 Massless semileptonic pseudoscalar decay rate

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 $V$,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.