What are the different types of long-lived hadrons and their properties?

[snorkack]

TL;DR Summary

Trying to review the list

Checking systematically the list of possible combinations of di- and triquarks...
There are 5 quarks that can form hadrons.
Diquarks formed of alike quark and antiquark are all short-lived:
π⁰ - 135,0 MeV; 0,085 fs; the rest even shorter
This leaves 10 pairs of unlike quark and antiquark:
1 pair of charged pions:
1) π^- - 139,6 MeV; 26 000 000 fs
2 pairs of kaons:
charged:
2) K^- - 493,7 MeV; 12 400 000 fs
neutral, with two different lifetimes:
3) K_L⁰ - 497,6 MeV; 51 100 000 fs
K_S⁰ - 497,6 MeV; 89 500 fs
3 pairs of D mesons:
2 charged:
4) D^- - 1869,6 MeV; 1040 fs
5) D_s^- - 1968,3 MeV; 500 fs
1 neutral, oddly unlike kaon a single lifetime:
6) D⁰ 1864,8 MeV; 410 fs
4 pairs of B mesons:
2 charged:
7) B^- 5279,3 MeV; 1640 fs
8) B_c^- 6275,6 MeV; 450 fs
2 neutral, each also a single lifetime:
9) B⁰ 5279,6 MeV; 1520 fs
10) B_s⁰ 5366,8 MeV; 1510 fs
Note one significant observation: all 10 unlike diquarks predicted by combinations have been seen and described with mass and lifetime.

 

[Orodruin]

Summary: Trying to review the list

I suggest looking in the PDG.

This leaves 10 pairs of unlike quark and antiquark:

Meson and baryon states are not solely determined by the quark-antiquark combination.

 

[snorkack]

PDG is generally the (indirect) source of my data. Looking in, I do not see the data there arranged in the specific way I prefer. So rearranging them for better organization.
Now to triquarks...
There are 4 possible combinations of 3 quarks of 2 types u and d: uuu, uud, udd, ddd
Now, 3 identical quarks like uuu and ddd can only have spin 3/2, or higher excitations. 2 identical and 1 different quarks can have spins 3/2 or 1/2, and 3/2 is a shortlived excited state.
1) uuu - Δ⁺⁺ 1232 MeV; but uud is 938 MeV and π⁺ 140 MeV, so total 1078 MeV and Δ⁺⁺ is a resonance
2) uud - p⁺ 938,3 MeV; stable
3) udd - n⁰ 939,6 MeV; 880 000 000 000 000 000 fs
4) ddd - Δ^- 1232 MeV; resonance
Combining 3 quarks of 3 types u, d and s has 10 options, 4 of which are u and d alone, described before. This leaves 6 new combinations. Again, 3 alike quarks must be spin 3/2, while 2 alike 1 different quark has spin 3/2 excited and 1/2 ground state. 3 different quarks has 2 states spin 1/2, of which 1 is a shortlived excited state.
5) uus - Σ⁺ 1189,4 MeV; 80 200 fs
6) uds - Λ⁰ 1115,7 MeV; 263 000 fs
7) dds - Σ^- 1197,4 MeV; 148 000 fs
8) uss - Ξ⁰ 1314,9 MeV; 290 000 fs
9) dss - Ξ^- 1321,7 MeV; 164 000 fs
10) sss - Ω^- 1672,4 MeV. 82 000 fs; Note that Ξ⁰(1315)+K^-(494) would be 1809 MeV. Unlike uuu and ddd, which are resonances, sss is not.
Which means that out of the 10 combinations of u, d and s, all are seen and described, and 2 of the 10 are confirmed resonances, 8 longlived.

 

[Orodruin]

Now, 3 identical quarks like uuu and ddd can only have spin 3/2

$\Delta(1620) 1/2^-$ would like a word …

 

[Orodruin]

I do not see the data there arranged in the specific way I prefer

Did you stop to think why? The way that you prefer does not seem to make much sense. Consider that the presentation in PDG is written by people who - generally - will have a better understanding of hadron physics than you do. Perhaps there is a reason as to why they have chosen to present things in a particular fashion and not in the way you seem to think preferable.

