Remarks about Pentaquarks

By Eli Comay, July 19, 2015

Pentaquark news has recently been published in the media [1]. This is a quite good opportunity for clarifying the physical merits of these objects.

Self-evident pentaquarks
The basic state of the most well-known example of a hadron, the proton, is characterized as an assembly of 3 quarks, called uud. Quantum Field Theory (QFT) tells us that it is possible to find additional particle-antiparticle pairs in any quantum state. And indeed, experiments carried out about 40 years ago have identified the existence of additional quark-antiquark pairs in the proton. This issue is documented in textbooks (see [2], pp. 281, 282). Hence, the actual proton state can be written as a function of these variables (qqq), (qqqqq), etc.

It means that the actual state of the proton contains a term which is a kind of “pentaquark.” In principle, this pentaquark term must have pairs of the same flavor like uu; dd; ss; cc; etc. On the other hand, additional pairs like ud are forbidden, for example because flavor will not be conserved.

Hereafter, pentaquarks of this kind are called self-evident pentaquarks.
penta1
A self-evident Pentaquark

QCD pentaquarks
Another idea of a pentaquark structure is nearly 30 years old [3,4]. The idea about these particles aims to show that Quantum Chromodynamics (QCD) allows the existence of stable quark states that are neither baryons (namely, states characterized by 3 quarks) nor mesons (namely qq states). The QCD predictions expect strongly bound pentaquarks of this kind. Indeed, the authors of [3] say that the pentaquarks “are likely to be stable with respect to their dissociation into a meson and a baryon.” Similarly, in [4] it is said that the pentaquark is “a bound state of a nucleon and an F (now called Ds).”
penta2
A QCD Pentaquark

penta3
QCD Pentaquark with explanation from CERN web site

Hereafter, pentaquarks of this kind are called ‘QCD pentaquarks’. An important feature of the QCD pentaquarks is that they contain a baryon and a qq pair, where q and q do not have the same flavor and at least one of them is heavier than the u,d quarks. QCD pentaquarks are expected to be stable with respect to strong interaction decays. Therefore, if they exist then they might have been detected accidentally even in the bubble chamber era.

The QCD pentaquark idea has launched a long list of theoretical publications and of experimental efforts aiming to detect QCD pentaquarks. The experimental efforts ended in vain. In conclusion, QCD pentaquarks have not been detected during more than 50 years. No accidental detection in ordinary experiments and no detection in experiments dedicated to a pentaquark discovery.

Pentaquark molecules
Another type of pentaquark is sometimes called ‘pentaquark molecule’. This type has a baryon and a meson, which are in a bound state, but the binding is due to an analog of the nuclear force, and not the strong force.

penta4
Pentaquark molecule with explanation from CERN web site

In the picture below the left pentaquark type is a ‘QCD Pentaquark’ and the right is a ‘Pentaquark molecule’.

penta5
The picture was taken from https://en.wikipedia.org/wiki/Pentaquark

Unbound pentaquarks
In the course of time, the pentaquark notion has been extended and unbound states of 4 quarks and an antiquark are also called pentaquarks. Hereafter, pentaquarks of this kind are called ‘unbound pentaquarks’. These objects consist of quarks whose flavor is the same as those of the QCD pentaquarks. Probably, the most famous candidate for an unbound pentaquarks is called Θ+ whose mass is around 1530 MeV.

penta6
Quarks of the Θ+ (an unbound pentaquark)

By the way – it is easy to tell whether a theoretical pentaquark is bound (like in the case of QCD pentaquarks) or unbound (like in the case of unbound pentaquarks). All you need to do is to sum up the masses of the particle decay products and to compare this sum to the mass of the particle before it disintegrates. If for every decay channel the sum of the mass of the decay products is greater than that of the pentaquark then the pentaquark is in a bound state. Here weak decay modes are ignored.

The fate of the unbound pentaquarks was similar to that of their older brothers – the QCD pentaquarks – namely, all experimental attempts ended empty handed. Thus, the Particle Data Group, which is the organization responsible for authorizing the existence of particles said about the Θ+ [5] “The whole story – the discoveries themselves, the tidal wave of papers by theorists and phenomenologists that followed, and the eventual “undiscovery” – is a curious episode in the history of science.”

