- #1
robousy
- 334
- 1
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