 

[snorkack]

I certainly had not seen your reply about Δ (1620) when I edited my post.
There would be 20 combinations of 3 quarks of 4 types, and 35 combinations of 3 quarks of 5 types. 10 of them are described before. This leaves 25 combinations:
11) uuc - Σ_c⁺⁺ 2454 MeV but udc is 2286 MeV, and π+ 140 MeV, so total 2426 MeV and uuc is a resonance
12) udc - Λ_c⁺ 2286,5 MeV; 202 fs
13) ddc - Σ_c⁰ 2454 MeV resonance
14) usc - Ξ_c⁺ 2467,9 MeV; 456 fs
15) dsc - Ξ_c⁰ 2470,9 MeV; 153 fs
16) ssc - Ω_c⁰ 2695,2 MeV; 268 fs
17) ucc - Ξ_cc⁺⁺ 3621,6 MeV; 260 fs
18) dcc - +1 unseen
19) scc - +1 unseen
20) ccc - +2 unseen
21) uub - Σ_b⁺ 5810 MeV, but udb is 5620 MeV and π+ 140 MeV, so total 5760 MeV and uub is a resonance
22) udb - Λ_b⁰ 5619,6 MeV; 1470 fs
23) ddb - Σ_b^- 5815 MeV resonance
24) usb - Ξ_b⁰ 5791,9 MeV; 1480 fs
25) dsb - Ξ_b^- 5797,0 MeV; 1570 fs
26) ssb - Ω_b^- 6046,1 MeV; 1640 fs
27) ucb - +1 unseen
28) dcb - 0 unseen
29) scb - 0 unseen
30) ccb - +1 unseen
31) ubb - 0 unseen
32) dbb - -1 unseen
33) sbb - -1 unseen
34) cbb - 0 unseen
35) bbb - -1 unseen

 

[snorkack]

Did you stop to think why? The way that you prefer does not seem to make much sense. Consider that the presentation in PDG is written by people who - generally - will have a better understanding of hadron physics than you do. Perhaps there is a reason as to why they have chosen to present things in a particular fashion and not in the way you seem to think preferable.

The way they do present the data makes a sense. What they are doing
https://pdg.lbl.gov/2022/tables/contents_tables.html
is presenting a lot of actual observations, what has been found about various reactions, and resonance excited states. N and Δ between them (4 combinations out of 35) take up 20 and a half pages out of 63. Doubly charming baryons (3 combinations they mention, only 1 of them seen) under a half.
You could just as well have a handbook of chemical compounds and reactions which is mostly full of reactions of element 6 (carbon - organic chemistry) and which has nothing whatsoever about element 87 (francium - too shortlived to observe compounds or reactions). This is useful - but what also is useful, and ubiquitous, is a periodic table, where element 87 takes up a square as big as element 6.
Now, as I demonstrated above, out of the 35 possible combinations of 3 quarks out of 5, 12 are unseen. This is nonrandom: out of the 13 possible baryons with 2 or more heavy quarks, only 1 doubly charming quark has been seen. In contrast, all 10 mesons have been seen - even the charming beautiful meson. No charming and beautiful baryon has been seen.
Out of the 23 seen baryons, 6 are confirmed to be resonances.

 

[Orodruin]

N and Δ between them (4 combinations out of 35) take up 20 and a half pages out of 63.

That would be because, contrary to your assumptions, there are several $N$ and $\Delta$ resonances and they are the most experimentally accessible ones.

 

[snorkack]

That would be because, contrary to your assumptions, there are several $N$ and $\Delta$ resonances and they are the most experimentally accessible ones.

I am not assuming that they don´t exist! I am very aware that there are many of them! However, they are all resonances - extremely short-lived excited states. Which is why I wanted to concentrate on longlived states, as I stated in title - states which do not have easy strong interaction decay paths and which therefore may end up living long and decaying by weak interaction... but which might also have a low probability of being produced in the first place.

 

[mfb]

dcc we probably have

All the unseen combinations have at least two heavy quarks (c,b), so their production rate is low. ucc has the advantage of having +-2 charge, which reduces the background.

Sorted by increasing difficulty we might find scc, ucb/dcb, scb with more statistics. Two b quarks or ccc and beyond... I guess people will try, but I'm not sure how much chance we have there.

 

[snorkack]

Counting the charges, I observe:
There are 6 pairs of charged mesons.
Baryons I count:
charge -1: 5 seen, 3 unseen
charge +1: 4 seen, 4 unseen
charge +2: 1 seen, 1 unseen (The seen one is ucc. The unseen one is ccc. Note that as I throughout exclude confirmed resonances, this excludes uuu and uuc).

 

[ohwilleke]

I would evaluate the question a little differently and focus on the bigger picture.

The Loveseat Of Long Lived Hadrons and the Long Lived Fundamental Particles

Hadrons

The "zoo of long lived hadrons" is more like a loveseat.

