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I wonder whether there is any theoretical interest in and/or experimental search for double charged bosons, probably to be called $W^{++}$ and $W^{--}$. The latter would obviously turn an electron into a positron by carrying away two units of charge, as well as the lepton number $\Delta L=2$. If existent, their mass could well be within the range of Higgs-searches at CERN.

Is there any 'particle data group' data on this? There only seems to be interest in $H^{\pm\pm}$ now. What would be the difference in experimental signature?

Is there any theoretical consideration? Note that I do not suggest that these should be gauge bosons in the usual sense. One possibility would be some compositeness of gauge bosons, thus resulting in the question whether and $W^{\pm\pm}\sim e^\pm e^\pm$ also are to be included along with $W^\pm \sim e^\pm \nu$.

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  • $\begingroup$ There may be models with these higher exotic charges of the bosons etc. but if you want particles at the LHC energy scale that can turn an electron into a positron, the particle either has to carry $\Delta L=\pm 2$, or its interactions have to violate the lepton number conservation law. If an LHC-scale particle were able to violate the lepton number conservation law, it would cause other lepton-number-violating processes (and probably also baryon-number-violating ones, including the decay of the proton) which are not observed. So this possibility is pretty much excluded. $\endgroup$
    – Luboš Motl
    Commented May 30, 2016 at 13:31
  • $\begingroup$ On the other hand, a gauge boson should carry $L=0$. So $W^{++}$ should better be a scalar, an exotic one. You may be imposing too many special conditions on your model of the Beyond the Standard Model physics. There are many models like that, many of them are studied but many of them may be quickly excluded because they predict additional consequences that are often safely known not to exist. $\endgroup$
    – Luboš Motl
    Commented May 30, 2016 at 13:32
  • $\begingroup$ @LubošMotl : Edited to include lepton number conservation and non-gauge nature of bosons. Still ruled out? $\endgroup$
    – NUU
    Commented May 30, 2016 at 13:41
  • $\begingroup$ I don't have a full proof but I am confident that if you want spin-1 bosons with a nonzero lepton number and LHC masses, they are ruled out. It's an extremely exotic beast if it carries both lepton number and spin-one. Gauge fields should be more blind towards leptons. You know, even leptoquarks which carry both lepton+baryon number are very exotic but to make it for gauge bosons that moreover couple to electrons, it's yet another league. $\endgroup$
    – Luboš Motl
    Commented May 30, 2016 at 13:46
  • $\begingroup$ OK, great, I realized that this is exactly what Paul Frampton has been trying to persuade me about, so I posted a "positive" answer about it. $\endgroup$
    – Luboš Motl
    Commented May 30, 2016 at 14:08

1 Answer 1

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I am answering a question after some clarifications.

If the gauge field maps the electron to a positron, it really connects the left-handed 2-spinor and right-handed 2-spinor in the Dirac's electron field into one multiplet. But that field is also a part of the $SU(2)_W$ doublet with the neutrinos. So the theory you are proposing wants to extend the electroweak (electron,neutrino) doublets at least to triplets.

These theories are studied, the simplest ones have $SU(3)_L$, an extension of the electroweak $SU(2)_L$, and the new gauge bosons indeed carry $L=\pm 2$. Some special models with three inequivalent generations but anomaly cancellation exist (the 331 model) and you find lots of papers of this kind if you search for papers co-authored by Paul Frampton:

https://arxiv.org/abs/hep-ph/9304294

Many similar papers (also co-authored by Sheldon Glashow, and boasting the "chiral color" brand) may be found by this search:

https://scholar.google.com/scholar?q=frampton+su(3)l&hl=en&lr=&btnG=Search

In recent years, I actually got a lot of e-mails and (rejected) blog posts from Paul Frampton who seems excited about them. He also believed that there are experimental signs in favor of such models. I am obviously no expert in "chiral color" but it seems to me that the number of such papers dropped significantly once the LHC began to produce nontrivial data.

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  • $\begingroup$ Now THAT is pretty exotic! What I had in mind is rather some (yet to be fully specified) composite model of (gauge) bosons. If $W^+$ would be some composite of $e^+$ and $\nu$, there should also be composites of $e^+$ and $e^+$ and so on... $\endgroup$
    – NUU
    Commented May 30, 2016 at 14:25
  • $\begingroup$ There can't be a bound state of an electron and a neutrino because it would have to be lighter than the electron (neutrino is almost massless) to be bound, and it would replace electrons in the atoms etc. Also, there's no strong enough interaction to hold neutrino bound to pretty much to anything. Moreover, I don't understand why you would discuss bound states, they are calculable from the Standard Model, right? $\endgroup$
    – Luboš Motl
    Commented May 30, 2016 at 14:57
  • $\begingroup$ Just an idée fixe, which I will probably discuss in another question. It's not really about 'bound' states... $\endgroup$
    – NUU
    Commented May 30, 2016 at 15:12
  • $\begingroup$ Do you think that "composite" and "bound" is something else here? Why? $\endgroup$
    – Luboš Motl
    Commented May 31, 2016 at 4:08

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