## Lepton universality

Electron, muon and tau are identical except for their invariant masses. They are identical with respect to the electromagnetic force because they carry the same electrical charge (-1). They are also identical with respect to the weak nuclear force because electrons, muons and tau are produced equally often in weak decays. We don’t understand why there are 3 copies of the same particle with different masses but physicists refer to this puzzling similarity of electron, muon and tau as “lepton universality.”

Experimental physicists have been testing the accuracy of lepton universality. Evidence (data collected at the LHCb experiment at CERN) have been growing, however, that the lepton universality might not be exact. Electrons, muons and tau leptons are probably NOT produced at the same rate in weak interactions after all. Physicists need more data to be sure about this effect but if it holds the violation of lepton universality points to new physics.

Read more in the LHCb presentation at Nagoya, in the LHCb publication, and in the Guardian blog.

DETAILS

Quick reminders

Leptons (electron, muon, tau and their corresponding neutrinos and their anti-particle versions) and quarks (u, d, c, s, b, t quarks and their anti-quarks) belong to a category known as fermions. Members of this category are the constituents of matter.

Photons, gluons and W, Z  belong to a category known as gauge bosons. Members of this category are the force carriers. Gauge bosons facilitate interaction. Photons facilitate the electromagnetic force. Gluons facilitate the strong nuclear force. W and Z facilitate the weak nuclear force.

Weak nuclear force is not really a “force”

Weak nuclear “force” facilitates transformations between the first column $\left[ u(L), c(L), t(L) \right]$ and the second column $\left[ d(L), s(L), b(L) \right]$ of quarks, and the first column $\left[ \nu_e (L), \nu_\mu (L), \nu_\tau (L) \right]$ and the second column $\left[ e (L), \mu (L), \tau (L) \right]$ of leptons as shown in the fermion table below.

In the fermion table below the “L” signifies left-handed and “R” right-handed chirality.

$u$ : up-quark
$c$ : charm-quark
$t$ : top-quark
$d$ : down-quark
$s$ : strange-quark
$b$ : bottom-quark
$\nu_e$ : electron type neutrino
$\nu_\mu$ : muon type neutrino
$\nu_\tau$ : tau type neutrino
$e$ : electron
$\mu$ : muon
$\tau$ : tau

Important reminder

Note that there are no right-handed neutrinos and weak nuclear force acts on left-chiral fermions only.

W and Z are very different from other gauge bosons

W is the only gauge boson that carries electric charge. Z is electrically neutral like the other gauge bosons (photons and gluons) but W and Z significantly differ from photons and gluons in another way. W and Z are massive whereas photons and gluons are massless.

In terms of mass, W and Z are between the Tau and the t-quark. W and Z are much heavier than the most massive lepton Tau but less massive than the most massive fermion t-quark.

Invariant mass of Tau = $1.77686 \pm 0.00012$ $GeV/c^{2}$
Invariant mass of Z = $91.1876 \pm 0.0021$ $GeV/c^{2}$
Invariant mass of W = $80.385 \pm 0.015$ $GeV/c^{2}$

Lepton universality

W and Z formations decay immediately. Negatively charged W can decay as follows (ignoring decay modes involving quarks and gluons and just focusing on the leptons) (and ignoring the decays of the $W^{+}$)

$W^{-}$ –> electron + electron type anti-neutrino

$W^{-}$ –> muon+ muon type anti-neutrino

$W^{-}$ –> tau + tau type anti-neutrino

Muon is 206.85 times heavier than electron and tau is 16.8 times heavier than muon. After adjustment for the masses the rates (probabilities) of the decays mentioned above are the same. This is known as “lepton universality.” Electrons, muons and tau are produced equally often in weak decays.