I wanted to take a break from our ongoing discussion of Feynman diagrams and the Standard Model to highlight what we’ve learned the true identities of the particles we now know and love.
The “fake” Particle Periodic Table
These days most people who read Scientific American or Dennis Overbye’s articles in the NY Times can list off the Standard Model particles off the top of their heads. Their list would look something like this (which we posted earlier):
These are, of course, the matter particles. Savvy science fans will also list off the photon, W, Z, and gluon as the Standard Model force particles. With these particles you can explain a whole swath of nuclear physics and chemistry. But the chart above doesn’t shed light on the electroweak (Higgs!) physics that leads to this structure.
For this reason, these aren’t the particles that physicists use when describing the theoretical structure of the Standard Model and its extensions. Instead, we distinguish between things like the “left-handed electron” and “right-handed anti-positron,” or the “transverse W polarizations” and versus the longitudinal polarization which is really a Goldstone boson stolen from a group of [four!] Higgses.
Instead of a lengthy recap of previous blog posts, let’s try to summarize with the right cartoon pictures. In doing so, we’ll get to learn something about the true hidden identities of the Standard Model particles and how they really interact with one another.
The true identities of the Standard Model particles
Let’s start with the electron. We learned that the electron is really a mixture of two chiral particles: a massless “left-handed electron” and a massless “right-handed anti-positron.” These two particles bounce off of the Higgs vacuum expectation value (vev) an convert into one another, leading to the massive particle that we just called the “electron” above.
(We denote the right-handed matter particle with a mustache to highlight that it’s really a totally different object.) The same story is true for the electrons two siblings, the muon and tau, and also for each of their antiparticles.
What about the neutrino? In the Standard Model, the neutrino is massless. We now know they have very small mass, but we’ll stick to the vanilla version of the theory. For this reason, the neutrino doesn’t have to bounce off of the Higgs vev and should be identified with only a left-handed neutrino.
I drew speed lines on the neutrino because the Standard Model neutrino travels at the speed of light due to being massless. I mention this to remind you that the reason why the massive electron could swap between being a “left-handed electron” (yellow particle above) and a “right-handed anti-positron” (green particle with a mustache) is that we could imagine being in a reference frame where the electron spins in the opposite direction, say by speeding past the electron along its trajectory. We can’t do that with the massless neutrino because it’s going at the speed of light; thus all neutrinos that we observe are left-handed.
The Standard Model quarks are all massive and behave just like the electron: they are a mixture of “left-handed quarks” (yellow) and right-handed anti-quarks (green with mustache). Also shown below are the different “color charge” that each quark comes in: red, blue, and green. This has nothing to do with actual colors in the visible spectrum, rather it’s a way of describing objects with three types of charge rather than just two (positive or negative).
There are two types of quarks: up-type (up, charm, top) and down-type (down, strange, bottom); they differ by their electric charge. Up-type and down-type quarks interact with one another through the massive W boson. Part of the theoretical structure of the Standard Model is that the W boson only talks to the left-handed particles (the yellow guys with no mustache)—we say that the Standard Model is chiral (compare this to the definition in chemistry and biology).
The W comes along with its also-massive cousin, the Z boson. We now know that massive gauge bosons come about when previously-massless gauge bosons “eat” a Goldstone boson. These ‘eaten’ Goldstone bosons are three of the four parts of the Standard Model Higgs, leaving one neutral particle which we call the Higgs. This entire process by which force particles have become massive has a fancy name, electroweak symmetry breaking.
In fact, in the picture above we show a very important feature of electroweak symmetry breaking: in addition to H0, the Z boson is also a mixture of a third W boson (called W3 above) and something we called the B boson. Like its charged siblings, the W3 only talks to left-handed particles, though the B is more sociable and will happily talk to both left- and right-handed particles. Note, however, that even here the Standard Model is biased: the “B charge” of a left-handed electron (yellow, no mustache) is different from the “B charge” of a right-handed electron!
What happened to the other leftover parts of the W3 and B? They form another force particle, the photon! The interesting thing about the photon is that it’s the electroweak force particle that didn’t eat any Goldstones—it’s the combination of gauge bosons that survived “electroweak symmetry breaking” without putting on weight. We say that “electroweak symmetry has broken to electromagnetism.” Unlike the full electroweak theory, electromagnetism is left/right democratic in how it talks to matter particles.
Since the photon has not eaten any Goldstone boson, it remains massless and travels at the speed of light. This sounds silly since it is light, so I should say that it travels at the “universal speed of all things which have no mass.” Speaking of which, there’s one more force particle that has nothing to do with electroweak symmetry and also is massless, the gluon:
There are actually eight gluons coming from different color and anti-color combinations, i.e. corresponding to different combinations of quarks and anti-quark colors that may interact with the gluon. (Astute readers will wonder why there aren’t nine combinations… this is due to a subtlety in group theory!)
What does this all buy us?
So we see that the Standard Model is actually a bit more complicated than the “fake” version that we showed at the top of the page. Even though it might not seem like it, the theory of this “more complicated” Standard Model is actually rather elegant and minimal. I should also say that calling the simple table a “fake” is too harsh: that is indeed an accurate description of the Standard Model after “electroweak symmetry breaking,” but it doesn’t illuminate the rich structure of interactions included in the theory.
For example, one would have never understood why nuclear beta decays (mediated by the W) always produce left-handed neutrinos. It also wouldn’t have been clear how “longitudinal vector boson scattering is rendered unitary” at high energies—in other words, the description of certain types of gauge boson scattering breaks down without something like a Higgs to keep the calculations under control.
The first example is a real matching of observed phenomenon to a theoretical framework. The second example shows how our theory is prediction about missing pieces that it needs to make sense. While it may sound dry, these are important points—this is part of the Scientific Method: we use observations of natural phenomena and build hypotheses (theories) that make predictions. We can then go and build and LHC (… as well as LEP and the Tevatron) to confirm or refute these predictions—the data from these experiments then feed back in to revise (or overthrow) our theories.
So now that we’re more or less up to speed with the moving parts of the Standard Model, we can push forward to figure out why we believe it should still break down at TeV-scale energies and give some hint of even more fundamental organizing principles. (This is the really exciting part!)
