$L^2$ norm of Riesz Potential of Disk

Question

I am interested in evaluating, or more precisely finding asymptotics in terms of $s$, of the following integral: $$2^{-s}\pi^{-1}\frac{\Gamma(\frac{2-s}{2})}{\Gamma(\frac{s}{2})}\int_{|x|\leq (2\pi)^{-1/2}}\int_{|y|\leq (2\pi)^{-1/2}} \frac{1}{|x-y|^s}dxdy,$$ where $x,y$ are in the plane. Since $$K(x-y) := 2^{-s}\pi^{-1}\frac{\Gamma(\frac{2-s}{2})}{\Gamma(\frac{s}{2})}\frac{1}{|x-y|^s} \tag{1}$$ is the kernel of the Riesz potential operator $(-\Delta)^{-s/2}$, it follows from Plancherel's theorem that (1) equals $$\|(-\Delta)^{-s/4}(1_{B(0,(2\pi)^{-1/2})})|_{L^2(\mathbb{R}^2)}^2 \tag{2},$$ where $1_{B(0,(2\pi)^{-1/2})}$ denotes the indicator function of the ball of radius $(2\pi)^{-1/2}$ centered at the origin. I am at a loss for evaluating/finding asymptotics for either the form (1) or the form (2), so any help would be appreciated.