I understand that we have three pairs of Leptons (generations).
$(\nu_e , e^-), (\nu_{\mu}, \mu), (\nu_{\tau}, \tau^-)$
But what is this principle of Lepton universality?
I have obviously tried googling it before asking in here, but all of the sites tend to just quickly run over it and I am not quite sure I understand exactly what it covers. So can someone please help me understand it or maybe give me a good source.
When energy in a given reaction is much larger than the masses of all leptons, these masses can be neglected. For example if you consider $W$ bosons decays, then $$M_W \gg m_\tau.$$ Tau is the heaviest among the charged leptons, so if you can neglect mass of the tau, you also can neglect masses of other leptons. But now you neglected the only quantity that distinguish between leptons. Except mass, all other characteristics (spin, charge, etc) are the same for $\tau$, $\mu$ and $e$. Since there is nothing that differentiate between leptons in the massless limit, all the decay rates and cross-sections have to be equal. For example $$\Gamma(W^+\rightarrow e^+ \nu_e )=\Gamma(W^+\rightarrow \mu^+ \nu_\mu ).$$ And this is what we call the lepton universality.
Lepton universality is the model, or proposition, that the interactions of leptons of any of the (six) flavors are described consistently and essentially completely as electroweak interaction, with
the three charged leptons (electron, muon, tau-lepton) carrying equal electro-magnetic charge (elementary negative charge, $Q[ \, \ell^- \, ] = -e$) and equal weak hypercharge, $\text{Y}_W[ \, \ell^-_{\text{left}} \, ] = -1$, $\text{Y}_W[ \, \ell^-_{\text{right}} \, ] = -2$, and
the three neutral leptons ($\nu_1, \nu_2, \nu_3$) carrying equal $Q[ \, \nu \, ] = 0$, and equal $\text{Y}_W[ \, \nu_{\text{left}} \, ] = -1$, $\text{Y}_W[ \, \nu_{\text{right}} \, ] = 0$,
and (obviously) neither of them being subject to strong interaction at all.
As a consequence, or prediction, there are certain expectations concerning relations (even approximate equalities) between several related quantities whose values typically may be expressed in terms of mass ratios; for instance
for relative branching fractions such as $\frac{\Gamma[ \, \pi^- \rightarrow \, e^- \overline\nu \, ]}{\Gamma[ \, \pi^- \rightarrow \, \mu^- \overline\nu \, ]}$ and $\frac{\Gamma[ \, \tau^- \rightarrow \, \pi^- \nu \, ]}{\Gamma[ \, \pi^- \rightarrow \, \mu^- \overline\nu \, ]}$, or
parameters of "scattering" of leptons; especially of neutrinos on other leptons, or on hadrons ...
In the limit of low momentum transfer i.e., $q^2\ll M_W^2$ and vanishing electron and muon mass, the electronic and muonic decay modes have equal decay rates i.e. $$\Gamma(\tau\to e^-\bar{\nu}_e\nu_\tau)=\Gamma(\tau\to \mu^-\bar{\nu}_\mu\nu_\tau)=\frac{G_Fm_\tau^2}{192\pi^3}.$$ The universality also holds for the coupling of $Z$ to different leptons. For example, within experimental error $$Z\to e^+e^-:\mu^+\mu^-:\tau^+\tau^-=1:1:1.$$
In short, the lepton universality refers to the fact that leptons of all three flavors couple to Z and W bosons in the same way.
Also, see: Exploring Lepton Universality
