# What is $\sigma_{i\eta i\eta}$?

In LHC experiments like, CMS there are variables like ieta which are used for designating the eta (pseudo rapidity) of each of the sub detector components.

There are several plots which I came across which are distributed over $\sigma_{i\eta i\eta}$. For example the following,

I came across the definition of $\sigma_{i\eta i\eta}$ which is as follows.

$$\sigma_{i\eta i\eta}=\left(\frac{\sum(\eta_i-\bar{\eta})^2\omega_i}{\sum\omega_i}\right)^{\frac 1 2}$$

$$\bar{\eta}=\frac{\sum\eta_i\omega_i}{\sum\omega_i}$$

$$\omega_i=max\left(0\,,\,4.7+log\frac{E_i}{E_{5\times 5}}\right)$$