= Solution
Assume first an ultrarelativistic <Charged current>[charged-current] interaction with negligible <electron> <mass> in the centre-of-mass <spin> analysis. Choose the incident <antineutrino> along $+z$. Its right <helicity> gives <spin> $+z$; the interacting <Helicity>[left-helicity] <electron> moves along $-z$ and also has <spin> $+z$. The total initial projection is $+1$. The final <antineutrino> and selected <electron> likewise have total <spin> $+1$ along the outgoing <antineutrino> direction. The spin-one <rotation> therefore gives
$$
\mathcal M\propto d^1_{11}(\theta^\star)=\frac{1+\cos\theta^\star}{2},\qquad
\boxed{\frac{d\sigma_{\mathrm{CC}}}{d\cos\theta^\star}\propto(1+\cos\theta^\star)^2.}
$$
An unpolarized <electron> target changes the <normalization> through the <spin> average, not this selected-current shape. For <electron> <antineutrinos> the <Charged current>[charged-current] diagram is the $s$-channel $W^-$ graph. A <Fermi interaction>[contact approximation] further requires $m_e^2\ll s\ll m_W^2,m_Z^2$.
\b[The full Standard Model also has <Neutral current>[neutral-current] $Z$ exchange.] In the contact limit it supplies a right-electron contribution as well as interference in the left-electron channel. With $g_L=1/2+\sin^2\theta_W$, $g_R=\sin^2\theta_W$, the full high-energy shape is proportional to $g_L^2(1+\cos\theta^\star)^2/4+g_R^2$. Thus the pure squared angular form is an explicitly stated <Charged current>[charged-current] approximation, not an exact prediction for all Standard Model contributions. At <momentum> transfers comparable to the <Electroweak gauge boson>[weak-boson] <masses>, propagators must also be retained.<Electroweak Model and Constraints on New Physics by J. Erler and A. Freitas (2024)>[§10.3.1, equation (10.30) and following electron-neutrino charged-current shift: both left- and right-electron weights]{ref}
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