- #1
CAF123
Gold Member
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I came across the following statements about renormalisation in the context of Compton scattering ##(\gamma q \rightarrow \gamma q##) and its QCD corrections:
1) 'The bare and renormalised couplings are equal at ##\mathcal O(\alpha_s^0)##, thus the renormalisation of the strong coupling in a bare coefficient function of order ##\alpha_s^j## only contributes at order ##\alpha_s^{j+1}##'
At tree level (##\mathcal O(\alpha_s^0)##) we have no loops so there is nothing to renormalise so I understand the first part of this sentence. But how does the latter part of the sentence come about?
2) 'With tree level considerations alone, there is nothing to predict because we don't really know what the couplings are and could take them at any scale. We have to go to ##\mathcal O(\alpha_s)## to get meaningful predictions out.'
What does 2) mean?
Thanks!
1) 'The bare and renormalised couplings are equal at ##\mathcal O(\alpha_s^0)##, thus the renormalisation of the strong coupling in a bare coefficient function of order ##\alpha_s^j## only contributes at order ##\alpha_s^{j+1}##'
At tree level (##\mathcal O(\alpha_s^0)##) we have no loops so there is nothing to renormalise so I understand the first part of this sentence. But how does the latter part of the sentence come about?
2) 'With tree level considerations alone, there is nothing to predict because we don't really know what the couplings are and could take them at any scale. We have to go to ##\mathcal O(\alpha_s)## to get meaningful predictions out.'
What does 2) mean?
Thanks!