Masses of Hadrons: Why are they so heavy?

Frank Dohrmann, Burkhard Kämpfer

We Need More Mass!

Text book examples clearly evidence that the mass of things in our material world is essentially made up of nucleons, i.e. protons and neutrons. Protons and neutrons belong to a group of particles which are called hadrons (from Greek, hadros = heavy, strong) due to their heaviness and strong interaction. Although we know the numerical values of these particle masses with high accuracy, it is a challenging question of modern physics to understand why particles actually obtain a mass. For instance, it is not clear why the mass of an electron has a specific value. Nor do we know why some quarks, which together with gluons make up the nucleon, have such a small mass: Up and down quarks are light; their masses are about a hundred times smaller than the mass of the nucleon. What is more, gluons do not have a mass at all.

Not only in the microcosm, but also in the macrocosm are we faced by the quest for masses and energies. Since 1999, astronomical observations have revealed that the objects in the sky (stars, nebulae, galaxies and clusters of them) constitute only a small fraction of the matter content in the universe. Indeed, most of the matter resides in forms which are unknown to us. Due to this they are named dark energy and dark matter, but we know almost nothing about them.

All these phenomena provide a strong motivation for physicists to better understand the origin of the mass of nucleon matter. The key to this seems to be the strong interaction among the constituents of nucleons. In a fictitious world with massless quarks, the mass of nucleons and thus atomic nuclei would be only 20 % smaller than in our real world.

Strange Probes

Experiments addressing these questions are often in need of specific probes. These particles are created by collisions in the laboratory.

Kaons (K^±) have distinct properties which let them behave differently from other hadrons. Due to this they were originally called “strange” hadrons. K^± may be produced through collisions of nuclei. Once the electron orbitals of an atom are stripped in this process, the remaining nucleus (ion) may be accelerated, and a beam of nuclei can impinge on a target nuclei. The kinetic energy of these colliding nuclei is partially converted into mass of newly produced particles. It is important to mention that for nucleus-nucleus collisions, K⁺ or K^– are produced inside the nuclear medium. Upon collision, the nuclear matter of both nuclei is compressed and heated up; nucleons of the nuclei are mixed and form a fireball in which a few newly produced particles are immersed.

The compression stage, subsequent expansion and final disintegration only last for about 3 x 10^-23 s altogether. Due to this short time scale for the violent evolution of the fireball a theoretical interpretation is difficult. Therefore, after initial experiments with beams of nuclei on nuclear targets, it was mandatory to perform a series of experiments in which a proton beam hits a nuclear target and produces K^±. The surrounding nuclear matter, through which the K^± have to penetrate, behaves nearly statically. An interpretation of such experiments is sophisticated. They were carried out by Kaon Spectrometer (KaoS) collaboration [1], a group of scientists from FZD, Technische Universität Darmstadt, Universität Frankfurt, Gesellschaft für Schwerionenforschung Darmstadt, Jagiellonian University Krakow and Universität Marburg. The experiments led to the conclusion that a K^- is modified in nuclear matter. It may thus be described effectively as an excitation with a mass reduced by 80 MeV relative to its vacuum mass, while the K⁺ mass is effectively increased by 20 MeV. K⁺ are produced associatedly with a Λ hyperon [2].

Di-Electrons – Direct Messengers

In experiments using K^± mesons, these may mix in nuclear matter with other excitations with the same quantum numbers as K^±. Thus some information is lost and the genuinely interesting spectral distribution is hardly accessible. In contrast, light vector mesons, ρ and ω – another group of hadrons – are better suited for penetration. A vector meson may decay into an electron-positron (e⁺e^-) pair, which is called di-electron. Measuring the momenta of e⁺ and e^- enables access to the spectral distribution of ρ and ω mesons. E⁺ and e^- only interact electromagnetically with nuclear matter. This interaction is so weak that the e⁺e^- pair leaves the nuclear medium nearly undisturbed, thus, carrying the wanted original information which is needed for unraveling how the parent hadrons ρ and ω acquire their masses.

Although this approach looks very promising, a number of experimental challenges have to be tackled when using these direct probes: (i) Only in one out of 10⁵ (10⁴) cases a ρ (ω) meson decays into an e⁺e^- pair. (ii) At energies, where ρ and ω mesons are produced, many other sources of e⁺e^- pairs are generated unintentionally, too. (iii) The e⁺ and e^- must be carefully separated from all other charged particles which occur much more frequently.

HADES

To build a detector which fulfills these challenging demands, more than 100 scientists from 19 institutions in ten countries joined in an international collaboration to build the High Acceptance Di-Electron Spectrometer (HADES). It is installed at the Gesellschaft für Schwerionenforschung (GSI) Darmstadt and uses various beams delivered by the accelerator SIS18: nuclei, protons or pions. Fig. 1 displays a cross section of HADES.

