transverse momentum

At a collider, the two beams come in along one straight line, so before they hit there is essentially no motion sideways — all the momentum points along the beam axis. After the collision, you can split each particle's momentum into two parts: the piece still pointing along the beam, and the piece pointing sideways, out away from it. That sideways piece is the transverse momentum, almost always written pT. It is the momentum a particle picked up perpendicular to the beams.

Why single out the sideways direction? Because of a powerful balance rule. Since the incoming beams carry no sideways momentum, conservation of momentum demands that the sideways momenta of everything produced must add up to zero. Add up the pT of every particle flying out of a collision, treating direction carefully, and the vector sum should cancel. Equally important, pT is barely affected by the unknown boost along the beam that randomly shakes hadron collisions — the boost is along the beam, so it leaves the sideways component nearly untouched, making pT a stable, trustworthy quantity.

These two facts make transverse momentum one of the most used quantities in collider physics. Particles with large pT came from something hard and interesting happening, so triggers and searches favour high-pT objects. And the balance rule lets physicists detect the undetectable: if the transverse momenta visibly fail to add to zero, the imbalance — the missing transverse momentum — betrays particles that escaped unseen, such as neutrinos or hypothetical dark-matter particles. You cannot see what left, but you can see the hole it left in the books.