running of coupling constant as a function of distance? There are many papers about the running of coupling strength as a function of momentum/energy scale, 
but are there any experimental papers about coupling strength as function of distance? 
Also, are there any good books about this topic?
oops ,really sorry i forgot to specify "experimental"paper
 A: I'm not sure if this is what you're asking about, but the energy scale has a one-to-one correspondence with the distance scale. For example, a particle of energy $E$ and mass $m$ has a wavelength
$$\lambda = \frac{h}{p} = \frac{hc}{\sqrt{E^2 - m^2c^4}}$$
This wavelength also represents the minimum scale of features that the particle is able to resolve, when it is used as a probe. So if you are analyzing a process that occurs on some characteristic distance scale $d$, you can find the energy associated with that scale by setting $\lambda = d$ and inverting the above equation,
$$E = \sqrt{m^2c^4 + \biggl(\frac{hc}{\lambda}\biggr)^2}$$
This tells you the approximate (minimum) energy of particles you will need to probe the process in question, and you can use that energy to evaluate the running coupling.
At high energies, or short distances (specifically, shorter than the Compton wavelength of the probe, $x \ll \frac{h}{mc}$), you can even neglect the mass and just use
$$E = \frac{hc}{\lambda}$$
