s-, t-, and u-channel processes

Two particles come in, two go out — but there is more than one storyline by which that can happen, and physicists give the main storylines short names: the s-channel, the t-channel, and the u-channel. Think of them as three different plots for the same cast of characters. In one plot the two incoming particles first fuse together; in another they brush past each other and swap something between them; in a third they do something in between. The letters s, t, and u are just labels for these distinct ways the collision can be wired up.

Concretely, in an s-channel process the two incoming particles annihilate or merge into a single intermediate particle, which then splits into the outgoing pair — like two streams meeting, briefly becoming one, then parting. In a t-channel process the incoming particles stay distinct and exchange a particle between them, deflecting each other — like two ships passing and tossing a rope across. The u-channel is similar to the t-channel but with the two outgoing particles swapped, which matters when those outgoing particles are identical. The names come from the Mandelstam variables s, t, and u, which are bookkeeping quantities built from the particles' energies and momenta that label each channel.

Why bother distinguishing them? Because the s-channel is exactly where resonances live: when the combined energy of the incoming particles matches an intermediate particle's mass, the s-channel contribution spikes into a Breit-Wigner peak, which is how new particles are discovered in colliders. The t- and u-channels, by contrast, dominate gentle deflections and give smoothly falling cross sections. For any given process, several channels can contribute at once, and because amplitudes are added before squaring, they can interfere — so getting the channels right is essential to predicting a cross section correctly.