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### Finding a five-leafed clover

Photo Credit: Cathy Händel, Published on http://www.suttonelms.org.uk/olla12.html

Sometimes when you’re looking for something else, you happen across an even more exciting result. That’s what’s happened at LHCb, illustrated in the paper “Observation of $$J/\psi p$$ resonances consistent with pentaquark states in $$\Lambda_b^0\to J/\psi K^-p$$ decays”, released on the arXiv on the 14th of July.

I say this is lucky because the analysts found these states while they were busy looking at another channel; they were measuring the branching fraction of $$B^0\to J/\psi K^+ K^-$$. As one of the analysts, Sheldon Stone, recalled to me, during the review of the $$B^0$$ analysis, one reviewer asked if there could be a background from the decay $$\Lambda_b^0\to J/\psi K^- p$$, where the proton was misidentified as a kaon. As this was a viable option, they looked at the PDG to see if the mode had been measured, and found that it had not. Without a certain knowledge of how large this contribution would be, the analysts looked. To their surprise, they found a rather large rate of the decay, allowing for a measurement of the lifetime of the $$\Lambda_b^0$$. At the same time, they noticed a peak in the $$J/\psi p$$ spectrum. After completing the above mentioned analysis of the $$B^0$$, they returned to the channel.

It’s nice to put yourself in the analysts shoes and see the result for yourself. Let’s start by looking at the decay $$\Lambda_b^0\to J/\psi p K^-$$. As this is a three body decay, we can look at the Dalitz Plots.

Dalitz plots from the decay $$\Lambda_b^0\to J/\psi K^- p$$. Compiled from http://arxiv.org/abs/1507.03414

The above Dalitz plots show all combinations of possible axes to test. In the one on the left, around $$m^2=2.3$$ GeV$$^2$$, running vertically, we see the $$\Lambda(1520)$$ resonance, which decays into a proton and a kaon. Running horizontally is a band which does not seem to correspond to a known resonance, but which would decay into a $$J/\psi$$ and a proton. If this is a strong decay, then the only option is to have a hadron whose minimum quark content is $$uud\bar{c}c$$. The same band is seen on the middle plot as a vertical band, and on the far right as the sloping diagonal band. To know for sure, one must perform a complete amplitude analysis of the system.

You might be saying to yourself “Who ordered that?” and think that something with five quarks hadn’t been postulated. This is not the case. Hadrons with quark content beyond the minimum were already thought about by Gell-Mann and Zweig in 1964 and quantitatively modeled by Jaffe in 1977  to 4 quarks and 5 quarks by Strottman in 1979. I urge you to go look at the articles if you haven’t before.

It appears as though a resonance has been found, and in order to be sure, a full amplitude analysis of the decay was performed. The distribution is first modeled without any such state, shown in the figures below.

Projections of the fits of the$$\Lambda_b^0\to J/\psi K^- p$$ spectrum without any additional components. Black is the data, and red is the fit. From http://arxiv.org/abs/1507.03414

Try as you might, the models are unable to explain the invariant mass distribution of the $$J/\psi p$$. Without going into too much jargon, they wrote down from a theoretical standpoint what type of effect a five quark particle would have on the Dalitz plot, then put this into their model. As it turns out, they were unable to successfully model the distribution without the addition of two such pentaquark states. By adding these states, the fits look much better, as shown below.

Mass projection onto the $$J/\psi p$$ axis of the total fit to the Dalitz plot. Again, Black is data, red is the fit. The inset image is for the kinematic range $$m(K p)>2 GeV$$.
From http://arxiv.org/abs/1507.03414

The states  are called the $$P_c$$ states. Now, as this is a full amplitude analysis, the fit also covers all angular information. This allows for determination of the total angular momentum and parity of the states. These are defined by the quantity $$J^P$$, with $$J$$ being the total angular momentum and $$P$$ being the parity. All values for both resonances are tried from 1/2 to 7/2, and the best fit values are found to be with one resonance having $$J=3/2$$ and the other with $$J=5/2$$, with each having the opposite parity as the other. No concrete distinction can be made between which state has which value.

Finally, the significance of the signal is described by under the assumption $$J^P=3/2^-,5/2^+$$ for the lower and higher mass states; the significances are 9 and 12 standard deviations, respectively.

The masses and widths turn out to be

$$m(P_c^+(4380))=4380\pm 8\pm 29 MeV$$

$$m(P_c^+(4450))=4449.8\pm 1.7\pm 2.5 MeV$$

With corresponding widths

Width$$(P_c^+(4380))=205\pm 18\pm 86 MeV$$

Width$$(P_c^+(4450))=39\pm 5\pm 19 MeV$$

Finally, we’ll look at the Argand Diagrams for the two resonances.