There are exactly two hadrons with mean lifetimes in excess of 10^-5 seconds: the proton, which is stable, and the neutron, which has a mean lifetime of about 15 minutes (879.6±0.8 s) when free and is stable in a bound state within a stable atomic nucleus.

(The complete stability of the proton is theoretical, but proton decay has never been observed and the experimental lower bound on the mean proton lifetime is not shorter than the age of the universe and then some.)

If you really want to be pedantic about it, you'd also include the anti-proton and anti-neutron, which have exactly the same mean lifetimes. But, in practice, the universe is so matter dominated (relative to antimatter) that, absent magnetic cages, anti-protons and anti-neutrons almost always annihilate swiftly upon coming into being when they bump into ordinary matter that is almost everywhere. So, anti-protons and anti-neutrons end up being short lived in practice even if they are not short lived in theory.

Leptons

The only charged lepton with a mean lifetime in excess of 10^-5 seconds, of course, is the electron, which like the proton is stable.

Neutrinos (which are neutral fundamental leptons rather than hadrons) are "metastable" (not really the right word) in the sense that they can oscillate between generations in some circumstances, but don't "decay" as such.

Stable Fundamental Bosons

Individual photons are stable, lasting until they are absorbed by a charged particle (possibly billions of years), or together with another photon lead to photo-production of something else.

As explained below, gluons don't precisely "decay' but are short lived because they are confined within hadrons and move at the speed of light over very short distances between color charged quarks and gluons.

The Zoo Of Short Lived Hadrons and Fundamental Particles

The muon and three kinds of spin zero pseudo-scalar mesons (and their antiparticles) have mean lifetimes of more than 10^-9 (i.e. one billionth) of a second.

The mean lifetime of a muon, the second generation electron, which is a fundamental particle in the Standard Model, is on the order of 10^-6 (i.e. a millionth) seconds. This is about 100 times as long as the three longest lived types of mesons discussed below. It can decay only via the weak force.

The charged pion made of an up quark and an antidown quark, the charged kaon made of an up quark and an antistrange quark, and the long form of the neutral kaon consisting of the linear sum of a down quark and an antistrange quark (which appears only in combination with the short neutal kaon linear combination of the difference between that particle with a much shorter mean lifetime), all have mean lifetimes on the order of 10^-8 seconds.

The Many More Very Short Lived Hadrons and Fundamental Particles (Lifetimes Less Than 10-9 s And More Than 10-25 s)

About a hundred other kinds of hadrons, tau leptons (i.e. third generation electrons), top quarks, W bosons and Z bosons all have mean lifetimes of less than a billionth of a second. Gluons are also effectively very short lived.

The Six Most Ephemeral Fundamental Particles

A tau lepton (i.e. a third generation electron) has a mean lifetime on the order of 10^-13 seconds, which is similar to the longer lived B mesons, D mesons, and spin-3/2 baryons, and is about 100,000 shorter than that of the longest lived mesons.

The Higgs boson's mean lifetime has not been measured experimentally to this precision (although there is a fairly strict experimentally measured upper bound on its mean lifetime), but it is predicted in the Standard Model to have a mean lifetime of 10^-22 seconds - similar to that of many hadrons with aligned spins, and about 1000 times as long as that of the top quark, W boson and Z boson.

Gluons are in principle as long lived as photons, but in practice, are only exchanged between color charged objects at very short range while moving at the speed of light, so they are in existence for only a time period on the order of 10^-24 seconds and certainly far less than 10^-9 seconds. Also, outside a high energy "quark-gluon plasma" gluons never appear outside of a hadron and their existence is only inferred indirectly rather than being directly measured in isolation.

The mean lifetime of a top quark (i.e. the third generation up type quark) is about 5*10^-25 seconds, which is about ten times shorter than the shortest lived hadron. And, since theory dictates that this time period is too short for hadronization to occur at any meaningful frequency, all hadrons should have longer mean lifetimes than the top quark.

The W boson and Z boson have mean lifetimes of about 3*10^-25 seconds, i.e. about 40% shorter than that of the top quark (which makes since because W bosons are what makes top quark decays possible).

Bottom Line

There is an eight order of magnitude difference between the mean lifetime of the neutron and the next longest lived hadron or charged lepton or massive fundamental boson. Even almost all of the atomic isotopes (some atomic elements don't even have truly stable isotopes) that we commonly think of as extremely unstable are longer lived than 10^-5 seconds.

