Why Do Some Books Only Consider Zero Mass Limit for Renormalization Group?

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Please teach me this:
Why some books only consider zero mass limit when they consider the renormalization group.I have been wondered this because the mass parameter multiplying with relevant operator,it become growth when momentum grows.
Thank you very much in advance.
 
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It seem that in high energy physics,we can consider the mass of particle is small.But how about the other physics?
 


''Zero mass limit'' I mean that we could use perturbative theory with mass parameter.
 

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