 Solution

Use natural units and invariant squared center-of-mass energy $s$. For a massless incident neutrino and an initially stationary electron,At the production threshold the final massless neutrino can have arbitrarily small center-of-mass energy, so the lower endpoint is $s=m_{\ell }^2$. The charged-current neutrino-electron threshold is consequentlyFor the three flavours, using precisely the masses given in this part, the answers are $0$ for ${\nu }_e$, $1.0994\times 10^4\mathrm{MeV}\simeq 11.0\mathrm{GeV}$ for ${\nu }_{\mu }$, and $3.0898\times 10^6\mathrm{MeV}\simeq 3.09\mathrm{TeV}$ for ${\nu }_{\tau }$. The zero threshold for the electron flavour is an infimum for elastic scattering; it does not imply a nonzero interaction rate at zero incident energy. The large heavy-lepton thresholds arise because most laboratory energy becomes center-of-mass motion against a very light target.