I know that a pion can take place of an electron in an atom, but pion is not an elementary boson, but a particle made of constituents. However, my question regards elementary particles. Are there bound states for elementary bosons like photons, W, Z etc(maybe something like gluonium - two gluons bound together). And if yes, were they observed or is it only what theory allows?
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$\begingroup$ I think there were candidates for glueballs, observed in LHC, but I would also like to know the current status on this. $\endgroup$– KosmJun 1, 2017 at 12:17
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$\begingroup$ There have been glueball candidates around since at least the 1980s. Unfortunately, light unflavoured mesons are such a mess of broad, overlapping states that we'll probably never unambiguously identify a glueball. See pdg.lbl.gov/2017/reviews/rpp2016-rev-scalar-mesons.pdf and pdg.lbl.gov/2017/reviews/rpp2016-rev-non-qqbar-mesons.pdf $\endgroup$– dukwonJun 1, 2017 at 19:24
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In the spirit of "gluonium", there are (hypothetically) glueballs which can have far more than just two gluons. There isn't much else you can do.
You could also have "bound" W bosons, but for example a proton-W system would have the proton orbiting the much more massive W, not vice versa. A $W^+W^-$ system would be short-lived like positronium (assuming the Ws lived long enough for annihilation, but their short lifetime is a problem for any W-binding system).
Failing that you have to hope a weak or gravitational force can give you a bounded elementary boson, though again it may be short-lived.
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1$\begingroup$ Ouch! A positronium lives for a ns, so a millionth of a second. But the Ws in such a hypothetical bound state would decay themselves in $10^{-21}$ sec, no? $\endgroup$ Jun 1, 2017 at 16:22
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$\begingroup$ @CosmasZachos It will end quickly due to either annihilation or the particles decaying, but I've not calculated which happens first. $\endgroup$– J.G.Jun 1, 2017 at 17:02
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1$\begingroup$ Yes, i blew a factor of 1000, not that it matters. The width of the W is ~2GeV, so the lifetime is $10^{-24}$ sec. That's absurdly short, which is why people discuss widths and not lifetimes for such particles. $\endgroup$ Jun 1, 2017 at 18:31
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1$\begingroup$ The top quark's lifetime is $\sim 5 \times 10^{-25}$, which is smaller than the characteristic timescale of the strong interaction, i.e. too short to form bound states. There's no chance of W bosons forming bound states: the characteristic timescales of the electromagnetic and weak interactions are much longer than that of the strong interaction. $\endgroup$– dukwonJun 1, 2017 at 19:33