Argand diagrams for the two $$P_c$$ states.
From http://arxiv.org/abs/1507.03414

Now you may be saying “hold your horses, that Argand diagram on the right doesn’t look so great”, and you’re right. I’m not going to defend the plot, but only point out that the phase motion is in the correct direction, indicated by the arrows.

As pointed out on the LHCb public page, one of the next steps will be to try to understand whether the states shown are tightly bound 5 quark objects or rather loosely bound meson baryon molecule. Even before that, though, we’ll see if any of the other experiments have something to say about these states.

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• Sebastian Kuhn

So far, I haven’t seen any explanation why this resonant state has to be a PENTAQUARK. After all, the quantum numbers are all non-exotic (i.e. can be explained in a standard 3-quark model) – the c c-bar cancel the net charm of the state. In fact, one could hypothesize a hybrid baryon (qqqg with explicit glue degree of freedom) that would decay into a proton and a J/psi (we know that ccbar couple strongly to gluons). The narrow width of the higher-lying state would simply be due to the fact that additional gluons must be exchanged to create the J/psi, which makes the state more long-lived.
Of course, it’s also possible for the J/psi to experience an attractive force with the proton, so it is just a “resonant scattering state” – which would seem the natural explanation for the wider, but lower-lying state they found.

• Amir Livne Bar-on

Is a particle with this quark composition and mass expected? Or is the theory too unwieldy to predict these properties from first principles?

• G. Sardin

Before considering the observation of exotic pentaquark particles, we think it is previously convenient to address some of the serious conceptual deficiencies of the standard model, which is highly fanciful in its approach. Its conceptual strategy is based on a set of combinations of abysmally artificial primordial elements, such as quarks and gluons. Their properties are highly bizarre and artificial: fractional charges, flavors, colors, convenient and arbitrary quarks masses, and all this strategy only applies to hadrons, leaving aside all other particles that remain structureless or with undefined structure. For much willingness one may put, the standard model approach is so illusory that there is no way to take it seriously.

Let’s break down the main conceptual artefacts of this model. It considers that hadrons are formed by six families of quarks (u, d, c, s, t, b) joined together by a complex gluonic field composed of height types of gluons. In addition, this model is not unitary because it includes other elementary particles not made of quarks, such as e.g. the six leptons (e, νe, μ, νμ, τ, ντ), the photon and the three intermediate bosons (Z, W+ and W‑). Thus, the standard model is based on a multiplicity of primary particles: 6 quarks and 6 antiquarks tri-chromatic, 8 gluons also tri-chromatic, 6 leptons and 6 antileptons, the photon and 3 intermediate bosons, which leaves it much to be desired as a unitary claim and the QCD has been profoundly misleading for already 50 years.

It is a deep intellectual error to think that, at the very starting point of matter, its elementary building blocks would have such a complex structure as the standard model gives them. The complexity of the structure of elementary particles from the standard model is highly incredible and artificial. Furthermore, the quark model has no reductive power. It appeals to 60 primary elements or key states: 36 different quarks (6 families of tri-chromatic quarks and antiquarks), and 24 different gluons (8 tri-chromatic types). Thus, it has no horizon of being unitary, moreover conceptually quite puzzling and showing a severe lack of realism. Frank Wilczek, Nobel laureate, 2004, said: “from the perspective of QCD, the foundations of nuclear physics appear distinctly unsound”.

As long as the standard model will remain the official one, in spite of being embarrassedly fantasist, the image of theoretical physicists of elementary particles will keep being pathetic, which is very much counterproductive for a credible and respectable image of theoretical physics, which should be careful in staying away of mathematically induced hallucinations.

• Correct, complex structure and functionality at a fundamental (basic) level is unneeded and quite impossible.

• Correct, complex structure and functionality at a fundamental (basic) level is unneeded and quite impossible.

All actions at the basic level can only be very simple, and everything absolutely has to work and form automatically.

Something like “color charge” is completely impossible and ridiculous

They say red, blue and green quarks are shooting anti-green, anti-blue and anti-red gluons at anti-quarks and changing the color charges so that the color charge is conserved. That stuff just has to be correct!

http://en.wikipedia.Org/wiki/Color_charge

• G. Sardin

As long as the standard model will remain the official one, in spite of being embarrassedly
fantasist, the image of theoretical physicists of elementary particles will keep being pathetic, which is very much counterproductive for a credible and respectable image of theoretical physics, which should be careful in staying away of mathematically induced hallucinations.

