= Massless neutrino-electron contact cross-section
{title2=$\sigma_\nu=G_F^2s(c_V^2+c_Vc_A+c_A^2)/(3\pi)$}
For a left-handed incoming neutrino, unpolarized <electrons>, and <electron> vector/axial couplings $c_V,c_A$, the <four-fermion interaction> gives $\overline{|\mathcal M|^2}=4G_F^2[(c_V+c_A)^2s^2+(c_V-c_A)^2u^2]$. Integrating massless <two-body Lorentz-invariant phase space> yields $\sigma=G_F^2s(c_V^2+c_Vc_A+c_A^2)/(3\pi)$. The <electron spin> average is included, while no <sterile neutrino> helicity is averaged in.
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