This is why the vast majority of ordinary matter in the universe is made up of protons, neutrons, and electrons (neutrino masses are so small that they don't much up a very large share of ordinary matter despite the fact that there are vast numbers of them in the universe and photons are massless), despite the hundreds of other possible hadrons and the two other possible charged leptons.

Note also that if dark matter particles exist, at least one kind of dark matter particle needs to be stable or at least metastable with a very long lifetime, although there could be a "dark matter particle zoo" of addition short lived dark matter particles.

Fun Fact

All of the mean fundamental and composite particle lifetimes in the Standard Model are derived quantities that can be calculated to the greatest precision that your measurements of the parameters of the Standard Model and your ability to do the calculations allows.

They are not themselves fundamental parameters (although the mean lifetime of the muon is the primary observable used to measure the Fermi's constant, which is the form in which the weak force coupling constant is normally used in calculations).

Observation

Decays of heavy fundamental particles are sensitive to the existence of undiscovered fundamental particles which could provide decay paths for the heavy particles.

But only if the undiscovered fundamental particles have some quantum number that is present in the original particle or can produce pairs of particles in the ends state that cancel each other out with respect to this quantum number. For example, a quark with lepton number zero can produce leptons as decay products, so long as they come in lepton-antilepton pairs.

So, the fact that the mean decay times of the fundamental particles and hadrons match the Standard Model expectation is a robust global confirmation of the completeness of the Standard Model menagerie of particles up to about 87 GeV (i.e. half the top quark mass), with only a few well defined exceptions (most famously a hypothetical quantum number called R-parity which would distinguish supersymmetric particles from non-supersymmetric particles).

 

[Orodruin]

Neutrinos (which are neutral fundamental leptons rather than hadrons) are metastable in the sense that they can oscillate between generations, but don't "decay" as such.

I would not characterise oscillations as metastability. It is more a question of the interaction states not coinciding with the mass eigenstates of the free Hamiltonian, which are the only relevant asymptotic states. The mass eigenstates do not oscillate but in certain processes the contributions from different mass eigenstates will interfere, leading to an oscillatory behaviour of the interactions.

 

[ohwilleke]

I would not characterise oscillations as metastability. It is more a question of the interaction states not coinciding with the mass eigenstates of the free Hamiltonian, which are the only relevant asymptotic states. The mass eigenstates do not oscillate but in certain processes the contributions from different mass eigenstates will interfere, leading to an oscillatory behaviour of the interactions.

Fair enough. I recognize that "metastability" was not precisely the right term although I am at a loss for a better one, which is why I explained what I really meant after that. But since it is qualitatively different than the kind of boring and complete stability you see in protons and electrons, even when there are lots of them in the same vicinity as each other, for example, it still bears mentioning.

 

[Orodruin]

although I am at a loss for a better one

What about "oscillations"?

Still, the point remains that the actual asymptotic states are stable and do not oscillate.

 

[snorkack]

As you may note, I targeted the gap between 100 fs (Ξ_c⁰ 153 fs) and 0,1 fs (π⁰ 0,085 fs) to call "long-lived". I was also inspired by post
https://www.physicsforums.com/threads/lhcb-discovers-three-new-exotic-particles.1016620/post-6649121
For example, to consider tetraquarks...
Pionium is a well described tetraquark. Its lifetime is predicted as 2,9 fs... The system π⁺+π^- has the same quark content as π⁰+π⁰ would have, yet it has very different properties. It decays/annihilates into π⁰+π⁰, unbound, but this is decay, not being the same system all along.
Neutral mesons might or might not be bound by strong interaction - but opposite charged mesons would be bound by electromagnetic interaction. 6 distinct mesons of each charge means 36 diquarks bound by electromagnetic interaction. Correct?

 

[malawi_glenn]

@snorkack from the first post, I have a hard time understand what your goal is.

Summary: Trying to review the list

Checking systematically the list of possible combinations of di- and triquarks

 

[snorkack]

@snorkack from the first post, I have a hard time understand what your goal is.

Inspired by ohwilleke´s request (in the post I quoted) for a systematic review of all possible tetra-, penta- and hexaquarks, including those not observed.
In order to do so, we would first need system to organize the possibilities, and systematic view of di- and triquarks. Which I tried to give.
5 quarks, and diquarks of alike quark and antiquark always being shortlived, means 10 distinct pairs of diquarks. 6 pairs of charged diquarks, 4 pairs of neutral diquarks which undergo oscillations.
6 diquarks of either charge means 36 electromagnetically bound tetraquarks. Correct?

