I am in the process of reducing tensor integrals down to a sum of scalar ones with the tensor structure factored out in some basis of decomposition. I am able to write some scalar products in terms of appearing propagators but I encountered one where I have something like $$\int_k \frac{k^2-m^2}{A_1(k) A_2(k) A_3(k) A_4(k)}$$ where ##A_i## are all different propagators depending on k and external momenta.(adsbygoogle = window.adsbygoogle || []).push({});

Now, turns out I can write ##k^2 - m^2 = A_3 - f(p_i) - m^2 - 2k \cdot g(p_i)##. The first three terms pose no problem but the k dependence in the last term does. For only this particular term, I was thinking of using Feynman parameters to write my denominator of four terms in terms of one single propagator as follows $$\frac{1}{A_1 A_2 A_3 A_4} \sim \frac{1}{(k^2 - \Delta)^4}$$ and then argue that under the integral $$\int d^dk \frac{k \cdot g(p_i)}{(k^2 - \Delta)^4} = 0$$ from symmetric integration.

So, myquestion is, without doing the lengthy calculation of feynman parameters is it true that I can write $$\frac{1}{A_1 A_2 A_3 A_4} \sim \frac{1}{(k^2 - \Delta)^4}$$ where the ##\sim## accounts for the three integrations over feynman parameters but otherwise crucially the k dependence is simply as shown?

Thanks!

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# I Generic Feynman parameterisation

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