Research Pentaquarks: Quasi-Molecular or Compact Systems?

31 March 2026

According to the quark model formulated in 1964, the strongly interacting particles of physics themselves are built from even more elementary components. Modern science considers these quarks indivisible. There are six different types, so-called flavors, of different masses that always occur in combination, never alone. Baryons, for example – which include protons and neutrons that make up the nucleus of all atoms – are composed of three light quarks. The shorter-lived mesons consist of one quark and one antiquark. Like the baryons, they are hadrons. Quarks are held together by the strong interaction.

Multiquark systems like pentaquarks, which consist of four quarks and one antiquark, were also predicted in 1964. Because their lifespan is extremely short, they cannot be measured directly but only through their decay products. Indirect evidence of several pentaquark resonances was first discovered in 2015 in the Large Hadron Collider of the European Organization for Nuclear Research in Geneva (Switzerland) as part of the LHCb experiment, in which researchers from Heidelberg University are playing a major role. The pentaquark system of the c\(\bar{c}\)uds configuration – the letters describe the type of quark – investigated in the latest calculations was experimentally proven for the first time in 2023 at CERN.

It is not completely clear yet which microscopic configuration these exotic systems of five quarks have, Prof. Wolschin notes. Are pentaquarks tightly packed states of matter bound to one another by the strong interaction? Or are they structures consisting of multiple particles like a meson and a baryon bound like the protons and neutrons in atomic nuclei or the atoms in molecules? Using the example of the c\(\bar{c}\)uds system, this was the question that Georg Wolschin pursued together with colleagues from Japan.

Because the masses of some of the quarks studied are quite large, the calculations are based on a non-relativistic model, in which the quantum mechanical five-body Schrödinger equation is solved with a specially developed method for three-, four-, and five-body systems. They also take into account so-called color excitations, which can facilitate the formation of pentaquark resonances. The resulting solutions of the Schrödinger equation were not compatible with a compact structure in the energy range of the pentaquark resonance measured at CERN. “At least for the c\(\bar{c}\)uds system, our results suggest that the spatial configuration of the quarks appears to correspond to a hadronic molecule,” explains Prof. Wolschin. In this case, the relatively weak residual interaction between meson and baryon would be crucial for creating this pentaquark resonance.

To understand what is called chromodynamics, pentaquark states are of major significance, says Georg Wolschin. According to this theory, the strong interaction between quarks is conveyed by the gluons and does not depend on the type of quark. “The experimental data show, however, that heavy quarks are necessary to form pentaquarks. The binding strength thus also depends on the quark mass but is insufficient in the system investigated here to form compact states,” emphasizes the Heidelberg physicist.

Researchers from the Japanese universities in Sendai and Osaka as well as the RIKEN Nishina Research Center in Wako near Tokyo also participated in the study. Prof. Dr Emiko Hiyama ran the numerical calculations using the “Genkai” supercomputer of Kyushu University; Prof. Dr Makoto Oka contributed substantially to the theory on special color excitations. The joint work was financed using Excellence funds from Heidelberg University. Funding was also provided by the Japan Society for the Promotion of Science. The results were published in the journal “Physical Review D”.