In this paper https://arxiv.org/pdf/1002.5020.pdf, they state the following in equation 66.
My guess is that this perhaps follows from some Bessel function related identity, but I was not able to get the desired answer that way. I also tried to just integrate it out with Mathematica, starting from the integration over kz, which is still straightforward, but then when I went to the integral over kx I get a whole jungle of functions like the Bessel function and the Struve function so that I had no clue how to reproduce ths very simple result from the paper. Note that it has a $\sim$ in front so perhaps there is a prefactor or a subleading term involved as well.