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The 4 momentum of a particle is given by $P=(M,\vec 0)$, and it decays into two daughters with $p_1$ and $p_2$. Then $P=p_1+p_2$ and $$p_2^2 = (P-p_1)^2 = P^2 -2P.p_1 +p_1^2$$ How do you get from this line to the fact that $$m_2^2 = M^2 -2ME_1 +m_1^2$$ It's something to do with being in the rest frame of the parent but I don't understand how to get from the equation with momenta to the one with masses.

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Very silly question. In particular the part I couldn't work out was why $P.p_1 = ME_1$ but the four vector $P$ is $(M,0,0,0)$ as we are in the rest frame of that particle, and $p_1 = (E_1, p_x, p_y, p_z)$ and the dot product of those is clearly $ME_1$.

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