The new “discovery”
Few days ago, the CERN LHCb collaboration has declared observations of two pentaquark states [6] which are unbound states of a meson called J/ψ and a proton. The present version of Wikipedia (July 19, 2015) contains an illustration showing the quark structure of these particles, which consists of uud + cc quarks (see [7]). These two states are unbound, having an extra mass of around 350 MeV or more.

penta7
Quarks of the new discovery

Since the J/ψ meson is a cc particle one concludes that the LHCb discovery is an excited state of the self-evident pentaquark category. Here, unlike the above-mentioned proton case, the LHCb state is unbound.

The following lines shows examples explaining why other known particles are pentaquarks of this kind. Namely, unbound self-evident pentaquark.

The 2014 PDG report [8] shows on p. 11 plots of the pion-proton cross section. The graph shows the well known resonance of the Δ(1232) baryons. These baryons are known for about 60 years. Now, Δ(1232) is certainly produced by the 5 quarks of the colliding proton-pion particles and it decays into the 5 quarks of a nucleon and a pion. Like the LHCb particle, the Δ(1232) is an unbound state. Here one finds M(proton) + M(pion) + 160 MeV ≈ 1232 MeV. Therefore, the Δ(1232) should join the pentaquark family. For this reason, by the new language of the CERN physicists, the Δ(1232) is a pentaquark.

The second example is the baryon N(1710) whose details can be found here. One of its decay modes consists of the ΛK particles. The Λ baryon state is characterized by the uds quarks whereas the K+ meson is characterized by the us quarks. Therefore, a part of the time the N(1710) baryon can be regarded as a pentaquark of the following structure

penta8
One possibility of the 5 quark structure of the N(1710) baryon

It is interesting to note that the N(1710) is analogous to the recent LHCb particle. They are related by replacing ss with cc.

A final remark. Unfortunately, the particle physics community does not mention that contrary to the original expectations, no candidate has ever been found for a strongly bound QCD pentaquark. This is certainly a QCD failure. By contrast, QCD supporters completely ignore these data (and many other kinds of data described in this site) and continue to boast that the entire Standard Model fits all experimental data. Here are just two examples:
A. On p. 149 of [9] the author cites Michio Kaku: “Consequently, it is no exaggeration to state that the Standard Model is the most successful theory in the history of science.”
B. In a Higgs symposium [10], M. Strassler refers to the Standard Model and says that it has “No confirmed conflicts with any existing experiments!” (The exclamation mark belongs to Strassler.)

References:
[1] http://press.web.cern.ch/press-releases/2015/07/cerns-lhcb-experiment-reports-observation-exotic-pentaquark-particles
[2] D. H. Perkins, Introduction to High Energy Physics (Addison-Wesley, Menlo Park, CA, 1987).
[3] C. Gignoux, B. Silvestre-Brac and J. M. Richard, Phys. Lett. B, 193, 323 (1987).
http://ac.els-cdn.com/0370269387912445/1-s2.0-0370269387912445-main.pdf?_tid=42fc3e00-2de1-11e5-bebf-00000aacb362&acdnat=1437288302_5e507a44269a6f55329fe0c3e5eeef9f
[4] H. J. Lipkin, Phys. Lett. B, 195, 484 (1987).
http://ac.els-cdn.com/0370269387900554/1-s2.0-0370269387900554-main.pdf?_tid=729e1c6e-2de1-11e5-867e-00000aacb35d&acdnat=1437288381_a9500305e0df49354fd033415141e614
[5] C. G. Whol, http://pdg.lbl.gov/2009/reviews/rpp2009-rev-pentaquarks.pdf
[6] http://arxiv.org/pdf/1507.03414v1.pdf
[7] https://en.wikipedia.org/wiki/Pentaquark
[8] http://pdg.lbl.gov/2014/reviews/rpp2014-rev-cross-section-plots.pdf
[9] Spencer Scoular: The Missing Science, the Theory of Everything, and the Arrow of Time (Universal Publishers, Boca Raton, 2008).
[10] http://higgs.ph.ed.ac.uk/sites/default/files/Strassler_Looking%20Beyond%20SM.pdf

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