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Phenomenology of Strange Resonances

Principal Investigator: Zoltán Fodor, Bergische Universität Wuppertal (Germany)
HPC Platforms: JUQUEEN of JSC and Hazel Hen of HLRS

The phenomenology of freeze-out and hadronization in heavy ion collision experiments greatly benefits from the availability of Hadron Resonance Gas model. This, however, assumes the complete knowledge of the particle spectrum in a broad range. Alas, many of the bound states have not been found yet. In this project, researchers narrow down on the missing states using large scale lattice QCD computations.

In the mass range between 0.14 and 2.5 GeV/c2 (approximately 2.5 — 45 x 10-28 kg) there is a large abundance of particles, called hadrons. These are bound states of three quarks (baryons) or of a quark and an antiquark (mesons). For the baryons, the neutron and the proton are the most ubiquitous examples, they are the main constituents of the nuclei in the atoms. The interaction of the proton and neutron inside of a nucleon can be modelled by mediating pions, which are the main examples for mesons. Many other compositions of three quarks are less stable, same have as short life time as 10-24 seconds. Such short lived particles, that exist as intermediate states in the interaction of more stable hadrons, are called resonances. E.g. the Delta resonance is produced in the collision of a pion and a proton.

More than 500 of such particles and resonances have been listed in the 2014 edition of the Particle Data Book [1]. It is inevitable that resonances are missed, and each new edition contains new arrivals to the list, or confirmations of vaugely established resonances. It is widely accepted, that the full list of particles is correctly predicted by the underlying theory, Quantum Chromodynamics. Indeed, the light end of the particle spectrum has been calculated from first principles and was found to be in agreement with experiment [2].

In the late 1960ies Dashen and collaborators have proposed a representation of Quantum Chromodynamics where the interaction between the hadrons are included as a spectrum of free-floating resonances [3]. This idea has been often confronted to state-of-the-art lattice QCD computations: the thermodynamics of a hadron gas was well described by the ideal gas built from the known hadrons. Discrepancies have been seen, however, in a special case [4].

In particle physics exeriments mostly protons, neutrons and nuclei consisting of protons and neutrons are used. These all consist of two types of quarks, called ‘up’ and ‘down’. There exists a third type, ‘strange’. Resonances containing one, two or three of such strange quarks play a significant role in the spectrum. Lattice studies have found that strange baryons are significantly more numerous than what we find listed in the Particle Data Book.

The challenge was to classify and quantify the abundance of missing resonances. For this purpose the researchers had to design observables that are accessible from simulation and sensitve to rare types of resonances. Since there are just too many individual resonances to look at one by one, a special technique was used. The resonances have been classified by the number of strange quarks and their spin, and their response to heating was computed in each class. In practice the partial pressures were calculated at temperatures matching the mass of the lightest hadron, the pion.

Some of these classes have much fewer states than others, so is the partial pressure in these classes by up three orders of magnitudes smaller than other in classes. In standard methods large cancellations between fluctuating contributions have prevented a detailed view.

To tackle the problem new imaginary forces have been introduced in this project, and the response of the hot hadron gas was studied. The Fourier components of the response function are sensitive to the contribution from hadrons with a specific quark content. This new type of simulation has resolved three orders of magnitude in the pressure, and can now be used to disambiguate between models that predict the abundance of missing resonace states.

[1] K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38, 090001 (2014).

[2] S. Durr et al Science 322 (2008) 1224-1227

[3] R. Dashen, S. K. Ma, H. J. Bernstein, Phys. Rev. 187, 345 (1969)

[4] A. Bazavov et al, Phys. Rev. Lett. 113, 072001 (2014), see also

Phenomenology of Strange Resonances Fig. 01: Partial pressures of hadrons in various sectors in a range of temperatures. We classified the particles by the number of strange quarks |S|, and, whether they are baryons (|B|=1) or mesons (|B|=0). Our data point are accompanied by the solid lines showing the would-be temperature dependence if the list in the particle data book was complete.
Copyright: University of Wuppertal

Phenomenology of Strange Resonances Fig. 02: Mass spectrum for six types of resonances in the particle data book (green) including not-yet-confirmed states (red) in the quark model (blue) and in the hypercubic quark model (violet).
Copyright: University of Wuppertal

Scientific Contact:

Prof. Dr. Zoltán Fodor
Institut für Theoretische Teilchenphysik
Fakultät für Mathematik und Naturwissenschaften
Bergische Universität Wuppertal, D-42097 Wuppertal (Germany)
e-mail: fodor [at]

November 2017