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Q & A: Particles of the Standard Model and Minimial Supersymmetric Model

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Most recent answer: 10/22/2007
Q:
Is my counting right?: There are 76 elementary particules in the standard model: 6 leptons + 6 anti-leptons, 6 quarks + 6 anti-quarks, 8 gluons which are their own antiparticules 3 weak bosons (W+, W-, Z) 1 photon + 1 graviton + 1 Higgs boson (which are their own antiparticules?) All doubled to account for their supersymetric counterparts.
- david (age 26)
montreal, canada
A:
That's pretty much right, although the counting isn't exactly consistent, and there are some things we do not yet know for sure.

One is the graviton. We do not yet have a satisfactory quantum theory of gravitation. If gravitons exist, they should have spin 2.

The other is supersymmetric counterparts. There is no direct experimental evidence for supersymmetry, although it does make the theories tidier in many ways. I wouldn't call these Standard Model particles either. We usually refer to the "MSSM" -- the Minimal Supersymmetric Standard Model as the supersymmetric extension of the Standard Model with the minimal number of new particles. It still gets classified as speculation at this point.

You mention 8 gluons, but these differ only by their color charges. You could then multiply your quark count by three to account for the fact that they can have different color charges, too. We often don't do that when listing particle content. Supersymmetric partners of quarks get the same color charges and interact with gluons too, so the same factor of three goes there too. It's important to keep around when computing production and decay rates.

So that's it for the Standard Model. When doubling this for the MSSM, you have to be very careful counting states, because the different spin states of the particles count as different particles! A left-handed electron has different interactions from a right-handed one (it interacts with W's while the right-handed one does not). There are therefore two supersymmetric partners of the electron, with possibly different masses. These two superpartners each has spin zero, so the number of states all adds up.

The photon, while it has a spin of 1, has only two spin states (polarizations) allowd -- most spin-1 objects can be in three states, +1, 0, and -1, but the photon is massless and is missing the 0-spin state. The W and Z also have spin one, but they have all three spin states allowed. The gluon and the graviton are also missing the zero-spin state.

In addition, in the MSSM, there are five (!) Higgs bosons, three neutral ones, h, H, and A, and two charged ones, H+ and H-.

Here's the boson counting for superpartners:

Neutral Standard Model bosons (and extra Higgs for the MSSM)

photon (2 spin states)
Higgs (3 particles, each with no spin)
Z(3 spin states)

Their superpartners have the same quantum numbers and can mix. There are therefore four spin-1/2 "neutralinos" in the MSSM (each has two states, for a total of eight states, to match the eight total states above). Each of the four neutralinos can have a different mass.

The gluino (superpartner of the gluon) has spin 1/2, with two states to match the 2 polarization states of the gluon. These all have the 8 color states. This one doesn't mix with the others because it has color charge.

The gravitino (superpartner of the graviton) has spin 3/2, and so has four allowed spin states, to match the four spin states of the graviton. The gravitino doesn't mix either; it has different interactions from the neutralinos.

The charged bosons are the

W+ (3 spin states)
H+ (1 particle with no spin)

and there are two spin-1/2 "charginos" (mixtures of the superparters of these four states). The negatively-charged bosons correspond to negatively-charged charginos.

That just about does it!

Tom


For some purposes, what matters is the number of different adjustable parameters in the model, not the number of different particles. As you can see the particle count depends a little on definitions. The general lore is that the current Standard Model has about 20 different parameters which don't come from some known theory. An example is the ratio of the mass of an electron to the mass of a muon. Another is the ratio of the electrical to the gravitational forces between two electrons./ mike w

(published on 10/22/2007)

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