= W-decay Jacobian peak
{c}
{title2=$p_T^{\max}=M_W/2$}
For an on-shell W with zero transverse recoil and <massless particle>[massless] <leptons>, $p_T=(M_W/2)\sin\theta$. Mapping both angular roots to one transverse <momentum> produces an integrable inverse-square-root edge. For a normalized polar distribution $3(1-\cos\theta)^2/8$, the density in $x=2p_T/M_W$ is $3x(2-x^2)/(4\sqrt{1-x^2})$. Finite width, transverse recoil and <particle detector>[detector resolution] smear the edge.
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