# IR divergences by analytic continuation of parameters

i had a discussion with a physicist i proposed that in order to avoid the IR divergence

$$\int_{0}^{\infty}dx(x-a)^{-3}x^{2}$$

we could propose as regularized value the value of F(-a) , where F is the integral

$$\int_{0}^{\infty}dx(x+b)^{-3}x^{2}$$ so if we could regularize this simply setting b=-a the IR divergence dissapear

is this method valid , to analytic continua with respect to some parameters into the real or complex plane.

## Answers and Replies

A. Neumaier
Science Advisor
i had a discussion with a physicist i proposed that in order to avoid the IR divergence

$$\int_{0}^{\infty}dx(x-a)^{-3}x^{2}$$

we could propose as regularized value the value of F(-a) , where F is the integral

$$\int_{0}^{\infty}dx(x+b)^{-3}x^{2}$$ so if we could regularize this simply setting b=-a the IR divergence dissapear

is this method valid , to analytic continua with respect to some parameters into the real or complex plane.

it is valid whenever you know (or can safely assume) that the quantity you want to compute is analytic along a path from a to -b.