I Upper end of nucleon overtones

[snorkack]

The spectrum of first generation resonances, counting Δ but including only 4 and 3 star particles (the latter in italics) goes:
p(938)1/2⁺
n(940)1/2⁺
Δ(1230)3/2⁺
N(1440)1/2⁺
N(1520)1/2^-
N(1535)1/2^-
Δ(1600)3/2⁺
Δ(1620)1/2^-
N(1650)1/2^-
N(1675)5/2^-
N(1680)5/2⁺
Δ(1700)3/2^-
N(1700)3/2^-
N(1710)1/2⁺
N(1720)3/2⁺
N(1875)3/2^-
N(1880)1/2⁺
N(1895)1/2^-
N(1900)3/2⁺
Δ(1900)1/2^-
Δ(1905)5/2⁺
Δ(1910)1/2⁺
Δ(1920)3/2⁺
Δ(1930)5/2^-
Δ(1950)7/2⁺
N(2060)5/2^-
N(2100)1/2⁺
N(2120)3/2^-
N(2190)7/2^-
Δ(2200)7/2^-
N(2220)9/2⁺
N(2250)9/2^-
Δ(2420)11/2⁺
N(2600)11/2^-

So, the series terminates around 2500 MeV.
What prevents existence of higher energy resonances?

 

[mfb]

PDG lists discovered particles only, with various degrees of certainty indicated by stars. There might be higher excited states but if they are wide (short-living) they can be impossible to find experimentally. If they are too wide it's questionable if we can talk about their existence as separate states at all.

 

[ohwilleke]

\What prevents existence of higher energy resonances?

Nothing.

In theory, higher energy resonances are possible, although hard to see. But, as @mfb correctly notes, "PDG lists discovered particles only" and those are the ones that we've discovered so far.

As @mfb also correctly notes, there might at some point be circumstances in which something intrinsically limits the possibility of discovering a more massive resonance. But there is no good reason to think that the current limit is anything more than a function of how much money we've spent so far on experiments and instrumentation designed to see it. If we spent another 500 billion Euros on a bigger and better collider than the LHC we would almost surely see at least a few higher mass excitations than we have so far, and would almost certainly verify or rule out some of the one or two star resonances seen so far.

 

[snorkack]

A mistake in my first post - wrong spin for one.
For example, the nucleons with lowest energy for a given spin:
p(938)1/2⁺****
N(1520)3/2^-****
N(1675)5/2^-****

N(1990)

7⁄2+

**

N(2220)9/2⁺****
N(2600)11/2^-***

N(2700)

13⁄2+

**

So, looking at the series - what in the known properties makes the N(2600) a *** particle, and N(1990) and N(2700) ** particles? Large width compared to the **** resonances like N(2220)9/2⁺? Low cross-section for formation? Why is there no observed N with spin 15/2, not even *? Can the mass, resonance width and formation cross-section of a nucleon of 15/2 spin be predicted?

 

[Astronuc]

4 and 3 star particles

If one were to consider two star (**), then one would note higher energy resonances.
** = evidence of existence is fair.

Isn't it a bit arbitrary to consider only **** and ***, which means "Existence is certain" or "Existence is very likely"? If one considers the ** entries, then one would observe ∆(2950) 15/2⁺, but the existence is fair (**). Ostensibly, there is some theoretical basis. So, to increase it to ***, what experimental evidence is needed?

From 2019 - https://pdg.lbl.gov/2019/reviews/rpp2019-rev-n-delta-resonances.pdf
compare to 2006 - https://www.jlab.org/conferences/Nstar/talks/Capstick.pdf (slides 9 and 13). Also see, cautionary notes on Slides 15 and 16.

Slide 15 of Capstick's 2006 presentation - "“In the search for ‘missing’ quark-model states, indications of new structures occasionally are found. Often these are associated (if possible) with the one- and two-star states listed in Table 1. We caution against this: The status of the one-and two-star states found in the Karlsruhe-Helsinki (KH80) and Carnegie-Mellon/Berkeley (CMB80) fits is now doubtful.”"

A seemingly more skeptical tone is expressed on Slide 16 - "1* states are a dream, 2* states are a fantasy," which is attributed to Steve Dytman, 2005

See also Capstick, Slide 21