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Flip Tanedo | USLHC | USA

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Particle Paparazzi: the private lives of the Standard Model particles (summary)

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!)

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  • Amir Livne

    Hello. I have 2 layman questions – I don’t know QFT at all, so sorry in advance if I totally missed the mark.

    1. Why are the degrees of freedom of the W called polarisations? Can you actually build an experimental stage that acts as a polariser, or is it just an analogy for something else?

    2. Do the portions of W3 and B shared in the Z boson and in the photon come in nice portions, like a small reduced fraction? Or is it a constant that should be explained with a deeper theory?

  • Hi Amir, great questions.

    1. The polarizations refer to spin angular momentum. For a gauge boson (“vector” particle) with quantum spin 1, these spin angular momentum states correspond to the “polarizations” that you’re used to for light—though now I refer to individual quanta rather than a classical wave (e.g. a photon versus a beam of light). You can in principle measure this polarization by measuring the angular momentum of the system, though experimentally this can be tricky. (I think the other bloggers may have a much better answer to this than me!)

    2. The portions of the W3 and B in the Z and the photon come in proportions that are dictated by the relative strength of their couplings. Before “electroweak symmetry breaking” (and you don’t need to worry about the details of what that term means), there are two distinct forces: the W force and the B force. After “electroweak symmetry breaking” the W and B forces mix up into the weak force (mediated by the W and Z) and electromagnetism (mediated by the photon).

    The W and B forces have different couplings: for example, the W only talks to left-handed matter particles with some coupling strength determined by an overall number and some “group theoretical” factors. The B will talk to both left- and right-handed matter particles but with different coupling strengths. The Higgs talks to both the W and B, and when the Higgs obtains a “vacuum expectation value” (i.e. when “electroweak symmetry breaking” occurs), it mixes up the W and B according to its coupling strength to each.

    So yes, there is a nice expression for the portion of W3 and B in the Z boson written in terms of the coupling strengths, and a nice explanation for where this expression comes from. This is another aspect that you would not have seen without writing down the “full” Standard Model instead of the “toy” version at the top of the post.

    Great questions!
    F

  • Wouter

    Flip,
    cool, but shouldn’t your “right-handed anti-positron” in the first pic, the green one with moustache, be either rotating the other way (or be pointing backward)?
    And, for the gluon calculus 3*3=8, maybe a hint as to where the ninth combination goes? I would have expected not 8 but 10 (includinhg some trivial identity do-nothing non-mediation).

  • Hi Wouter—these cartoons of the ‘chiral fermions’ can get tricky because it’s easy to interpret them in the opposite way… and at the end of the day they are just cartoons. 🙂 I drew the things spinning in the same direction because I didn’t want to make it look like angular momentum is being violated… but I think the bottom line is that the cartoon picture is heuristic with respect to those details. 🙂

    Now for the gluons: indeed, 3*3 = 9, so there’s some quark–antiquark pair which does not couple to gluons. It turns out to be the quantum superposition: (red-antired + blue-antiblue + green-antigreen). The reason for this somewhat technical: the matrix of gluon couplings is traceless—this is sort of the “minimal” color structure for a force. In other words, I could have written a theory that has 9 generators, but such a theory is overkill to describe what we know about the strong force.

  • You’ve drawn the photon so it appears to have more W3 content that B. Shouldn’t that be the other way round?

  • Hi Adrian–good point! Let me make an appeal that these pictures are just cartoons and aren’t meant to convey any technical detail. 🙂

  • Dear Flip,

    I am very impressed with your blog – keep up the good work.

    I believe you have a typo (or the equivalent for a figure) – your down quark appears to have a component of a u_L (rather than d_R).

    Best wishes,
    Harry

  • Doh! I believe the component in the figure should be d_L

  • Hello Harry, absolutely right. I’ll try to fix that later on… but if not then it’ll be my badge of shame for this post. 🙂 Thanks! -F

  • Rene Kail

    Thx for the interesting posts on Particle Physics. However, the posts are too much disconnected, so you cannot always find what you are searching for.

    In the illustration for the down quark u_L should be replaced by d_L.
    What does the asterisk * mean in the antiquark representation?
    Some more detailed description of this subject would be welcome.

  • Hi Rene. Thanks for pointing out the error, you’re indeed correct. (I’ll try to get around to changing this, but it might end up falling through the cracks since things are hectic at the moment.) The star means antiparticle; I admit the naming scheme is a little inelegant. There is something called the “dR-bar” which has the charge of an anti-down quark. It is right-handed. The starred version is a particle with the charge of a down quark that is left handed. This thing is different from dL. The diagram shows that the dL and the dR-bar* mix between themselves.

    I apologize that the posts are too disconnected—the original post has something of a table of contents to help unify everything. Also, if you might want to refer to my lecture notes which I based on these blog posts: http://www.lepp.cornell.edu/~pt267/undergradparticles.html

    Otherwise, I’m doing the best that I can to contribute to the blog while doing research full time. 🙂

  • Daniel Connor

    I want to say that I have learnt a lot from your posts. I had a good non mathematical understanding of the standeard model but your posts have filled in the gaps in my understanding. One thing I think a new post could be on is the feynman diagram rules for the odd bosons like the x z and b bosons because I still dont know what they do.

  • Daniel Connor

    I’ve done some research in to the B boson but I think something in my understanding is wrong. If the Z boson and Photon are both made of the same bosons then they should react with the same particles but the Z boson reacts with neutrinos and the photon doesn’t. This makes no sense to me. Why cant the photon react with the neutron if the z boson made of the same stuff+Goldstone can?