= Higgs decay to longitudinal W bosons
{c}
{title2=$\Gamma_{LL}=\frac{G_Fm_H^3}{8\pi\sqrt2}\sqrt{1-4x}(1-2x)^2$}
For $x=m_W^2/m_H^2<1/4$, the on-shell longitudinal pair contributes the displayed tree-level partial <decay width>. In the <Higgs boson> rest frame, its <polarization vectors> have contraction $(m_H^2/2-m_W^2)/m_W^2$. Multiplying by the <Higgs boson coupling to W bosons> gives $|\mathcal M_{LL}|^2=m_H^4(1-2x)^2/v^2$; the <two-body Lorentz-invariant phase space> then gives the width. The sum over transverse polarizations adds $8x^2$ to the longitudinal polynomial. Below threshold, physical decays through virtual <W bosons> require a different multiparticle calculation.
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