free parameters of the Standard Model

Even our best theory of particles is not a machine that spits out every number from scratch. The Standard Model has a set of dials — numbers it cannot predict and must instead get from experiment. Think of a recipe that gives perfect instructions but leaves the oven temperature blank for you to fill in by tasting. Those blanks are the model's free parameters.

There are around nineteen of them in the basic Standard Model (a couple more if you include neutrino masses). They include the masses of the quarks and charged leptons, the strengths of the three forces (the coupling constants), the way quark flavors mix, the mass of the Higgs boson, and the value of the Higgs field that fills space. Once you measure these dials once, the theory predicts a vast number of other things with great precision — but the dials themselves are inputs, not outputs. Nothing in the model explains why the electron has the mass it does, or why the forces have the strengths they do.

Physicists find this both impressive and unsatisfying. Impressive, because nineteen-odd numbers buy you an enormous range of correct predictions. Unsatisfying, because a truly fundamental theory might be hoped to explain those numbers rather than borrow them. The hunt for a deeper theory is partly a hunt to derive some of these parameters from a smaller, simpler starting point — and several patterns among them, like the strange smallness of neutrino masses, are taken as hints that such a deeper theory exists.