Does the proton have n-pole excited states? Or n-pole excited states exist only for A>1?
Yes, http://pdglive.lbl.gov/listing.brl?fsizein=1&exp=Y&group=BXXX005 [Broken] lists states with up to L=5. The higher states are presumably too short-lived to have been significantly measured.
That's interesting. Because, if you search for excited states of the proton , you will find only the delta+ as an excitation, like this:
Obviously you were searching in the wrong place. The PDG is the right place to go. You can follow the references given there for more information that's not in their summary tables.
Incidentally, the [itex]\Delta[/itex]s have isospin 3/2, so they're not really excited states of the nucleon. They are a new family of particles.
The decay chains include the delta as intermediary states to proton. I think it is not very insightful to try to distinguish families of particles.
Yes and the muon decays to an electron, but we do not say that the muon is an excited state of the electron. It is precisely the quantum numbers like isospin that distinguish between families of particles.
But the muon, as far as the SM is concerned, is a fundamental particle. Those are excited states, just like the nucleons in a nucleus, or electrons in orbitals.
Yes that's true and so that was a bad example. It's not really wrong to think of the appropriate Deltas as excited states of the nucleons. They are excited states of uud and udd, but differ from the nucleons in that they have all quark spins aligned. So they are analogous to hyperfine structure in the hydrogen atom, rather than radial or angular momentum excitement. The uuu and ddd Deltas are of course not excited states of the nucleons.
Just calling the Deltas excited states seems to miss some important structure, which is the reason I was against the idea. I should not have said that it was wrong.
As an aside, the decay chains really can be misleading if you attempt to declare some high energy state an excited state. For example, both [itex]\Delta^+[/itex] and the charmed meson [itex]\Lambda_c^+[/itex] can decay to [itex]p\pi^+ \pi^-[/itex].
I am interested in the high state itself, figure out its properties, energies, etc. Not in how to detect it, so, I am not thinking in how false positive signals would be filtered.
I don't believe that there are any reliable ways to study hadron spectroscopy other than on the lattice. For example http://inspirehep.net/record/810135?ln=en is a recent study of the excited nucleon states in a lattice model. You can get get the citations to that paper from the link to search for any followup work.
The detection problem with very high level excited states is that the decay width is very large when compared to the mass of the state. So these are very broad bumps in the spectrum and can't be resolved against the background of other events.
I don't agree.
The Δ+ has the same quark content as the proton (uud), so it is a 'proton-excitation in spin- and isospin-space'. The same applies to the Δ0 which is an excitation of the neutron. This can be seen by the decay channels
[tex]\Delta^+ \to p+\gamma[/tex]
[tex]\Delta^0 \to n+\gamma[/tex]
which are allowed but suppressed by a branching ratio < 1% compared to nucleon-pion decay channel with ~100%.
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