Whither electrons and/or quarks? Question about the Standard Model

Factual Questions
1

Does the Standard Model account for why there are quarks and electrons and neutrinos? I seem to recall that it’s an unanswered question why they have all these flavors with different masses, but IANAPhysicist. Do we know why there should be this fermion with an electric charge of -1 that doesn’t seem to be made of anything smaller? Do we know why quarks should have 1/3n electric charge? Do we know why we can have an electric monopole but not a color monopole, if that’s the correct term?

Does the Standard Model answer these questions or does it merely say that this it the way it is.

Does String Theory go farther in trying to answer these questions?

Thanks,
Rob

2

Well, IANAP likewise, but a quasi-philosophic answer would be: At some level of detail, the answer must be simply “Because that’s just the way it is”.

If there are explanations in the Standard (or any) Model for the OP’s questions, they must necessarily rest upon even more fundamental constructs (like, possibly, for example, String Theory), so the ultimate question “Why, Daddy?” just gets pushed down a layer.

From what I can make out from reading stuffs about Quantum-anything (much of right here on this message board), the current thinking is that all “solid matter” is just an illusion, the reality being that the Universe is just a sea full of several mysterious “forces” sloshing around. Where these “forces” happen to pile up (like wave crests meeting to create a bigger wave crest), these forces create the emergent appearance of solid matter that we think we see. And apparently, these forces can act upon each other so that these confluences of “crests” that glom together might, in some cases, stay together, thus creating long-lived particles like protons (which I read somewhere have a statistical half-life greater than the estimated lifetime of the Universe); while other “particles” are very ephemeral and decay in microseconds.

3

There are a lot of different questions here, so I’ll take a stab at only a few.

Depends on what you mean by ‘why’. The standard model describes quite a few processes that produce quarks, electrons, neutrinos, and any other particle in it. For example, beta decay is the common process in which a neutron decays via the weak interaction into a proton, an electron, and a neutrino. Some of the confusion around this sort of behavior is about where the end-products— the proton, electron, and neutrino— are to begin with. Despite the term ‘decay’, a proton isn’t a bag containing the other particles that gets ripped open, causing them to spill out. It’s an interaction; there really isn’t any classical analogue to particle creation or destruction, whether in classical mechanics or classical quantum mechanics. In another direction, consider what happens when an electron and positron annihilation, releasing a pair of photons. The same process can happen in reverse, creating a position and electron from a pair of energetic photons. The two fermions aren’t sitting around beforehand; they’re just the effects of a new distribution in energy, quantum numbers, and so on.

Experimentally, we don’t see electron decay. Processes have to conserve certain quantitites: energy, momentum, electric charge, and a few more exotic things. If there were smaller particles for the electron to decay into (producing the energy, electric charge, etc. that we observe in the electron), then it would in fact decay into them. We don’t see that, so presumably those constituent particles don’t exist.

This is a tricky question. The short answer is anomaly cancellation and gauge theory. The long answer is the short answer with more math.

4

well the long answer may be to explain why guage theory, quarks properties, chromatic theory, pauli exclusion principle… all seem like a sensible start, but don’t really work.

Perhaps the Weyl mesons, the perturbative theory, the …-2,-1,0,1,2,3 quantisations of the various properties (eg for electric charge its 1/3 , 2/3, 1 of e, but if the unit was 1/3rd e, then its 1,2,3 … ) point to the idea that its really when the fields fit together in some way… such as its possible to pair them and possible to three leaf clover… but not more ?

The Weyls, observed just recently, point toward “The fields add together nicely” as the explanation, the perturbation particles stability suggest that there’s some tolerance in the fit.

5

To add a bit: electrons don’t decay, but other particles do decay into electrons. The *muon *and the tau can be thought of as “heavy electrons”, since they behave like electrons except with much larger masses. They are also unstable and decay into electrons (and some other particles). Electrons appear to be the end of the chain.

6

The books have to balance. Not at every instant but, when everything is tallied, all of the numbers have to come out right.

There’s a kind of event, or interaction, called beta decay. Actually, there are a few forms of beta decay, and I’ll only talk about one of them, because it’s easier. I’m going to talk about β[sup]−[/sup] decay, which is when a neutron turns into a proton.

A neutron has a charge of zero. A proton has a charge of +1. Now, we know that charge is conserved, which means that it can’t be created or destroyed, which means that if you have zero charge going into the interaction, you have to end up with zero net charge coming out of it. Therefore, β[sup]−[/sup] decay creates an electron, with charge -1. +1-1 = 0. Check.

There is, of course, a further check to this theory: We can observe electrons. They’re charged particles. They make nice little tracks in the bubble chambers because they disturb other charged particles, like the ones in the atoms the gas in the bubble chamber is made from.

