I would like to prove that the following integral is logarithmically divergent.(adsbygoogle = window.adsbygoogle || []).push({});

$$\int d^{4}k \frac{k^{4}}{(k^{2}-a)((k-b)^{2}-x)((k-y)^{2}-a)((k-z)^{2}-a)}$$

This is 'obvious' because the power of ##k## in the numerator is ##4##, but the highest power of ##k## in the denominator is ##8##.

However, it is the highest power of ##k## in the denominator that is ##8##. There are other terms in ##k## in the denominator of the form ##k^7##, ##k^6##, etc.

I was wanting a more formal proof that the integral is logarithmically divergent.

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# A Logarithmic divergence of an integral

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