# What Would be the Experimental Signature of Composite Leptons?

So far, the quarks and leptons appear to be fundamental particles. But they're complicated enough that there's always been some speculation that they might be composite.

What experimental evidence would be needed to show that a lepton is composite?

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1
Of course this is motivated by rumors mentioned in Dr. Motl's blog. There's been some experimental searches for excited leptons such as: Phys.Lett.B525:9-16,2002, H1 Collaboration: C.Adloff, et al, Search for Excited Neutrinos at HERA arxiv.org/abs/hep-ex/0110037 – Carl Brannen Mar 14 '11 at 21:44
– Gordon Mar 15 '11 at 6:03
Great question, (future?) Dr Brannen. Let's see how the answers match the quality. :-) BTW the top-antitop asymmetry could be a sign, too - assuming that the up-quark and top-quark share something in their composite setup. – Luboš Motl Mar 15 '11 at 6:47
@Luboš Motl, I hope to see a top-antitop asymmetry post on your blog soon. And unfortunately, to get to be "Dr. Brannnen", I first have to get into grad school. I'm looking at 3rd tier (and lower) grad schools right now. – Carl Brannen Mar 15 '11 at 22:48
LOL at Georg's ESL edit of title. – Carl Brannen Mar 16 '11 at 2:30

## 5 Answers

CMS has a preprint out where they are searching for compositeness in dijet angular distributions.

The measured dijet angular distributions can be used to set limits on quark compositeness represented by a four-fermion contact interaction term in addition to the QCD Lagrangian.

They set limits.

I will guess that angular distributions of two lepton events will be in the search of lepton compositeness.

Considering that the compositeness of nuclei and compositeness of nucleons were cleanly found by deep inelastic scattering, I would be very doubtful of interpretations using levels of monte carlo calculations that would give such a drastic conclusion to deviations from QCD.

One would have to wait for lepton colliders . From LHC I would need two leptons at a vertex to get the other end of deep inelastic scattering. There is nothing that can beat form factors, imo.

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With the right equipment and enough energy you can look for all the usual naive stuff:

• Deviations from the Bhabha scattering cross-section in unpolarized $l + \bar{l}$ or $l + l$ scattering. In particular if there is missing energy in the reaction that might indicate an excited state in the products.
• Resonance peaks in in $l + \bar{l}+ \to l' + \bar{l}'$. (Of course you can do this with $q + \bar{q} \to l + \bar{l}$ too, but the QCD corrections to the quark vertex makes the theory harder and may hide the signal.)

I think this is part of the case for a muon collider, but none of it is on the table for experiments running right now.

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Dear dmckee, that's nice but imagine, just for the sake of an argument, that a member of CMS says during a press conference at some point in 2011 that the CMS has collected evidence of lepton compositeness. What do you think that they would have to have seen in order to make similar surprising statements? ... I didn't quite understand why the deviations you mention - their very being - would be characteristic of lepton compositeness as opposed to any new physics. – Luboš Motl Mar 15 '11 at 6:49
@Lubos: This kind of bump-hunting is necessary, but not sufficient. You're absolutely correct about that. Using lepton beams reduces the complexity in terms of possible initial states, but of course does not prevent QCD from interfering at the loop level. – dmckee♦ Mar 15 '11 at 18:26

One signature could be similar to that of a parton model. Suppose leptons are composed of internal particles, preons or rishons or what-ever-ons. At low energy the lepton will appear to be composed of the valence partons (lepto-partons?), which might just be the lepton itself. As one transforms to a high energy frame, then in the limit this momentum goes to infinity the Lorentz contraction of the lepton makes other modes, or higher energy partons in excited states, apparent in scattering experiments. There would then be a Bjorken scaling to scattering amplitudes which act as signatures of the internal constituents of a lepton.

Another signature could be some deviation in the magnetic moment of the electron. The magnetic moment is $$\mu_s~=~-g_s\mu_{bohr}S/\hbar.$$ For a Dirac electron with the EM field "turned off" the g-factor is $g_s~=~2$. In QED this is $g_s~=~2.00231930436$. If the electron is a constituent particle then there might at some scale be a deviation from the QED expected result.

What might these constituents be? Most likely any such deviation would to my mind be some stringy physics which due to extra large dimension and related matters is exhibiting an influence on a scale we can detect. I don’t like the idea of quarks and leptons as composite objects. This is largely because the energy in binding this system together would be much larger than the masses of the partons. This would present us with horrendous problems far surpassing those seen with quarks and QCD.

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• Composite electrons, muons and taus ought to be much easier to detect in high energy conditions where an electomagnetic field influences decay product paths than composite neutrinos (which are damned hard to observe much of anything about without elaborate and not very statistically powerful purpose built experiments like those being discussed at Neutel11).

If components parts of electon-like leptons had a charge other than -1 (or +1 for antiparticles), the path that even briefly unconfined lepton components took ought to be possible to reverse engineer with great precision (and without a lot of the QCD background issues that make some of the other calculations harder to do -- because you'd be looking at the distribution pattern of where the decay products end up in space relative to the collision point, rather than how many there were).

IIRC, there has been some recent experimental signals that show these kinds of unexpected and unexplained spatial distribution patterns.

• Another way to see composite electrons in confined state would be to detect events with signatures that are like mesons or exotic baryons, but much lighter that had previously been screened out of data since we weren't looking for anything like that in that mass range. For example, suppose that you revised your decay data sorting software and suddenly saw several dozen decays of a particle that was behaving like a Delta plus plus baryon (spin 3/2, charge +2, ddd), but with a mass on the order of 123 eV instead of 1232 MEv.

• A third possiblity would be that you could look at processes that appear to show beyond the Standard Model CP violation and do some kind of cluster analysis of the data that show one group of events that closely match the Standard Model and a separate group of events that has some pattern that distinguishes it and then show how a composite lepton model could explain the pattern common to the "excess group".

• Strong evidence of B-L non-conservation that seems to be coming from something in the lepton sector.

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In my humble opinion, there are sufficient experimental and theoretical data to consider things to be composite because of their permanent coupling to other things. The problem is in recognizing this permanent coupling and implementing it correctly in our theories.

Let us consider the simplest case of scattering a neutral particle, neutrino, from a charged particle, electron:

$\nu + e^- \rightarrow \nu + e^-$. (1)

It is, however, unlikely to scatter from a charge elastically because there are thresholdless excitations - photons. In other words, the real charge ($e^-$) is a complicated system including the electromagnetic degrees of freedom and the electron in it is only a part of it. So the true scattering process is written differently:

$\nu + e^- \rightarrow \nu + e^- + \gamma_1 + \gamma_2 + ...$ (2)

Again, exciting a target (= inelastic processes like (2)) is the first and the principal evidence of the target being compound. And we know from the exact QED equations about this permanent coupling but we do not initially consider the charge to be coupled and write rubbish like (1). This is our grave conceptual error. So inelastic processes like

$\nu + e^- \rightarrow \nu + e^- + \gamma +$ other neutral stuff (3)

testify that our target (electron) is not so simple ;-).

We still do not note evident things and decouple coupled things in our minds and on the paper. Our methodology of "switching the coupling on and off" is wrong - it implies a possibility of perturbative "coupling" as if it were "weak". It is never weak. When we manage to describe QED correctly, it will be easier to see how other leptons and quarks (and other quasi-particles in composite things) are related to each other.

Take an atom as a composite system and scatter from its nucleus or electron. What is a signature of its being composite? Inelastic channels and resonances.

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