# Ultraviolet via dimensional regularization

1. Jul 16, 2011

### kassem84

The integral:
$\int$d$^{3}k$$\frac{1}{k^{2}+m^{2}}$
is linearly divergent i.e. ultraviolet divergent.
However, If one performs dimensional regularization to the above integral:
$\frac{1}{(2\pi)^d}$$\int$d$^{d}k$$\frac{1}{k^{2}+m^{2}}$=$\frac{(m^{2})^{d/2-1}}{(4\pi)^{d/2}}$$\Gamma(1-d/2)$
As you can notice that the poles of the Gamma function are for even dimension i.e. d=2,4,6..etc and that the integral is convergent for d=3 for example!!!
What is the reason behind this convergence? Is it due to the Veltman's formula:
$\frac{1}{(2\pi)^d}$$\int$d$^{d}k$$(k^{2})^{n-1}$ = 0, for n=0,1,2,..
I am dealing with a divergent integral of power divergence (ultraviolet, quadratic, quartic,... and no logarithmic divergence). Do you advise me to use dimensional regularization or other methods?