Integral Analysis: Equality of Lorentz Structures

[ppg]

Hi, I am a newcomer, and i have a question about an integral shown as follows,

$$\int d^{3}p_{2} \frac{1}{2E_{2}} d^{3}p_{3} \frac{1}{2E_{3}} \delta^{4}(p-p_{2}-p_{3}) p_{3}^{\alpha} p_{3}^{\beta} p_{2}^{\mu}$$

Is this integral equal to (just considering Lorentz structures)

$$A(p^{2})g^{\alpha\beta}p^{\mu}+B(p^{2})g^{\beta\mu}p^{\alpha}+B(p^{2})g^{\mu\alpha}p^{\beta}$$

where the coefficients of the last two terms should be the same because of the symmetry of the integral variables $$p_{3}^{\alpha} p_{3}^{\beta}$$

Thank u for ur help!

 

[CompuChip]

It's been a while since I did such HEP integrals, so I can't give you an answer off the top of my head. But I want to give you a tip, since you have posted the formulas in valid LaTeX code anyway: if you wrap them in tex-tags (put [ tex] at the beginning and [/ tex] at the end, and take out the spaces in both they will be nicely rendered by LaTeX. For inline (i.e. $ ... $) you can replace tex by itex in both tags. That will make your post a lot more readable, probably giving you faster responses as well.

Quote my message to see the codes used:
$$\int d^{3}p_{2} \frac{1}{2E_{2}} d^{3}p_{3} \frac{1}{2E_{3}} \delta^{4}(p-p_{2}-p_{3}) p_{3}^{\alpha} p_{3}^{\beta} p_{2}^{\mu}$$
[...] integral variables $p_{3}^{\alpha} p_{3}^{\beta}$.