# Evaluate one loops integral

1. Feb 3, 2013

### eoghan

Hi!
In evaluating the scalar triangle with two massive external legs using the Feynam parametrization, I have

$$\int\frac{d^dl}{(2\pi)^2}\frac{1}{[l^2+i\eta][(l+p)^2+i\eta][(l+p+q_2)^2+i\eta]}=C\int_0^1 d\alpha_1 d\alpha_2 d\alpha_3\delta(1-\sum\alpha_i)\frac{1}{D^{\frac{d}{2}-3}}$$
where $C$ is a constant factor and
$$D=-[\alpha_1\alpha_3q_1^2+\alpha_2\alpha_3q_2^2-i\eta]$$
Now the paper says:
Factorizing out $−q2$ with the right $i\eta$ prescription and defining $r=\frac{q_1^2}{q_2^2}+i\eta$
we have
$$D=(-1-i\eta)q_2^2\alpha_3(\alpha_1r+\alpha_2)$$
I don't understand this factorization: how can $i\eta$ be factorized out?