Hitting things to find out what they are
By this rung you have the machinery in hand. You can read a Feynman diagram as a story of incoming and outgoing particles trading something in between; you know that squaring the amplitude and folding in the room-to-move of phase space gives a cross section, the effective target area a reaction presents. This guide turns that calculating power outward, toward the experiment itself. Because here is the oldest trick in physics: when you cannot open something up, you throw things at it and watch how they bounce. Scattering is that trick, refined into our sharpest tool for seeing the unseeably small.
The first big question to ask of any collision is brutally simple: did the things that came out match the things that went in? If two protons go in and the same two protons come out, just redirected, that is one kind of event. If they go in and a spray of brand-new particles comes out, that is something else entirely. That single yes-or-no — same cast, or new cast? — is the dividing line between elastic and inelastic scattering, and it is the place every reading of a collision begins.
Elastic vs inelastic: did the cast change?
In elastic scattering, the colliding particles survive unchanged and simply leave with their directions and energies rearranged — like two billiard balls clicking apart. Total kinetic energy is conserved in the everyday sense, and crucially the particles themselves are identical before and after. Rutherford's famous gold-foil experiment was elastic: alpha particles bounced off nuclei and flew away still as alpha particles, but the rare hard bounces revealed that the atom's positive charge sits in a tiny dense nucleus rather than smeared out. Elastic scattering is gentle in identity but can still be sharply informative about shape and size.
In inelastic scattering, the cast changes. Some of the incoming kinetic energy is no longer kept as motion — it is converted, by mass-energy equivalence (E = mc-squared put to work), into the rest mass of new particles, or used to excite a target into a heavier, short-lived state. Smash two protons hard enough and you can get the original protons plus a freshly minted pion; pour in more energy and you make whole sprays of hadrons. Nothing is created from nothing here: energy is simply paying for mass. There is a minimum collision energy, the threshold energy, below which a given new particle cannot appear at all — you cannot mint a coin you cannot afford.
elastic: p + p -> p + p inelastic: p + p -> p + p + pi0 (energy bought a new pion)
Deep inelastic scattering: the proton is not solid
Now push inelastic scattering to an extreme. In the late 1960s at SLAC, physicists fired very high-energy electrons straight into protons. Recall the rule that high-energy beams act as microscopes: the higher the energy, the shorter the wavelength of the probe, so a fierce electron beam resolves smaller and smaller distances inside the target. When the electrons came in hard enough, they did not just nudge the proton — they tore deep inside it and shattered it into a spray of new particles. This is deep inelastic scattering: deep meaning high energy and short distance, inelastic meaning the proton does not survive.
The surprise was in how often the electrons bounced hard. If the proton's charge were a soft, smeared-out blob, almost every electron would glide past with only a small deflection. Instead, an unexpectedly large number ricocheted at steep angles — the same telltale signature Rutherford had seen for the nucleus, now one level deeper. The proton's charge was not spread smoothly; it was concentrated in tiny, hard, point-like lumps inside. The electrons were bouncing off pieces of the proton, not off the proton as a whole.
Those point-like pieces were the quarks (and the gluons binding them), the first hard experimental evidence that the proton is composite, not fundamental. The way the proton's contents share its momentum is captured today in a parton distribution function — a map of how likely you are to find a given quark or gluon carrying a given fraction of the proton's momentum. A subtlety worth being honest about: most of the proton's mass is not the mass of the three quarks at all. It is the energy of the churning strong-force field that confines them — QCD binding energy, not the Higgs — which is a very different story from how the quarks themselves get their (small) masses.
Three storylines: the s-, t-, and u-channels
Switch back to the theorist's chair. Two particles come in, two go out — and there is often more than one way to wire up the diagram that connects them. Physicists name the main wirings the s-channel, t-channel, and u-channel. Picture them as three different plots for the same cast. In the s-channel, the two incoming particles first merge into a single intermediate, which then splits back apart into the outgoing pair — they fuse, pause as one, and re-emerge. In the t-channel, the particles never fuse; they slide past each other and toss something across the gap between them, like two skaters exchanging a ball. The u-channel is the t-channel's twin, used when the two outgoing particles are identical and you must also count the version where their roles are swapped.
The names come from the Mandelstam variables s, t, and u, the three tidy invariant combinations of energy and momentum you met when learning to describe collisions without picking a frame. Each channel is dominated by one of them: the s-channel by s (the total energy-squared of the collision), the t-channel by t (related to the momentum transferred sideways). Naming the channel after its variable is just bookkeeping that tells you, at a glance, which quantity controls how the intermediate line behaves.
The channels are not rival realities — they are different contributions you must add together. When the same incoming and outgoing particles can be reached by an s-channel and a t-channel diagram, the rules of the amplitude demand that you sum the diagrams *before* squaring, so the storylines can interfere. The s-channel hides a special drama: when the collision energy lands right on the mass of a real intermediate particle, the s-channel contribution surges and you see a resonance — a sharp peak in the cross section that announces a particle wanting to be born. That is, quite literally, how many particles were discovered.
From a bounce to a measurement
Put the pieces together and you have the working loop of the whole field. A theorist draws the diagrams for a process — choosing the right channels, summing them, squaring, folding in phase space — and out comes a predicted cross section. An experimenter then collides beams, counts how many of that kind of event actually happen, and divides out the luminosity (how intense the beams were) to read off the measured cross section. Theory hands over a number; experiment hands back a number; the field lives or dies on whether they match.
Keep one honesty in view. The intermediate lines inside these channels — the fused blob in the s-channel, the tossed object in the t-channel — are virtual particles: a calculational device, an internal bookkeeping line, never something you catch in a detector. Only the external legs, the real particles entering and leaving, are observed. The resonance peak is the closest a virtual line comes to declaring itself real, and even then what you measure is the cross section it shapes, not the line itself. Scattering is powerful precisely because it stays disciplined about this: it predicts and measures probabilities, and lets the unobservable internals do their work quietly in the math.