Past exam of the particle and nuclear physics course of the University of Cambridge / 2014 / Paper 1 / 3 / a / i

Set $c=1$ and use metric $(+---)$. In the rest frame of B, $p_B=(m_B,0)$ and $p_C=p_B+p_t$. Since $p_t^2=0$,The denominator is $m_B$ because this is the B rest frame, not the C rest frame. In this frame C and $t$ have equal, parallel three-momenta.