There’s another problem: A neutron weighs more than a proton. It isn’t much but, you guessed it, mass is conserved. Mass can be conserved by converting it into energy, but that isn’t happening here. We can detect gamma rays, too, and we aren’t seeing any. Further, nothing’s going fast enough for the extra mass to have been converted into momentum. Therefore, either mass isn’t being conserved or we’re missing something.

Since mass conservation holds absolutely in every other interaction, the smart money was that we were missing something.

So we could predict the properties of the particle we needed: Small, because the missing mass was small, and not electrically charged, because the emission of the electron took care of that, and, besides, we could detect a small electrically charged particle.

We knew it was small for another reason: It wasn’t jostling anything else loose. It had to be small, or else it would have disturbed some atomic nucleus enough to leave evidence of its passing.

Anyway, that takes you up to 1931, when Wolfgang Pauli first hypothesized the existence of what we now call the neutrino. It took until 1956 to actually detect the damned things. Why? They’re small neutral particles, which can pass through bulk matter, like plants or humans or planets, like tiny snowflakes falling through wide mesh: Most of them pass right through and don’t do anything at all. The few which do interact, do so so minutely, it gets lost in the noise of everything else. It requires tons of pure water in deep salt mines to detect the barest fraction of the billions of neutrinos the Sun shoots through us every second.

So that should give you some idea of how we can predict the existence of particles decades before we get to observe them, simply by determining which particles must be necessary and which properties they must have based on our theories. Of course, the theories could be wrong, but keep in mind that every new theory has to make all of the same successful predictions the existing one did, and then some.

Well, that was extremely over-simplified. In fact, it left out a whole particle: The existence of the W[sup]−[/sup] boson is firmly beyond the scope of this post.

http://www.astro.wisc.edu/~larson/Webpage/neutrinos.html

7

Irrelevant. No matter how much energy you give a neutrino, it’ll never have any more than a minuscule chance of interacting with other particles. Electrons, protons, or other non-neutrino particles with the same energies, meanwhile, will interact just fine. The fact that neutrinos interact only weakly is completely unrelated to the fact that they have very low mass: One could just as well have a high-mass weakly-interacting particle, and in fact it’s widely expected that the dark matter is made up of some sort of such a particle (or assortment of such particles).

8

I guess I am asking is what questions does the Standard Model answer with “because I said so.”

As an analogy, Feynman related a story wherein his father asked him to notice that a ball in his wagon stayed still when the wagon moved. We know what the ball will do, and we can do all sorts of calculations and predictions, but why it should do this, no one knows.

9

The Standard Model consists basically of a list of fundamental particles, and a set of rules for the interactions between those particles. Those are the “because I say so” of the theory. Of course some things emerge from that layer, too, like the wide variety of different ways that quarks can be combined into hadrons.

10

To an extent, yes. We don’t know why the particle content of the Standard Model is exactly what it is, but the mathematical structure of the Standard Model does require certain conditions to hold for the fundamental particles. Of note is the cancellation of “anomalies” in the model, where a certain arithmetic combination of the charges of the fundamental particles has to equal zero for the model to work out mathematically. So you can’t just dial, say, the electron’s charge around and still have a mathematically sound theory.

The existence of three quark colors ties directly to the type of fundamental symmetry used to describe the strong force (by design of the Standard Model, since it needs to describe nature at the end of the day). And this number three is related to the 1/3n charge on quarks: that is, all “up” quarks taken together (blue + red + green) have an integer charge, and this feeds into the anomaly cancellation. So, from a fairly fundamental symmetry built into the Standard Model, you get 1/3n charges for quarks.

(I’ve glossed over the distinction between “charge” and the messier but more relevant quantity “hypercharge”, but the story is the same.)

The anomalies cancel in the Standard Model within single families (or generations), so the above does not have any bearing on why there are three families of fundamental particles. There needn’t be three families in the Standard Model, aside from anthropic reasons. There are theories beyond the Standard Model that attempt to motivate the existence of three families.

Sort of. The Standard Model certainly describes this without any trouble and without having to “patch” it in, but that’s different from knowing why it needs to be so in nature. Also, the math describing the strong force is notoriously hard to work with analytically, so the fact that colors are confined is known through simulation or approximate calculations with the Standard Model (plus the actual experimental evidence, of course).

String theory is more directed at building a deeper mathematical scaffolding on which to describe the forces of nature. In particular, it would be nice if gravity could be unified with the other forces so that they all can be described in somewhat parallel language, possibly cleaning up some of the uglier aspects of the Standard Model along the way. As a side note, string theorists tend to work with simpler universes (though not simpler mathematical underpinnings for the models) than what we see in nature. Issues like “there are actually three families of fermions” are complications usually not relevant to the main line of work.

11

I might be mistaken here, but I don’t think there’s even any particular reason known why the number of quark families “should” be the same as the number of lepton families.

12

They have to match in the Standard Model to keep it renormalizable. You couldn’t kill just, say, the top and bottom quark and still have a working theory.