interact proportional to some constant and then to decouple you take the limit where the constant goes to zero. But I’m unsure if this is correct because the papers are unclear about the process of decoupling and Google is not helping.

I’m reading maggiore right now, there might be some info in there.

So what is a formal definition of decoupling and how do we proceed to study it?