- 334

- 1

## Main Question or Discussion Point

Hey folks,

I'm reading the paper: http://arxiv.org/abs/hep-ph/0301168

and I'm trying to make sense of the first line of eqtn 44 where he states that we can write:

[tex]\frac{1}{2}\sum \int\frac{d^{2n}k}{(2\pi)^{2n}}log(k^2+\frac{m^2}{L^2})[/tex]

as

[tex]-\frac{1}{2}\sum\int\frac{d^{2n}k}{(2\pi)^{2n}}\int_0^\infty ds\frac{1}{s}e^{-(k^2+\frac{m^2}{L^2})s}[/tex]

It seems to me that the last integral in 's' is somehow a way of expressing the log term, but I can't really see how. I tried the integral and it diverges. Any ideas here folks???

Thanks!!

Richard

I'm reading the paper: http://arxiv.org/abs/hep-ph/0301168

and I'm trying to make sense of the first line of eqtn 44 where he states that we can write:

[tex]\frac{1}{2}\sum \int\frac{d^{2n}k}{(2\pi)^{2n}}log(k^2+\frac{m^2}{L^2})[/tex]

as

[tex]-\frac{1}{2}\sum\int\frac{d^{2n}k}{(2\pi)^{2n}}\int_0^\infty ds\frac{1}{s}e^{-(k^2+\frac{m^2}{L^2})s}[/tex]

It seems to me that the last integral in 's' is somehow a way of expressing the log term, but I can't really see how. I tried the integral and it diverges. Any ideas here folks???

Thanks!!

Richard