 

[malawi_glenn]

a systematic review of all possible tetra-, penta- and hexaquarks

Meson and baryon states are not solely determined by the quark-antiquark combination.

and same goes for tetra-, penta-, and hexaquarks.
It is a bit more complicated than just combining valence quarks.

 

[snorkack]

It is a bit more complicated than just combining valence quarks.

Complications are present, but they are few enough that the combinations of valence quarks still seems the useful fraework to note them in. In case of flavoured diquarks - 10 combinations - the one complication I noted is different behaviour of neutral meson oscillations: neutral kaons form 2 states with drastically different lifetimes while neutral D, neutral B and strange B, though they do oscillate, keep a single lifetime.

 

[malawi_glenn]

Complications are present, but they are few enough that the combinations of valence quarks still seems the useful fraework to note them in

You can not figure out the number of possible hadrons and "exotic hadrons" by this method. Think about it, if it was this simple then someone else would have already have done it.

flavoured diquarks

diquarks with valence quark heavier than u,d?

 

[snorkack]

diquarks with valence quark heavier than u,d?

No, diquarks where valence quarks are not each other´s antiquark. So including π^- but excluding J/Ψ

 

[vanhees71]

I would not characterise oscillations as metastability. It is more a question of the interaction states not coinciding with the mass eigenstates of the free Hamiltonian, which are the only relevant asymptotic states. The mass eigenstates do not oscillate but in certain processes the contributions from different mass eigenstates will interfere, leading to an oscillatory behaviour of the interactions.

I'd say that strictly speaking we can't observe neutrinos as "particles" at all since only mass eigenstates can be interpreted as particles (asymptotic free single-particle Fock states), but those we can't create in any way. What we can observe are the weak decay of, say, a neutron and the detection of the anti-neutrino in some reaction with the detector, and I think it's safe to say that this indeed is all we have observed about neutrinos anyway.

 

[Orodruin]

but those we can't create in any way

That’s a bit too strong in my opinion. You can observe separate mass eigenstates if your experimental setup let's you distinguish them. This can occur by effects such as decoherence due to wave packets no longer overlapping or through matter interactions. For example, solar neutrinos produced above the MSW resonance are essentially pure $\nu_2$ states and even if they were not the different mass eigenstates would decohere on the way from the source to the detector.

 

[snorkack]

You can not figure out the number of possible hadrons and "exotic hadrons" by this method. Think about it, if it was this simple then someone else would have already have done it.

People commonly discuss stuff like "baryon octet" and "baryon decuplet" without paying attention to the complications. I use the combinations and do note the (few) complications.

 

[malawi_glenn]

People commonly discuss

who are people and what do they discuss?

without paying attention to the complications.

Hadron physics researchers do, well did. Nowadays we know that we can not figure out the hadron zoo with just these simple arguments. It is a static quark model for hadrons.
https://www.physicsforums.com/insights/a-beginners-guide-to-baryons/#The-Eightfold-Way

Still have no idea what you are trying to do. First it seemed that you were listing long lived hadrons, and then you mentoned tetraquarks and such.

 

[snorkack]

who are people and what do they discuss?

Hadron physics researchers do, well did. Nowadays we know that we can not figure out the hadron zoo with just these simple arguments. It is a static quark model for hadrons.
https://www.physicsforums.com/insights/a-beginners-guide-to-baryons/#The-Eightfold-Wayhttps://www.physicsforums.com/insights/a-beginners-guide-to-baryons/#The-Eightfold-Way

Yes, and that article has irritatingly absurd sounding statements. (I wasn´t confident that objections in comments to article itself would get addressed - better to start a new thread).
"why there are precisely eighteen such particles"
"The baryons in the decuplet are even less stable than those in the octet, again explaining that their fleeting existence is only confirmed by specialized experiments to create them for a few instants before they decay."

Reference: https://www.physicsforums.com/insights/a-beginners-guide-to-baryons/#The-Eightfold-Way

These two statements are literally somewhat true, but only somewhat.
The thing is, one of the "octet" does not really belong. While Σ⁰ does have mass close to the charged Σs, and behaves similarly on strong interaction, it is drastically shorter lived... because unlike the charged Σs, it is an excited state of a lower lying baryon (Λ⁰). Only 7 of the "octet" are lowest states of unique quark combinations, capable of decaying by weak interaction or not at all (proton).
The decuplet is the full set of quark combinations - including the combinations of 3 alike quarks which "octet" excludes. So 7 of the decuplet are excited states of the "octet", and as such resonances.
This leaves the issue of the 3 corners. And now the interesting thing is that although Δ⁺⁺ and Δ^- are unique quark combinations, they have allowed paths for strong decay and are therefore resonances. In contrast to Ω^-, which is not.
There are thus 8 longlived baryons consisting of 3 light quarks - not 18, nor 10, nor the 8 called "octet". But the decuplet is nevertheless a vital framework to organize the 8 that do have long lives.

