Standard Model’s Failing Predictions

The family of particle composed of quarks is called Hadrons. This group is divided into 2 sub-categories called Baryons and Mesons. The dominant force determining the Hadronic structure is called the Strong Interaction.

In the 1960s the understanding was that the structure if Hadrons can be explained such that a baryonic quantum state is characterized by 3 quarks, and the Meson state is characterized by a pair of quark-antiquark.

According to Comay’s model, Baryons contain a core with three units of magnetic monopole charge, binding 3 quarks to it, each carrying one magnetic monopole negative charge unit. These monopoles obey to the Regular Charge-Monopole Theory. This state is equivalent to a non ionized atom containing a nucleus carrying a positive electric charge, and electrons carrying a negative electric charge. Mesons are a bound quark-antiquark pair, in analogy to positronium, which is an electron- anti-electron (called positron) bound state. A quark combination which does not correspond to the above usually gets labeled “exotic”. So far no experimental evidence for the existence of exotic hadrons has been confirmed [1].

A few years after the discovery of quarks, a theory called Quantum-Chromo-Dynamics (QCD) was formulated, in order to explain the Strong Interactions and the Hadronic structure. QCD became the part of the standard Model dealing with the Strong Interactions. It turns out that QCD has no constraint on the existence of exotic hadrons [2]. That’s how, based on this theory, papers published in the scientific literature predicted the existence of quite a few exotic hadrons as well as their corresponding nuggets of matter.

Before we get into the details, we should say a few general words about QCD’s framework. This theory defined 3 kinds of charges called “colors”. According to one of QCD’s structural constraint, a free hadron has to be “white”, i.e., to contain an equal quantity of the three colors. The existence of mesons is explained by a pair of quark and antiquark bound together by an attraction force. In addition, and in order to account for the existence of the proton and the other baryons, QCD suggests that there is also an attractive force acting between the quarks. The constraint preventing “non-white” hadrons from being experimentally measured reduces the number of particles allowed by QCD. But in spite of this limitation, QCD still allows the existence of quite a few exotic hadrons as well as various particle nuggets. In this page we present a list of particles which should exist according to QCD fans, and although they were not yet found, they are still being looked for. Another group of particles was supposed to be discovered, but when experimental endeavors failed, QCD followers found arguments explaining this failure.

Dibaryons are a family of particles composed of 6 quarks. Their existence had been predicted back in 1977 by Robert Jaffe. The existence of dibaryons was considered plausible from the QCD perspective, and some of them are even expected to be stable. This particle group was called H (from Hexa – its 6 quarks components) [3]. It was emphasized that the bond between these quarks was expected to be strong. Here one should note that unlike the Strong Interactions, the binding energy of the proton and neutron in the deuteron is relatively very small (the deuteron’s binding energy is about 2.2 MeV).

According to Comay’s model, quarks repel each other, and therefore 6 quarks could only live together within 2 cores, like in the deuteron, which is the bound state of a proton and a neutron. In order to illustrate it, one could say that inside the deuteron, the force attracting the proton’s quarks to its core is the Strong Interaction, and the force attracting the same quarks to the neutron’s core is weaker (the Strong Nuclear Force, which is the Strong Interaction’s residual force). Similarly, the neutron’s quarks are attracted to their core through the Strong Interaction, and to the proton’s core through a weaker nuclear force. Hence, attraction forces between hadrons are analogous to the van der Waals force, which is the attractive force between non-ionized molecules. The Strong Nuclear Force is a residual force and is some 2 orders of magnitude weaker than the Strong Interactions. Therefore, a state where two hadrons are bound by the Strong Interaction would be impossible.

Up to now, dibaryons have never been found [4].

A pentaquark is a proton (or a neutron) bound to a meson. According to QCD, these particles are bound by the Strong Interaction, and are expected to be discovered. Their existence was predicted in 1987, and since then, hundreds, if not thousands of papers were written about them. Some of the papers even sorted the pentaquarks into several particle categories, and detailed the properties of each of these hypothetical pentaquark particles. In 2003, the LEPS laboratory in Japan announced their discovery, but repeated experiments refuted this finding.

In parallel to what was argued with regard to dibaryons, Comay’s model refutes the existence of pentaquarks as well. First of all, all the hadrons (particles containing quarks) are neutral with regard to their total magnetic charge. The proton can be compared to a non-ionized atom, and the meson can be compared to a positronium, which is a bound state of an electron and a positron. Therefore, the link between two hadrons should be comparable to what is found in the deuteron, which is a bound state of a proton and a neutron. In the deuteron, the binding energy is about 2.2 MeV, and the strong binding energy is of the order of magnitude of hundreds of MeV. Furthermore, for every pair of quark-antiquark forming a meson, the total spin of the lightest meson (which are the natural candidates for composing pentaquarks) cancels out. In this respect these mesons are similar to noble gas, which does not form chemical compounds. Comay’s model predicts therefore that strongly bound pentaquarks will never be found.

PDG, the Practical Data Group, is the international organization which has the authority to establish the existence and the properties of particles. PDG’s latest report on the subject of pentaquarks resumes the situation as follows: “… There are two or three recent experiments that find weak evidence for signals near the nominal masses, but there is simply no point in tabulating them in view of the overwhelming evidence that the claimed pentaquarks do not exist…”. The report concludes: “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” [5].

