We have the integral 
$$
E =
−\,{1 \over \left(\,2\pi\,\right)^{3}}\int\_{\mathbb{R}^{3}}\,
\mathrm{d}^{3}k\,
{\mathrm{e}^{\mathrm{i}\vec{k}\cdot\left(\,\vec{x}\_{1} - \vec{x}\_{2}\,\right) } \over \vec{k}^{\,2} + m^{2}}
$$

Could someone explain the following passage found in A. Zee, QFT in a Nutshell, 2nd edition page 28:

> 
> We identify $E$ as the potential energy between two static sources. Even without doing
>  the integral, we see by dimensional analysis that the characteristic distance beyond which
>  the integral goes to zero is given by the inverse of the characteristic value of $k$, which is
>  $m$. Thus, we expect the attraction between the two sources to decrease rapidly to zero over
>  the distance $1/m$.
>  The range of the attractive force generated by the field $ϕ$ is determined inversely by the
>  mass $m$ of the particle described by the field. 
> 
> 
> 

I have not heard the phrases characteristic distance/value before and how do we deduce its values through dimensional analysis?