Still have no idea what you are trying to do. First it seemed that you were listing long lived hadrons, and then you mentoned tetraquarks and such.

Yes. Responding to ohwilleke´s challenge - I demonstrated that all predicted diquarks are known, but a lot of triquarks are unseen. Now the next thing is to offer an organization to predict tetraquarks, pentaquarks, hexaquarks.

Tetraquarks might be bound by strong force or electromagnetic force. Pionium is well known. Therefore other electromagnetically bound tetraquarks can be predicted.

 

[malawi_glenn]

Now the next thing is to offer an organization to predict tetraquarks, pentaquarks, hexaquarks.

https://arxiv.org/abs/1903.11976

Tetraquarks might be bound by strong force or electromagnetic force. Pionium is well known. Therefore other electromagnetically bound tetraquarks can be predicted.

You need to figure out the binding mechanism
https://inspirehep.net/files/637dc391e37edd5ba312bd3d01c740ff

 

[snorkack]

You need to figure out the binding mechanism
https://inspirehep.net/files/637dc391e37edd5ba312bd3d01c740ff

Any opposite charged particles can get bound by electromagnetic force, unless their width is bigger than their Bohr energy.
Neutral hadrons might get bound by strong force - the only known case so far is p and n, and this only in case of aligned spins, not in case of opposed spins.

 

[malawi_glenn]

Any opposite charged particles can get bound by electromagnetic force, unless their width is bigger than their Bohr energy.

Classically yes.
You also have to care about the strong force you can not treat the pions in pionium as two "heavy" electrons/positrons
this is a nice overview
This is a good paper: https://arxiv.org/abs/hep-ph/9905543v2
and this is a nice overview https://arxiv.org/abs/0711.3522v2

 

[snorkack]

Classically yes.
You also have to care about the strong force, you can not treat the pions in pionium as two "heavy" electrons/positrons
this is a nice overview https://arxiv.org/abs/0711.3522v2

Page 4 (Chapter 1 Introduction):

The distance rB ≃ 220 fm is much smaller than the
hydrogen radius, but still much larger than the range of strong interactions, which
is typically of the order of a few fm. It is for this reason that strong interactions
do not change the structure of the bound–state spectrum in a profound manner.
At leading order in an expansion in α, the energy of S-wave states of pionic
hydrogen is still given by the standard quantum–mechanical formula

This
corresponds to a lifetime τ1 ∼ 10−15 s, which is much smaller than the lifetime of
the charged pion, τπ ∼ 10−8 s, so that the pion in the atom can be considered a
practically stable particle. Despite of its short lifetime, pionic hydrogen can be
considered a quasi-stable bound state, since the pion travels many times around
the proton before decaying, as the ratio 1
2 μcα2/Γ1 ∼ 10³ indicates.

I had a general impression to that effect, but thanks for providing authoritative confirmation to my opinion.
So, a tetraquark, pentaquark or hexaquark is characterized by strong interaction as perturbation to electromagnetics - strong decay paths if they exist (but leptonic atoms may also decay by lepton capture, even though this is weak rather than strong) and strong interaction energy level shifts.
The review discusses pentaquarks π^-p and Kp.
Obviously all longlived negative diquarks would be prone to forming such pentaquarks, because their Bohr timescale is 10^-18 s or less, but their free lifetime exceeds 10^-13 s. This means that we also have
3) D^-p
4) D_s^-p
5) B^-p
6) B_c^-p
What are their strong energy shifts and decay widths?
I note something about D_s^-p...
D_s^- is not charming because it is anticharming. Therefore, it cannot possibly react to form a charming baryon. The quark is the strange one.
But look at the masses:
D_s^- 1968,3 MeV
D⁰ 1864,8 MeV
p 938,3 MeV
Λ⁰ 1115,7 MeV
so: D_s^-+p=2906,6 MeV
D⁰+Λ⁰=2980,5 MeV
Cannot see a strong decay for D_s^-p.

 

[malawi_glenn]

You also have to care about the strong force you can not treat the pions in pionium as two "heavy" electrons/positrons

I should have written "the symmetries of the strong interaction"