= Tau-neutrino charged-current threshold
{title2=$E_{\rm thr}=((m_\tau+M_X)^2-M_T^2)/(2M_T)$}
For a nearly massless incident <tau neutrino> and stationary target of <mass> $M_T$, the initial <Mandelstam variables> give $s=M_T^2+2M_TE_\nu$. At threshold the final <tau lepton> and the lightest allowed recoil system have no relative <momentum>, so $s=(m_\tau+M_X)^2$. This proves the formula. A free <neutron> recoil channel gives approximately $3.45\,\mathrm{GeV}$; an <electron> target has a different recoil and a threshold near $3.09\,\mathrm{TeV}$.
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