Quarks of power

about @LHCbExperiment #pentaquark discovery

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Once upon a time, there was a controversy in particle physics. There were some physicists who denied the existence of structures more elementary than hadrons, and searched for a self-consistent interpretation wherein all hadron states, stable or resonant, were equally elementary. Others, appalled by the teeming democracy of hadrons, insisted on the existence of a small number of fundamental constituents and a simple underlying force law. In terms of these more fundamental things, hadron spectroscopy should be qualitatively described and essentially understood just as are atomic and nuclear physics.⁽¹¹⁾

The need of the partons

From FermiLab Today

When we descrive the collisions between particles, we calculate the cross section, the area of the distribution of the collisions' products. The mathematical object used to calculate the cross section are the structure functions, that mathematically describes the inner structure of the particle. In 1969 studying the deep inelastic scattering J. D. Bjorken^{(4, 18)}, in order to explain the experimental results, proposed a particular property for the hadronic structure function in the cross section called scaling. In the same year Richard Feynman^{(5, 18)} suggested the necessity to adopt a new description of hadrons: they had to be made by smaller components, more elementary than the hadrons themselves. These components are called partons.
The Feynman's thesys was immediatly verified by Bjorken and Paschos^{(6, 7, 18)}, in this way starting a great discussion about the parton models, described in the paper by De Rújula, Georgi and Glashow quoted at the beginning of the post⁽¹¹⁾ (an interesting review of the parton model and its story is in Greenberg⁽¹⁸⁾).
Probably the most strong motivation to adopt the parton model to describe hadrons is the great production of particles in the ring particles accelerators⁽⁵⁾. So, theoretical physicists produced a lot of model, but the most succesfull is the quarks model, developed by Murray Gell-Mann⁽¹⁾ and Georg Zweig^{(2, 3)}, that introduced a new quantum number, the flavor. The first formulation involved three type of quarks (and so three flavors): up, down and strange. To this first set of elementary particles in 1970 the quark charm was added by Glashow, Iliopulos and Maiani⁽⁸⁾ and finally in 1973 Kobayashi and Maskawa⁽⁹⁾ completed the family with the two last quark, top and bottom, named by Harari⁽¹⁰⁾ in 1975.

Three quarks for Muster Mark!
Sure he has not got much of a bark
And sure any he has it's all beside the mark.

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from Finnegan's Wake by James Joyce

Living in a colored world

But the quark model have a great problem, the $\Omega^-$ is composed by three quark strange and it would be symmetrical; at the other hand, according to the Pauli principle, it must be antisymmetric⁽²⁰⁾. So, in order to resolve this problem, Greenberg in 1964 proposed the idea that quark didn't obey to the Pauli statistics, but to another type of statistics⁽²⁰⁾.
So in 1966 Moo-Young Han and Yoichiro Nambu proposed a model with nine quarks, with massive gauge bosons, but some years later, in 1971, Fritzsc and Gell-Mann proposed a new more succesful solution:

We considered nine quarks, as Han and Nambu had done, but we assumed that the three quarks of the same type had a new conserved quantum number, which we called "colour". The colour symmetry $SU(3)$ was an exact symmetry. The wave functions of the hadrons were assumed to be singlets of the colour group. The baryon wave-functions are antisymmetric in the colour indices, denoted by red (r), green (g) and blue (b)⁽²⁰⁾.

Left: colors; right: anticolors - via en.wiki

With the introduction of colors in quark model, some of the others problem between theoretical predictions and experimental data was solved: Fritzsch and Gell-Mann, also with Heinrich Leutwyler, developed the quantum chromodynamics, with 8 gabe bosons called gluons⁽²⁰⁾.
One year later the introduction of chromodynamics, in 1973, Politzer, Gross and Wilczek showed that the new theory is asymptotically free, an important properties in order to explain why quarks aren't free at the usual energies.
In this way the theory is ready to explain all hadrons discovered in the particles accelerators, and it can provide also some interesting prevision like the pentaquark.

The road to the pentaquark

Left: the bag pentaquark; right: the meson-baryon molecule - via en.wiki

A pentaquark is a particular particle constituted by four quarks and one anti-quark. There should be two type of pentaquark: the bag pentaquark and the meson-baryon molecule. The first introduction of such type of quarks' arrangment is dued by Jaffe^{(12, 21)} and Strottman^{(13, 21)} and named pentaquark for the first time by Lipkin^{(14, 21)}.

Pentaquarks come into two types, exotic and nonexotic. Exotic pentaquark have an antiquark with a different flavor than any of its four quarks. For example, Lipkin proposed a search for a pentaquark made from ($\bar c suud$) where $\bar c$ is a charm antiquark. An example of nonexotic pentaquark si ($\bar s suud$), which has the same quantum numbers as a proton ($uud$) with a virtual $\bar s s$ pair. Such a state could be easily confused with an excited state of the proton, where one of the ($uud$) quarks goes into a higher orbital, since they both have the same quantum numbers and a higher mass than the proton. Since exotic pentaquarks can be readly distinguished by their quantum numbers, as measured by experiments, exotic pentaquarks are less ambiguous and hence are more interesting.⁽²¹⁾

In the first decade of the third millennium there was three experimental claims of a pentaquark: $\Theta^+$ ($uudd \bar s$, exotic), predicted in 1997 by ⁽¹⁵⁾ with a mass of 1530 MeV and observed in 2003 by LEPS⁽¹⁶⁾ with a mass of 1540 MeV and $4.6 \, \sigma$; $\Phi^{--}$ ($ddss \bar u$, exotic); $\Theta^0_C$ ($uudd \bar c$, exotic). All of these observation are refused dued to the poor statistics⁽¹⁶⁾. In 2008 the Particle Data Group concluded in this way the story⁽¹⁷⁾:

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 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.

