I wanna clarify some issues about renormalization in the ¯MS scheme that I glossed over when I first learnt about this stuff. I am following http://arxiv.org/abs/1411.7853 section 3.1. The gluon part of the QCD Lagrangian is considered and the renormalized coupling and gluon field are written
g=ˉμϵZggRAμ=√ZAARμ
where ˉμ=μ√2πeγE/2. It is immediately stated that the renormalization constant takes the form
Zg=1+αs(μ)4πZ11ϵ+(αs(μ)4π)2(Z22ϵ2+Z21ϵ)+(αs(μ)4π)3(Z33ϵ3+Z32ϵ2+Z31ϵ)+…
I don't see why it should be obvious that Zg should take this form. What justifies this?