Solution (source code)

= Solution

Both the left-handed <electron> and the electron <neutrino> participate in <weak charged currents> through $W^\pm$, and both have <weak neutral currents> mediated by the <Z boson>. Their <electromagnetic interactions> differ: the <electron> has electric charge $-e$ and couples to the <photon>, while the <neutrino> is electrically neutral and has no tree-level electromagnetic coupling.

In the minimal massless-neutrino <Standard Model>, the active neutrino has only a left-handed particle state and a right-handed antiparticle state. The <electron> has both chiralities: its right-handed component has <electromagnetic interactions> and a <weak neutral current>, but no <weak charged current>. Its nonzero mass comes from a <Yukawa coupling> to the <Higgs field>; the minimal massless-neutrino model contains no right-handed neutrino for an analogous Dirac mass term.

\b[Observed <neutrino oscillations> establish nonzero neutrino mass-squared differences.] Atmospheric muon-neutrino disappearance depends on travel distance and energy, and solar electron neutrinos convert into other active flavors; reactor and accelerator oscillations provide complementary evidence. In propagation, the relative phase of two mass eigenstates is $\Delta m_{ij}^2L/(2E)$. If all masses were zero there would be no such relative phase. Thus at least two neutrino mass eigenstates are nonzero in the three-neutrino description with two independent measured splittings. A flavor state is a superposition of mass eigenstates, so the evidence does not assign a single definite mass to a flavor label.