Center-of-mass energy ($E_{\mathrm{com}}^2=-P_{\mu }{P}^{\mu }$)

For future-directed particles with total four-momentum $P$ and metric signature $(-+++)$, the positive square root of $-P_{\mu }{P}^{\mu }$ is their energy in the frame where total spatial momentum vanishes. Its invariant definition remains valid at a collision in spacetime.