Fig. 1: Cross section of the HADES detector with acronyms denoting important components (RICH: Ring Imaging Cherenkov, MAGNET: superconducting magnet coils, MDC I-IV: Multi-wire Drift Chambers, TOF/TOFINO: Time-Of-Flight walls, Shower: shower detector). MDC III (highlighted in red) was built by the FZD. The detector is azimuthally symmetric around the Z-axis (blue horizontal line labelled Z, which depicts the beam direction; the red dot indicates the target position).

The FZD contributed to HADES, building the third plane of tracking detectors. Each plane contains six multi-wire chambers, each of which consists of six anode and seven cathode layers. Inside each chamber roughly 7000 thin wires (ø 20 μm Tungsten, ø 80 μm Aluminum) are mounted with a spatial accuracy of 20 μm. The wire layers are enclosed in a chamber filled with a specific gas mixture. The chambers operate at high voltages up to 2000 V. Fig. 2 gives an impression of the size of one chamber. Four planes of tracking detectors allow reconstructing trajectories of charged particles the momenta of which are calculated.

Fig. 2: Mounting and testing one of the six multi-wire chambers during a detector workshop at the FZD. The six chambers are arranged hexagonally, forming a large frustum around the beam direction. Their position is coloured red in fig. 1.

Fig. 3 shows a first important result of HADES [3]. Together with the measured data, simulations of various sources of e⁺e^- are displayed. Understanding these contributions is a demanding task and requires additional input from other experiments. This is adapted via models [4] which in turn ascribe the heaviness of hadrons to their intimate relation to the Quantum chromodynamics (QCD) vacuum structure. In this way the mass of hadrons and, thus, of the visible matter in the cosmos can be explained quantitatively by QCD, the theory of strong interaction.

Fig. 3: The first physics results from HADES. On display: count rate of e⁺e^- pairs, normalized to the number of pions, as a function of the invariant mass of e⁺e^- pairs, M_ee. Symbols are for measured data, while curves depict estimates for various contributions to the spectrum. These estimates cannot account for the data. Sophisticated theoretical models are needed to extract information from data on the modification of the spectral distribution of ρ and ω mesons which are embedded in compressed nuclear matter arising from the collisions of carbon nuclei at beam energy of 2 GeV per nucleon.

Charming Prospects

The results of KaoS and HADES opened the door to answer the question on the origin of the masses of hadrons. Regarding the much needed complementary information, new opportunities will arise from the Facility for Anti-proton and Ion Research (FAIR) which is under construction in Darmstadt. Among the core experiments of FAIR are nucleus-nucleus collisions. The accelerator SIS300 will deliver ion beams in an energy region in which the maximum compression of nuclear matter is expected. Moreover, FAIR provides a new degree of freedom: charm. Similarly to kaons, which are characterized by strangeness, D mesons carry a charm quark content. This makes them a very sensitive probe of the external strong interaction field and is complementary to the information obtained from HADES and KaoS. Using this hadronic probe, further detailed insight into the complex architecture of hadrons and their mass generation is expected.

A large international collaboration has formed to build the Compressed Baryon Matter (CBM) experiment at the site of FAIR in Darmstadt. The task of the Rossendorf group is to develop Resistive Plate Chambers (RPC) – modern detectors with a time resolution better than 100 ps. They have to work even at very high particle rates.

Due to the excellent timing properties of its electron beam (5 ps resolution) the time resolution of RPCs is tested using electrons from the FZD linac ELBE. Moreover, the intensity of ELBE’s electron beam offers an extremely valuable tool for testing the rate capability of modern detectors. Various test series with prototypes were already conducted at ELBE with promising results [5]. This necessary progress in instrumentation also provides cost-saving tools ready for application, e.g. for imaging devices in medicine. In this way, technology transfer and development is accomplished while the primary goal to address fundamental problems of physics, such as the heaviness of hadrons, particularly protons and neutrons, is tackled.

[1] First observation of in-medium effects on phase space distributions of antikaons measured in proton-nucleus collisions, W. Scheinast et al. (KaoS Collaboration), Phys. Rev. Lett. 96, 072301 (2006).

[2] Angular distributions for ^{3, 4}He bound states in the ^{3, 4}He (e, e’ K⁺) reaction, F. Dohrmann et al. (E91-016 Collaboration), Phys. Rev. Lett. 93, 242501 (2004).

[3] Dielectron production in C12+C12 collisions at 2 AGeV with HADES, G. Agakishiev et al. (HADES Collaboration), Phys. Rev. Lett. 98, 052302 (2007).

[4] Evidence for in-medium changes of four-quark condensates, R. Thomas, S. Zschocke and B. Kämpfer, Phys. Rev. Lett. 95, 232301 (2005).

[5] Testing timing RPC detectors at the Rossendorf electron linac ELBE, R. Kotte, F. Dohrmann, J. Hutsch, L. Naumann and D. Stach, Nucl. Inst. Meth. A 654, 155 (2006).