So what do we do with these protons? Basically we smash them into material and see what happens. In our experiment we smash them onto a target and collect pions from the collisions. Pions are nuclear glue. Imagine I throw a pion at you and you're a neutron. Then you'll be attracted to me. Light does the same thing when two opppositely charged particles interact.
Anyway these pions don't live forever, otherwise there'd be chunks of pions around! They live for about 20 billionths of a second (at rest) longer if moving close to the speed of light. They decay into particles called muons. Muons live about 2 millionths of a second. An interesting thing about muons is that they are like heavy electrons. In our experiment the muons capture on liquid hydrogen (at about 10 degrees above absolute zero). They knock the electrons out and form little atoms. Since they are 200 times heavier than electrons, the atoms are much smaller. The muon gets absorbed by the proton. That is what we want to see. Our detector looks for when light is given off during the muon's absorption. It is very rare for light to be given off. We have stopped over 3 trillion muons but have seen the light only 300 times or so.
The muon interacts with the proton in the liquid hydrogen by the electromagnetic and the weak forces. The weak force explains radioactive decays such as the neutron decay into a proton plus an electron. The weak force isn't entirely understood for the proton since it is a complicated object made up of quarks and gluons. The weak force between quarks and gluons are understood quite well, but how quarks and gluons come together to give the weak interaction of the proton is not well known, experimentally, but there are some pretty good predictions. We are testing those predictions.
Because of the properties of the proton, its interaction with muons contains many terms. We think of the proton as a current made up of these pieces. The proton can interact with a muon by first emitting a pion, the mediator of the strong nuclear force, which decays by absorbing the muon and emitting a muon neutrino. The fact that the pion decays like this puts a constraint on the current and thus relates a few of the components of the current. What it does is relate one constant that is well known from nuclear beta decay (neutron decays into a proton, electron, and an electron antineutrino) to another constant that our experiment will be the first to measure accurately, hopefully.
Parenthetically, the interaction is called the weak interaction, because, for example, a neutrino, which only interacts via the weak and gravitational forces, is unlikely to be scattered even after passing through the entire earth. In contrast, a high energy light ray might make it only a few centimeters before its energy is completely transformed.