cross section and event rate
/ cross-SEK-shun /
Imagine throwing darts blindfolded at a wall with a few targets nailed to it. How often you hit a target depends on two things: how big each target is, and how fast you throw the darts. A cross section is the physicist's measure of how 'big' a particular kind of collision is — how likely a given process is to happen when two particles pass each other. The event rate is how often that process actually occurs per second, which combines the cross section (the size of the target) with how intensely the beams are crossing (how fast you throw).
Cross section has units of area, and it really does behave like an effective target area: a larger cross section means the process happens more readily. It is measured in barns and, far more commonly in particle physics, tiny fractions of a barn (a picobarn is a trillionth of a barn, a femtobarn a thousand times smaller still). The event rate is simply the cross section multiplied by the luminosity, the measure of how densely and frequently the beams are colliding: rate = cross section times luminosity. So a rare process (small cross section) can still be studied if you crank up the luminosity enough, and a common process floods you with events even at modest luminosity.
This relationship is the economic engine of collider physics. The Standard Model predicts a cross section for every process — producing a Higgs, making a top-quark pair, scattering two quarks — and these range over many factors of a billion. Comparing the measured rate to the predicted cross section is how you test the theory or hunt for something new: an excess of events over the predicted rate is a hint of new physics. The key honest point is that you never measure a cross section directly; you measure a rate, then divide out the luminosity and correct for everything your detector missed, so a cross-section measurement is only as trustworthy as your luminosity and efficiency estimates.
At the LHC the cross section for producing a Higgs boson is about 50 picobarns, while the total proton-proton cross section is about 100 millibarns — roughly two billion times larger. So Higgs events are buried in an enormous flood of ordinary collisions, and only the high luminosity makes their rate survivable.
A bigger cross section is a bigger target; the rate is that target size times how hard the beams collide.
A cross section is not a literal physical size of a particle — it is an effective target area for a particular process, and the same particle has wildly different cross sections for different reactions.