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- Why preon models aren't taken more seriously than they are
So, we had a set of messages about "rishons" which are a subcategory of models called "preon models" or "quark-lepton compositeness". The question of why these models aren't taken more seriously than they are is a good one, but unfortunately the question was wrapped in posts more likely to generate heat than light. So, here goes. I will try and keep things at an I-level, but by the nature of the discussion, it will need to be upper-division I.
(1) Preons don't really explain anything. "Elementary particles aren't truly elementary: they are composed of "preons", which are elementary" is the argument, and that just moves things down one more level of turtles. In the case of rishons, we replace four kinds of fermion with two. Is that really a vast improvement?
(2) There is no experimental evidence of quark or lepton compositeness. The limit for electrons is a few TeV (I am too lazy to look this up) and the mass is half an MeV. So there's a factor of maybe 10 million difference in scales. The equivalent number for atoms (and indeed, the experiments are analogs of the Rutherford-Geiger-Marsden experiment) is 100,000. So while one can never say that we won't find evidence if we just look a little harder, it's also true that we have looked pretty hard.
(3) Think about how this must work quantum mechanically. As said above, electrons are very small - length scale of TeV. (If lengths in TeV are confusing, you can convert to meters using the factor 200 MeV fm = 1). That means that their constituents need to be highly localized - i.e. have a small Compton wavelength, and thus be heavy. That means they need to be bound deeply in order for the composite to have a low mass. How deeply? If an electron is made up of two 10 TeV preons, they are bound by 199999999488998 eV. Every digit there is significant - this is called "fine tuning", Two quantities that have nothing to do with each other - the preon mass and the strength of its binding force -need to be the same to many decimal places.
(4) Preon models struggle with flavor. Why are there 3 generations of quarks and leptons? One way around this is to have 3 generations of preons. But this makes point 1 even worse. Now we replace twelve kinds of fermions with six. Does one really want to argue that twelve is unacceptably huge and six is just fine? Probably not.
The second way around this is to say that the 2nd and 3rd generations are just excited states of the first. The problem is that this induces decays that are not observed, like μ→eγ at a very, very high rate. This decay should dominate, when in fact its so rare it has never been seen. Furthermore, in (3) we discussed what the preon potential must look like: very, very small in spatial extent, and very, very deep. This sounds a lot like a delta function, and a delta function has only one bound state. Not three.
(5) Preon models have trouble with proton decay. Because quarks and leptons are made of the same kind of stuff, decays should exist like p→e+X. It is difficult to keep the rate under the 1034 year bound. Most theories need some sort of fix to this. Rishons do this by having some fortunate cancellations, so the lifetime is ~Λ8/m7 where m is the proton mass. This means that the relevant energy scale is 100,000 TeV, not 10 TeV. That, in turn, works out to a fine-tuning that is 10,000 more finely-tuned.
So, while these models aren't excluded, most folks don't pay them much mind: they have lots of problems, little predictive power, aren't necessary to explain anything, and there is no evidence for them in the data.
(1) Preons don't really explain anything. "Elementary particles aren't truly elementary: they are composed of "preons", which are elementary" is the argument, and that just moves things down one more level of turtles. In the case of rishons, we replace four kinds of fermion with two. Is that really a vast improvement?
(2) There is no experimental evidence of quark or lepton compositeness. The limit for electrons is a few TeV (I am too lazy to look this up) and the mass is half an MeV. So there's a factor of maybe 10 million difference in scales. The equivalent number for atoms (and indeed, the experiments are analogs of the Rutherford-Geiger-Marsden experiment) is 100,000. So while one can never say that we won't find evidence if we just look a little harder, it's also true that we have looked pretty hard.
(3) Think about how this must work quantum mechanically. As said above, electrons are very small - length scale of TeV. (If lengths in TeV are confusing, you can convert to meters using the factor 200 MeV fm = 1). That means that their constituents need to be highly localized - i.e. have a small Compton wavelength, and thus be heavy. That means they need to be bound deeply in order for the composite to have a low mass. How deeply? If an electron is made up of two 10 TeV preons, they are bound by 199999999488998 eV. Every digit there is significant - this is called "fine tuning", Two quantities that have nothing to do with each other - the preon mass and the strength of its binding force -need to be the same to many decimal places.
(4) Preon models struggle with flavor. Why are there 3 generations of quarks and leptons? One way around this is to have 3 generations of preons. But this makes point 1 even worse. Now we replace twelve kinds of fermions with six. Does one really want to argue that twelve is unacceptably huge and six is just fine? Probably not.
The second way around this is to say that the 2nd and 3rd generations are just excited states of the first. The problem is that this induces decays that are not observed, like μ→eγ at a very, very high rate. This decay should dominate, when in fact its so rare it has never been seen. Furthermore, in (3) we discussed what the preon potential must look like: very, very small in spatial extent, and very, very deep. This sounds a lot like a delta function, and a delta function has only one bound state. Not three.
(5) Preon models have trouble with proton decay. Because quarks and leptons are made of the same kind of stuff, decays should exist like p→e+X. It is difficult to keep the rate under the 1034 year bound. Most theories need some sort of fix to this. Rishons do this by having some fortunate cancellations, so the lifetime is ~Λ8/m7 where m is the proton mass. This means that the relevant energy scale is 100,000 TeV, not 10 TeV. That, in turn, works out to a fine-tuning that is 10,000 more finely-tuned.
So, while these models aren't excluded, most folks don't pay them much mind: they have lots of problems, little predictive power, aren't necessary to explain anything, and there is no evidence for them in the data.
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