Matter and its interactions

The rest mass of a specified system is determined by its total energy in the frame where its total momentum is zero, when such a frame exists. For a composite system, its rest mass includes the energy of motion, fields and interactions in its rest frame. Adding the masses of isolated constituents can therefore miss most of the answer.

The proton is the important example. Its three valence quarks specify its net quark content: two up quarks and one down after quark-antiquark pairs are accounted for. The full quantum state also contains gluon and quark-pair contributions. They are not three static beads whose masses almost add to a proton. The strongly interacting quark and gluon system accounts for most of the proton's rest energy. Quantum chromodynamics, or QCD, is the theory used to calculate that dynamics.

The neutrinos of the Standard Model carry neither electric charge nor QCD colour. They therefore lack the ordinary electromagnetic and strong interactions that make many other particles easy to stop. Their weak interactions have small probabilities at familiar energies. Small mass is a separate fact.

A detector compensates by offering many targets, collecting many incoming neutrinos and waiting. Most neutrinos leave no record. A rare interaction can create a charged particle or excite a nucleus, producing a signal that the apparatus can amplify and identify.

Here is a counting example. Suppose the chance of a detectable interaction per crossing neutrino is one in a million, under specified conditions. Ten million crossings then give an expected ten events. Expected does not mean exactly ten in every run. Backgrounds, efficiency and statistical fluctuations must be included before the count can be interpreted.