Two-body decay threshold ($M\ge m_1+m_2$)

In the rest frame of the parent particle, four-momentum conservation requires $M=E_1+E_2\ge m_1+m_2$. For two equal masses the daughter momentum magnitude is $\frac{1}{2}\sqrt{M^2-4m^2}$; the two-body decay phase space closes at $M=2m$. For a finite constant decay amplitude, the decay width tends to zero at this threshold.