Centrality and collision parameter b Can someone tell me what does it 20-30% collision centrality mean in terms of impact parameter b?
 A: The most general relationship is
$$c(b) = \frac{\int_0^b \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b}{\int_0^\infty \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b} = \frac{1}{\sigma_\text{inel}}\int_0^b \frac{\mathrm{d}\sigma}{\mathrm{d}b}\mathrm{d}b\tag{1}$$
(source, one of many). 
In practice, we usually use the Glauber model to describe heavy ion collisions, and this model predicts an impact parameter dependence of the differential cross section which can be (very roughly) approximated as
$$\frac{\mathrm{d}\sigma}{\mathrm{d}b} \approx \begin{cases}2\pi b, & b \le b_\text{max} \\ 0, & b > b_\text{max}\end{cases}$$
where $\pi b_\text{max}^2 = \sigma_\text{inel}$. That reduces equation (1) to
$$c(b) = \frac{\pi b^2}{\sigma_\text{inel}}$$
for $b < b_\text{max}$.
You do have to be careful because sometimes (rarely) a different definition is used, $c(b) = 1 - \pi b^2/\sigma_\text{inel}$. Just pay attention to whether large centrality values correspond to peripheral (the former definition) or central (the latter) collisions.
In practice, this is all somewhat approximate anyway, because you can't definitively identify the centrality of a collision from the information collected by a detector. All you can do is estimate the centrality based on how many particles come out and how strongly they are scattered. If you get a lot of particles coming out roughly perpendicular to the beamline (pseudorapidity $\eta\sim 0$), then that means a lot of nucleons were involved in the collision, and thus it is characterized as central. If there are few particles coming out perpendicular to the beamline, then few nucleons were scattered, meaning the collision was peripheral.