The search for pentaquarks is still going on.

Glueballs are particles composed singularly of gluons, without quarks. According to the Standard Model, this quantum state is allowed because gluons contain “color” and act through the Strong Interaction. According to theoretical calculations of Standard Model fans, glueballs could be formed in the current particle accelerators.

According to Comay’s Model, there are no gluons and no colors, and there can obviously be no glueballs.

In spite of all the experiments, the existence of glueballs has not been confirmed up to now.

Strange Matter
The existence of stable nuggets of matter composed of baryons, each of which resembles the Lambda 1116 baryon (which means a combination of 3 u, d, s quarks) has been predicted by QCD fans [6].

This type of electrically neutral nuggets is called strange quark matter, and its abbreviation is SQM. The search for SQM covered every possible place, including within terrestrial minerals and lunar rocks brought over from the moon [7].

Comay’s model refutes the existence of SQM. Binding energy between baryons is supposed to be comparable to the nuclear binding energy. For a typical nucleus, this energy is about 8 MeV, times the number of nucleons (the word nucleon refers to both the proton and the neutron). On the other hand, the energy of the lambda baryon is some 180 MeV higher than that of the nucleon. It is clear that a 180 MeV energy can not be stabilized by 8 MeV. Therefore, since the Lambda disintegrates within less than a billionth of a second, SQM is not supposed to exist. And experiments are consistent with this conclusion.

Other exotic combinations
In the framework of QCD, many possible combinations of exotic particles are allowed. One of them is called tetraquark, which is supposed to be a stable state of two quarks and two antiquarks. The existence of none of these hypothetic particles was ever confirmed. The latest PDG review [1] contains a long list of references to scientific literature discussing them.

The search is going on
According to Standard Model’s QCD, stable states such as the proton, in which quarks attract each other, are possible. In addition, the screening phenomenon known from Electromagnetic Theory does not exist in this case. For these reasons, QCD allows the existence of many quark and anti-quark combinations, bound by the Strong Interaction. Some of these combinations should be rather stable, and some of them are very stable, such as Strange Quark Matter and pentaquarks. In spite of that, and in spite of the incredible efforts of looking for them over several decades, the existence of such particles has never been established, just as Comay’s model predicts.

The efforts to discover this kind of particles are still going on, including in the current LHC experiments at CERN.

[1] C. Amsler et al. (Particle Data Group) (2008) “Review of Particle Physics: Pentaquarks”. Physics Letters B667, 1 (2008) see in [1]
[3] R.L. Jaffe, “Perhaps a Stable Dihyperon?”. Physical Review Letters 38 195, 1977
[4] After several years scientists found some explanation and stopped looking for them
[6] E. Witten, Phys. Rev. D 30, 272 (1984)
[7] K. Han et al., Phys. Rev. Lett. 103, 092302 (2009)


5 thoughts on “Standard Model’s Failing Predictions

  1. Dear Eli,
    On the pentaquark prediction, there is now significant evidence that this particle exists. For example the SVD-2 Collaboration confirmed its earlier observation of the Theta+ signa at the level of 8sigma Also in 2014 the LHC confirmed the existence of the tetraquark (Z(4430)-) with a significance of over 13.9sigma. Your new theory would have to explain the existence of these exotic particles.

    • Hi Stephen
      Can you send me a reference to this evidence? Pentaquark is a baryon which strongly bound to a meson. This cannot exist by Comay model. However, some phycisists use the term pentaquark to other kinds of bonds between a baryon and a meson. I will look into the article and see what kind of pentaquark they found.

      • Dear Ofer,
        A review of the status of the pentaquark is given in “Present status on experimental search for pentaquarks” arxiv: 1403.4455v1. In it the authors show the results of the experiments that detected a pentaquark. They also give the results of those that did not.

        A reference for the discovered tetraquark is arxiv: 1404.1903v1


    • Dear Stephan.

      Let us consider the following points.

      1. The QCD pentaquark idea says that a pentaquark is a strongly bound state of 4 quarks and an antiquark. The mass of the \Theta particles > 1500 MeV which is greater than the sum of the proton and the kaon mass. Hence, if the \Theta particles exist then they are an unbound proton-kaon states and certainly NOT strongly bound pentaquarks of QCD. The same relations exist for the \Theta_C and the sum of the proton and the D+ meson.

      2. The Particle Data Group is the authorized organization for the publication of particle existence and of their properties. Seven years ago, they have published the following extremely negative report about pentaquark existence . As of today, they have not published a different opinion.

      Either of these points negates the existence of QCD’s pentaquarks.

      Referring to the tetraquark report of LHCb.

      The \psi ‘ meson is now called \psi(2S)) (see ).
      Its mass is 3686 MeV (see ). Thus, the sum of the mass of \psi(2S)) and a pion is less than 4000 MeV whereas the mass of the reported tetraquark is 4430MeV. Therefore, the reported data certainly do not describe a QCD strongly bound state of 4 quarks.

      Cheers, Eli

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