= Massless semileptonic pseudoscalar decay rate
{title2=$d\Gamma/ds=G_F^2|V|^2\lambda^{3/2}|f_+(s)|^2/(192\pi^3M^3)$}
For a <pseudoscalar meson> of mass $M$ decaying into a <pseudoscalar meson> of mass $m$ and two massless leptons through a <weak charged current>, the <transverse massless leptonic current> selects $f_+(s)$. With hadronic current normalized as $(p+k)^\mu f_+(s)+(p-k)^\mu f_-(s)$ and flavour coefficient $V$,
$$
\frac{d\Gamma}{ds}=\frac{G_F^2|V|^2}{192\pi^3M^3}\lambda(s,M^2,m^2)^{3/2}|f_+(s)|^2,\qquad 0\leq s\leq(M-m)^2.
$$
The <Källén function> has mass dimension four, and the coefficient has mass dimension $-7$. This <decay rate> assumes the stated form-factor normalization and no additional isospin factor. It follows by the <integrated massless leptonic tensor> and the pion momentum change of variable in the parent's <centre-of-momentum frame>.
Back to article page
