Error in Srednicki renormalization?

  • #1
21
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On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$

But after taking a log and dividing by 2 he arrives at
$$ln[m_{ph}] = ln[m] \left [ \left ( \frac{5}{12}\alpha(ln \frac{\mu}{m}) +\frac{1}{2} c' \right ) + O(\alpha^2)\right]$$

Why is there no ln on the $$\frac{5}{12} \alpha$$ term?
 

Answers and Replies

  • #2
1,006
105
He is using the relation
[tex]\ln(1 + x) = x + O(x^2)[/tex]
Here ##x## has an ##\alpha## in it, so the ##O(x^2)## term is absorbed into the ##O(\alpha^2)##.
 
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  • #3
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Thanks!
 

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