center-of-mass frame
/ abbreviated CM, or CoM /
When two cars approach a head-on collision, there is a natural viewpoint from which the wreck looks symmetric: the spot, somewhere between them, that they are both rushing toward. From that vantage the total momentum is zero — every bit of leftward push is matched by an equal rightward push. The center-of-mass frame is exactly this balanced viewpoint, applied to colliding particles. It is the frame, moving along with the collision, in which the total momentum of all the particles adds up to zero.
More precisely it should be called the center-of-momentum frame, because what is set to zero is the total momentum, not a literal center of mass. In this frame two colliding particles approach with equal and opposite momenta, smack together, and the products fly out in a balanced pattern. The single most important quantity here is the total energy available in this frame, traditionally written as the square root of s. That number is the real budget for creating new particles, because in the center-of-mass frame none of the energy is wasted on the system as a whole flying forward.
This frame is where physicists prefer to think about what a collision can produce. A modern collider like the LHC is built precisely to put the laboratory and the center-of-mass frame nearly on top of each other: two beams of equal energy hit head-on, so the lab already sees zero total momentum and the full beam energy is available for creating mass. That is why colliders reach far higher effective energies than firing one beam at a stationary target, where much of the energy is squandered carrying the debris forward.
The available collision energy is sqrt(s). At the LHC two 6.5 TeV proton beams collide head-on, giving sqrt(s) = 13 TeV — all of it usable for making new particles.
In the center-of-mass frame total momentum is zero, so the whole energy budget goes into creating mass.
The name 'center of mass' is a borrowed convenience; the defining property is zero total momentum, so 'center-of-momentum frame' is the more accurate term, especially for massless particles that have no mass to center.