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I tried to calculate one of the problems in the textbook Gauge Theory of Elementary Particle Physics by Ta-Pei Cheng and Ling-Fong Li.

On page 248 you can find the following calculation of a loop integral: enter image description here

After the scond $=$ is there a $\gamma\cdot k$ missing? $$...\bar u_e(p-q)(1+\gamma^5)\gamma\cdot k\;u(p)...$$ instead of $$...\bar u_e(p-q)(1+\gamma^5)u(p)...$$ Because the mass dimension do not match. Am I right or did I make a bad mistake? I think they neglect terms with $m_e$ here, which would be OK.

With $c_i=\frac{g^2e}{4}U^*_{ei}U_{\mu i}$ and $\gamma\cdot p\;u_\mu(p)=m_\mu u_\mu(p)$.

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  • $\begingroup$ Mistakes in equations are not uncommon. Do they say anywhere about that term being left off as it is small, etc. ? $\endgroup$
    – Jiminion
    Commented Apr 1, 2015 at 14:22
  • $\begingroup$ @Jiminion No. I did not find any comment to this term. $\endgroup$
    – Matthias
    Commented Apr 1, 2015 at 14:23
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    $\begingroup$ Looks like you are right -- dimensions do not match up... $\endgroup$
    – Kostya
    Commented Apr 1, 2015 at 14:34
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    $\begingroup$ Contact the publisher. Maybe there is a reward! $\endgroup$
    – Jiminion
    Commented Apr 1, 2015 at 14:35

2 Answers 2

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It seems to be an error (due the the units mismatch).

You should doublecheck the errata page and perhaps contact the publishers.

http://www.umsl.edu/~chengt/gaugebooks.html

The errata is for the 1997 edition. It doesn't seem to mention this page.

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    $\begingroup$ Jep. I checked this website and wrote a mail to them. $\endgroup$
    – Matthias
    Commented Apr 1, 2015 at 14:52
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This actually, correctly, refers to pp.422-427 of Cheng and Li. The above calculation is for "Diagram d", which is p.425 of their superb text. They DO make the approximation of zero electron mass, first line, top, p.426, which is perfectly legitimate, considering how vastly shouted down a half MeV is at the scale involved here.

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