**An Explanation of Fundamental Particle Physics That Doesn't Exist Yet**

My favorite explanation is one that does not yet exist.

Research in fundamental particle physics has culminated in our current Standard Model of elementary particles. Using ever larger machines, we have been able to identify and determine the properties of a whole zoo of elementary particles. These properties present many interesting patterns. All the matter we see around us is composed of electrons and up and down quarks, interacting differently with photons of electromagnetism, W and Z bosons of the weak force, gluons of the strong force, and gravity, according to their different values and kinds of charges. Additionally, an interaction between a W and an electron produces an electron neutrino, and these neutrinos are now known to permeate space—flying through us in great quantities, interacting only weakly. A neutrino passing through the earth probably wouldn't even notice it was there. Together, the electron, electron neutrino, and up and down quarks constitute what is called the first generation of fermions. Using high energy particle colliders, physicists have been able to see even more particles. It turns out the first generation fermions have second and third generation partners, with identical charges to the first but larger masses. And nobody knows why. The second generation partner to the electron is called the muon, and the third generation partner is called the tau. Similarly, the down quark is partnered with the strange and bottom quarks, and the up quark has partners called the charm and top, with the top discovered in 1995. Last and least, the electron neutrinos are partnered with muon and tau neutrinos. All of these fermions have different masses, arising from their interaction with a theorized background Higgs field. Once again, nobody knows why there are three generations, or why these particles have the masses they do. The Standard Model, our best current description of fundamental physics, lacks a good explanation.

The dominant research program in high energy theoretical physics, string theory, has effectively given up on finding an explanation for why the particle masses are what they are. The current non-explanation is that they arise by accident, from the infinite landscape of theoretical possibilities. This is a cop out. If a theory can't provide a satisfying explanation of an important pattern in nature, it's time to consider a different theory. Of course, it is possible that the pattern of particle masses arose by chance, or some complicated evolution, as did the orbital distances of our solar system's planets. But, as experimental data accumulates, patterns either fade or sharpen, and in the newest data on particle masses an intriguing pattern is sharpening. The answer may come from the shy neutrino.

The masses of the three generations of fermions are described by their interaction with the Higgs field. In more detail, this is described by "mixing matrices," involving a collection of angles and phases. There is no clear, a priori reason why these angles and phases should take particular values, but they are of great consequence. In fact, a small difference in these phases determines the prevalence of matter over antimatter in our universe. Now, in the mixing matrix for the quarks, the three angles and one phase are all quite small, with no discernible pattern. But for neutrinos this is not the case. Before the turn of the 21st century it was not even clear that neutrinos mixed. Too few electron neutrinos seemed to be coming from the sun, but scientists weren't sure why. In the past few years our knowledge has improved immensely. From the combined effort of many experimental teams we now know that, to a remarkable degree of precision, the three angles for neutrinos have sin squared equal to 1/2, 1/3, and 0. We do need to consider the possibility of coincidence, but as random numbers go, these do not seem very random. In fact, this mixing corresponds to a "tribimaximal" matrix, related to the geometric symmetry group of the tetrahedron.

What is tetrahedral symmetry doing in the masses of neutrinos?! Nobody knows. But you can bet there will be a good explanation. It is likely that this explanation will come from mathematicians and physicists working closely with Lie groups. The most important lesson from the great success of Einstein's theory of General Relativity is that our universe is fundamentally geometric, and this idea has extended to the geometric description of known forces and particles using group theory. It seems natural that a complete explanation of the Standard Model, including why there are three generations of fermions and why they have the masses they do, will come from the geometry of group theory. This explanation does not yet exist, but when it does it will be deep, elegant, and beautiful—and it will be my favorite.