Tuesday, 1 December 2015

quantum field theory - Is there a mistake in a QFT textbook?


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 $\gamma\cdot p\;u_\mu(p)=m_\mu u_\mu(p)$.



Answer



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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