$W^{++}$ / $W^{--}$ Bosons in theory and experiment 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 $W^\pm \sim e^\pm \nu$.
 A: 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.
