Confusion about the Z factor(Renormalization factor)

  • #1
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In Peskin's textbook chapter 7 Radiative Corrections: Some formal developments (page 229), he said the Z factors are irrelevant for calculations at the leading order of perturbation theory, but are important in the calculation or higher-order corrections.

My question is how can the Z factor be irrelevant for calculations at the leading order of perturbation theory. Thanks.
 

Answers and Replies

  • #2
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In Peskin's textbook chapter 7 Radiative Corrections: Some formal developments (page 229), he said the Z factors are irrelevant for calculations at the leading order of perturbation theory, but are important in the calculation or higher-order corrections.

My question is how can the Z factor be irrelevant for calculations at the leading order of perturbation theory. Thanks.
Z is the field-strength renormalization factor
 
  • #3
DarMM
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At the lowest order in perturbation theory it is just ##1##.
 
  • #4
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At the lowest order in perturbation theory it is just ##1##.
@DarMM thank you. Now I got it, for electron, $Z_2^(-1)=1-\frac{d\Sigma}{d\slashed{p}}|_{\slashed{p}=m}$, at the leading-order contribution, electron self-energy is 0, so Z=1.
 
  • #5
DarMM
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Yes exactly. Note that the singularities in ##Z## and hence the need to renormalise it arise from the fact that ##Z## is not analytic in the coupling constant, so Taylor expanding it causes divergences.
 

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