Higher the complexity of fundamentals and of descriptive mathematics, lower the probability of coincidence with physical reality, and farther from its reliable description. In our opinion, quarks, with their colours, fractional charges, counterfeit masses, and the eight types
of gluons, are the equivalent of the epicycles, the deferents, the equant and the circular orbits of the Ptolemaic system. As long as the quark model will remain an enforced mainstream model, ahead standpoints will be inhibited. The official symptomatic omission of straightforward deductions challenging the Standard Model, is an inappropriate, counterproductive strategy.

Many theoretical physicists are much satisfied with the Standard Model. However, at long run so much complacency is not advisable. What they have really proved in excellence
is their expertise in adjusting data. Though, math, which is certainly a key tool in physics, is however a human development (and perhaps of some civilized sympathetic aliens too!). As such, it can serve as well to describe physical reality as to falsify it.

Nature does not know about math, it is just due to physical interactions. In its endless chores it makes no calculation, it only interacts, otherwise it would be as clumsy as we are, and most of the time would be wrong or not know what to do, just like us. In our opinion this tendency to equate mathematics with physical reality is a subtle form of animism, but this is another story. Certainly, physical laws do not depend on our math to know how to operate, and when we change them they do not vary accordingly in order to please us.

So, before speculating about pentaquarks we believe it would be convenient to address more fundamental ones.

• Complex structure and functionality at a fundamental (basic) level is unneeded and quite impossible.

All actions at the basic level can only be very simple, and everything absolutely has to work and form automatically.

Something like “color charge” is completely impossible and ridiculous

They say red, blue and green quarks are shooting anti-green, anti-blue and anti-red gluons at anti-quarks and changing the color charges so that the color charge is conserved. That stuff just has to be correct!

http://en.wikipedia.Org/wiki/Color_charge

• nikkkom

You are free to produce a simpler model which matches experimental data as well as SM does. Until you do, your rants will be ignored.

And BTW, there aren’t 24 gluons. There are eight. They are not “tri-chromatic”, gluon color charges are more complex than quark colors. You don’t even know the stuff you critisize.

• nikkkom

This .gif is a simplification.
According to it, only 6 kinds of gluons are possible (red-antigreen, red-antiblue; green-antired, green-antiblue; blue-antired, blue-antigreen). This allows for a simplistic visual representation how, say, a green quark sends green-antiblue gluon to blue quark, changing their colors and also exchanging momentum.

But math doesn’t work as visual pictures. In particular, QCD math postulates that color charge corresponds to SU(3) symmetry group, gluon field corresponds to adjoint representation of this group, and SU(3) group has eight generators in adjoint representation, not six. Therefore, there must be eight gluons. Even wikipedia’s “Gluon” article explains this.

• Yes, everything you wrote there is obviously correct.

• G. Sardin

Effectively, there are only eight remaining independent color states, the “eight types” or “eight colors” of gluons. Since these states can be mixed together, there are diverse ways of presenting them, which are known as the “color octet”. A usual list is:

(r b*+ b r*)/√2, (r g*+ g r*)/√2, (b g*+ g b*)/√2, (r r*+ b b*) / √2

-i(r b*+ b r*)/√2, -i(r g*+ g r*)/√2, -i (b g*+ g b*)/√2, (r r*+ b b* – 2 g g*)/√6

Really, may these complex formulations of the mixed color states of the made-up ghostly gluons have any pinch of verisimilitude? Can it be really thought that the QCD standpoint on gluons colors has any sheen of realism or is it just a convenient mathematical adjustment? QCD has many conceptual flaws, much artificially hidden under a great deal of mathematical cosmetics.

Still, the quark composition of the neutral pion is said to be:(u u*+ d d*)/√2.
One wonders what physical sense may have such a workaround fractional composition of quarks. Wouldn’t it rather be a purely mathematical arrangement devoid of any physical sense? Mathematics should not be equated with physical reality! Nowadays, theoretical physics has become quite speculative, which is much harmful for its credibility. Not attending critics is a non evolutionary counterproductive attitude.

I have been working on the elaboration of more simple and realistic foundations of elementary particles physics. The approach has several interesting developments, such as e.g. nuclei avidity for neutrons, why it increases as nuclei get heavier, an opening out to quantum vacuum, a straightforward solution to the irrational incongruity of the wave-particle duality by taking into account the surrounding quantum vacuum, etc… that will be progressively uploaded at “researchgate”.

So, please stay heedful, you may even unexpectedly change your mind about the virtuosity of the SM!