In the meanwhile LEPS observed another time the pentaquark⁽¹⁹⁾, in this case with a mass of 1524 ± 4 MeV with $5.1 \, \sigma$: the search for an exotic pentaquark continues.
And the nonexotic? Following Hicks this type of pentaquark are less interesting, but in some sense are more simple to detect, and on the 14th July, 2015, LHCb observed the first nonexotic pentaquark, $P_c^+$ ($\bar c cuud$)⁽²²⁾ in two states, one with a mass of 4450 MeV and the other with a mass of 4380 MeV.

The Feynmann diagram of $P_c^+$

This new particle is not something we've been actively looking for, explained Patrick Koppenburg at New Scientist, but this discovery could help to improve our knowledge of the strong interaction and allow us to distinguish between the two main models of pentaquarks, the bag state and the baryon-meson molecule.
In the end a little curiosity: Maxim Brilenkov et al. proposed in 2013 to explain the dark matter and dark energy using the quark bag model.

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(1) Gell-Mann, M. (1964). A schematic model of baryons and mesons Physics Letters, 8 (3), 214-215 DOI: 10.1016/S0031-9163(64)92001-3
(2) G. Zweig (1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking (pdf). CERN Report No.8182/TH.401.
(3) G. Zweig (1964). An SU(3) Model for Strong Interaction Symmetry and its Breaking: II (pdf). CERN Report No.8419/TH.412.
(4) Bjorken, J. (1969). Asymptotic Sum Rules at Infinite Momentum Physical Review, 179 (5), 1547-1553 DOI: 10.1103/PhysRev.179.1547 pdf)
(5) Feynman, R. P. (1969). "The Behavior of Hadron Collisions at Extreme Energies". High Energy Collisions: Third International Conference at Stony Brook, N.Y. Gordon & Breach. pp. 237–249
(6) Bjorken, J., & Paschos, E. (1969). Inelastic Electron-Proton and $\gamma$-Proton Scattering and the Structure of the Nucleon Physical Review, 185 (5), 1975-1982 DOI: 10.1103/PhysRev.185.1975 (pdf)
(7) Bjorken, J., & Paschos, E. (1970). High-Energy Inelastic Neutrino-Nucleon Interactions Physical Review D, 1 (11), 3151-3160 DOI: 10.1103/PhysRevD.1.3151 (pdf)
(8) Glashow, S., Iliopoulos, J., & Maiani, L. (1970). Weak Interactions with Lepton-Hadron Symmetry Physical Review D, 2 (7), 1285-1292 DOI: 10.1103/PhysRevD.2.1285
(9) Kobayashi, M., & Maskawa, T. (1973). CP-Violation in the Renormalizable Theory of Weak Interaction Progress of Theoretical Physics, 49 (2), 652-657 DOI: 10.1143/PTP.49.652
(10) Harari, H. (1975). A new quark model for hadrons Physics Letters B, 57 (3), 265-269 DOI: 10.1016/0370-2693(75)90072-6
(11) De Rújula, A., Georgi, H., & Glashow, S. (1975). Hadron masses in a gauge theory Physical Review D, 12 (1), 147-162 DOI: 10.1103/PhysRevD.12.147
(12) Jaffe, R. (1977). Multiquark hadrons. II. Methods Physical Review D, 15 (1), 281-289 DOI: 10.1103/PhysRevD.15.281 (pdf)
(13) Strottman, D. (1979). Multiquark baryons and the MIT bag model Physical Review D, 20 (3), 748-767 DOI: 10.1103/PhysRevD.20.748
(14) Lipkin, H. (1987). New possibilities for exotic hadrons — anticharmed strange baryons Physics Letters B, 195 (3), 484-488 DOI: 10.1016/0370-2693(87)90055-4 (full text on osti.gov)
(15) Diakonov, D., Petrov, V., & Polyakov, M. (2014). Exotic anti-decuplet of baryons: prediction from chiral solitons Zeitschrift für Physik A Hadrons and Nuclei, 359 (3), 305-314 DOI: 10.1007/s002180050406 (arXiv)
(16) W-M Yao,, & et al. (2006). Review of Particle Physics Journal of Physics G: Nuclear and Particle Physics, 33 (1), 1-1232 DOI: 10.1088/0954-3899/33/1/001, in particular read The Cosmological Parameters 2006 by Ofer Lahav, Andrew R Liddle
(17) Amsler, C., & et al. (2008). Review of Particle Physics Physics Letters B, 667 (1-5), 1-6 DOI: 10.1016/j.physletb.2008.07.018 pdf)
(18) Greenberg O.W. (2008). The parton model, Compendium of Quantum Physics, 255-258. arXiv: 0805.2588v3
(19) LEPS collaboration (2009). Evidence for the $\Theta^+$ in the $\gamma d \to K^+ K^- pn$ reaction by detecting $K^+ K^-$ pairs Physical Review C, 79 (2) DOI: 10.1103/PhysRevC.79.025210 (arXiv)
(20) Fritzsch, H. (2012). The history of QCD. CERN Courier, Sept, 27. pdf)
(21) Hicks, K. (2012). On the conundrum of the pentaquark The European Physical Journal H, 37 (1), 1-31 DOI: 10.1140/epjh/e2012-20032-0
(22) LHCb collaboration, R. Aaij, B. Adeva, M. Adinolfi, A. Affolder, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander & S. Ali (2015). Observation of $J/ψp$ resonances consistent with pentaquark states in ${Λ_b^0\to J/ψK^-p}$ decays, arXiv: 1507.03414v1