Quantum numbers of fundamental particles?

[Marjan]

Which are (basic?) quantum nubers of fundamental particles?

I am having problems becouse a lot of expresions are used on sites on the web: el. charge, color charge, mass, taste, spin, barion & lepton number... to many

 

[quantumdude]

Hi, and welcome to PF.

The quantum numbers of fundamental particles are:

1. Spin, which is intrinsic angular momentum.

2. Electric charge, which determines how particles couple to EM fields.

3. Color, which determines how particles couple to gluon fields.

4. Flavor (including isospin up/down, strangeness, charm, bottomness and topness), which determines how particles couple to massive vector boson fields.

5. Lepton number (and also electron number, muon number, and tauon number)--which are conserved for some reason unbeknownst to us at this time.

6. Baryon number--Also conserved for some unknown reason.

7. Parity--Which describes how a particle transforms under spatial reflection.

8. C-Parity--Which describes how a particle transforms under charge conjugation.

Another one that could be added is "T-Parity" (if I may coin a term), which describes how particles transform under time reversal. However, this is usually not listed in the Particle Data Group because the product PCT (Parity, Charge Conjugation, and Time Reversal, respectively) is conserved under any circumstance, so specifying P and C automatically determines T.

 

[Marjan]

Hi back to you Tom and thank you for answer, very clearly. I like your page PF (and P in general ;)

So, mass isn't quantum number! I guess becouse it is "only" interaction with Higgs boson. Can it really be calculated precisely?

For most q. numbers I found values on the web. But I have still priblems with:

3. Color - many sources say "red", "green"... but that is just silly! I can not find real values of so called color properties for quarks (for example)...!?

I also don't find values for Parity and C-Parity... this two (or three with T-Parity) can not be calculated from rest of the q. numbers?

 

[selfAdjoint]

The strong charge is determined by a representation of the group SU(3). It has three values, each with an anti-value. They follow the rules that each charge+anticharge = no charge, and sum of all three charges = sum of all three anticharges = no charge. These rules recall the familiar subtractive color rules, which is why the three charge values were named after colors. Gluons carry two strong charges and quarks one. When a gluon interacts with a quark the three charges present add according to the rules to determine the charge the quark winds up with. This means the strong charge of a quark is constantly changing.

Parity for spinning particles depends on their handedness, which should be described in the tables. C-parity is just based on electric charges; +1 for positive charges and -1 for negative charges and 0 for neutral particles.

 

[quantumdude]

So, mass isn't quantum number! I guess becouse it is "only" interaction with Higgs boson. Can it really be calculated precisely?

Right, mass is not a quantum number in the Standard Model. Also, it can't be calculated from the Standard Model. The masses of elementary particles are put in by hand.

3. Color - many sources say "red", "green"... but that is just silly! I can not find real values of so called color properties for quarks (for example)...!?

If vectors in "color space" can be represented by a column vector with 3 components, such that:

|red>=(1 0 0)^T
|green>=(0 1 0)^T
|blue>=(0 0 1)^T

then transformations among the colors can be represented by using the Gell-Mann Matrices. I'll write more later when I have more time, unless someone beats me to it.

I also don't find values for Parity and C-Parity... this two (or three with T-Parity) can not be calculated from rest of the q. numbers?

You don't find them? Well, then, you aren't looking in the right place!

You should be looking at the Particle Data Group website. Click on "Particle Listings 2003".

Here's a sample page for the p⁰ Meson. The quantum numbers P and C are listed right at the top.

Hope that helps,

 

[Marjan]

Very usefull links. I think it would be nice if even more physics informations would be avalible in free WikiPedia. It is great.

Now I can see more clearly on quantum nubers.

I suppose that antiparticles have ALL quantum nubers just opposite than their particles. Right?

I also found out that only fermions have flavor, and only quarks have color charge. Interesting! All particles in S.M. have spin for example...

Do flavor and color charge have any physical units?

 

[bkfizz02]

Do flavor and color charge have any physical units?

This is similar to a question that my journal club likes to talk about. (We specifically have discussed what Isospin IS).

Anyways, color charge in strong interactions is similar to conventional charge in E&M. In E&M, charge has it's own unit, coulomb. Coupling constants relate how *strong* 1 unit of charge is. A charge interacting with an E&M field is analogous to a strong charge interacting with a strong field.

Flavor usually refers to the different brands of leptons.

Leptons have specific flavors -- these are the names that we are familiar with as eigenstates of the weak interaction -- the electron, muon and tau. I like to think of a muon as a particle that has 1 unit of muness or muon charge. Again, you can't attach a physical unit to these properties, but you can usually find tables that tell you the value of lepton number for various particles. Then when considering interactions which respect conservations laws, you can conserve each of these flavors independantly.

Particle Le ("electronness") Lmu ("muness") Ltau ("tauness")

electron +1 0 0
positron -1 0 0
muon (neg) 0 +1 0
antimuon (pos) 0 -1 0
tau (neg) 0 0 +1
antitau (pos) 0 0 0

The neutrinos also carry these flavor numbers.

Often in particle physics,i try to think about the property of a term like "color charge", and what it means for interactions, rather than try to slap units on them and throw them into equations.

 

[jtolliver]

Hi, and welcome to PF.
2. Electric charge, which determines how particles couple to EM fields.

5. Lepton number (and also electron number, muon number, and tauon number)--which are conserved for some reason unbeknownst to us at this time.

6. Baryon number--Also conserved for some unknown reason.

Electric charge is not a fundamental property; it can be calculated from the hypercharge(the generator of the U(1) part of the SM gauge group) and the isospin(a generator of the SU(2) part).

Weinberg shows in Quantum theory of fields(Vol 1) that any renormalizable lagrangian with poincare symmetry conserves lepton number, which is why it is thought to be an 'accidental symmetry'. Likewise for baryon number.

 

[quantumdude]

Electric charge is not a fundamental property; it can be calculated from the hypercharge(the generator of the U(1) part of the SM gauge group) and the isospin(a generator of the SU(2) part).

Perhaps I'm missing something, but why can't you say that electric charge is fundamental, and that hypercharge is not?

Weinberg shows in Quantum theory of fields(Vol 1) that any renormalizable lagrangian with poincare symmetry conserves lepton number, which is why it is thought to be an 'accidental symmetry'. Likewise for baryon number.

Thanks for the tip, I'll have to read up on that. I've been looking for an excuse to buy Weinberg's books anyway!

 

[jtolliver]

Perhaps I'm missing something, but why can't you say that electric charge is fundamental, and that hypercharge is not?

the hypercharge is in the center of the electroweak group.

 

[selfAdjoint]

And the center of a noncommutative group is the set of elements of the group that do commute with each other. So this is a statement anout fundamental symmetries of the physics, which would be taken as deeper than the observable values of something.

 

[Haelfix]

Ack. Lepton number is not conserved in the standard model, and is an accidental symmetry.

T'Hooft did work on this about 10 years ago, and there was quite a buzz for awhile. Unfortunately the nonconservation of lepton number is violated by something like 1 in (insert number with 93 zeros). So for most purposes, its fine to think of it as so. The explanation for this is ... nontrivial and you have to know something about tqft.

Moreover, GUT theories nearly always break Lepton number, and we already are pretty sure that neutrino oscillations breaks everything heurestically