Chapter 9: Fundamental Physics

Section 14: Elementary Particles

Particle masses

The measured masses of known elementary particles in units of GeV (roughly equal to the proton mass) are: photon: 0, electron: 0.000510998902; muon: 0.1056583569; τ lepton: 1.77705; W: 80.4; Z: 91.19. Recent evidence suggests a mass of about 10^-11 GeV for at least one type of neutrino. Quarks and gluons presumably never occur as free particles, but still act in many ways as if they have definite masses. For all of them their confinement contributes perhaps 0.3 GeV of effective mass. Then there is also a direct mass: gluons 0; u: ~0.005; d ~0.01; s: ~0.2; c: 1.3; b: 4.4; t: 176 GeV. Note that among sets of particles that have the same quantum numbers—like d, s, b or γ, Z—mixing occurs that makes states of definite mass—that would propagate unchanged as free particles—differ by a unitary transformation from states that are left unchanged by interactions. When one sets up a quantum field theory one can typically in effect insert various mass parameters for particles. Self-interactions normally introduce formally infinite corrections—but if a theory is renormalizable then this means that there are only a limited number of independent such corrections, with the result that relations between masses of different particles are preserved. In quantum field theory any particle is always surrounded by a kind of cloud of virtual particles interacting with it. And following the Uncertainty Principle phenomena involving larger momentum scales will then to probe progressively smaller parts of this cloud—yielding different effective masses. (The masses tend to go up or down logarithmically with momentum scale—following so-called renormalization group equations.)

The Standard Model starts off with certain symmetries that force the masses of all ordinary particles to be zero. But then one assumes that nonzero masses are generated by spontaneous symmetry breaking. One starts by taking each particle to be coupled to a so-called Higgs field. Then one introduces self-interactions in this field so as to make its stable state be one that has constant nonzero value throughout the universe. But this means that as particles propagate, their interactions with the background give them an effective mass. And by having Higgs couplings be proportional to observed particle masses, it becomes inevitable that these will be the masses of particles. One prediction of the usual version of this mechanism for mass is that a definite Higgs particle should exist—which in the minimal Standard Model experiments should observe fairly soon. At times there have been hopes of so-called dynamical symmetry breaking giving the same effective results as the Higgs mechanism, but without an explicit Higgs field—perhaps through something similar to various phenomena in condensed matter physics. String theory, like the Standard Model, tends to start with zero mass particles—and then hopes that an appropriate Higgs-like mechanism will generate nonzero ones.

From Stephen Wolfram: A New Kind of Science [citation]