The HADES experiment, located at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, investigates the equation of state (EoS) of Quantum Chromodynamics (QCD) matter created in central collisions of heavy- and medium-mass nuclei at beam energies of a few GeV, employing both electromagnetic and hadronic probes. In addition, the experiment maintains dedicated programs aimed at the study of hadron properties in p+p and pion-induced reactions. A particular focus of this report is the reconstruction of higher-order cumulant ratios of proton and light-nuclei multiplicity distributions in Ag+Ag collisions, which constitute sensitive probes of critical phenomena due to their direct connection, within the framework of statistical mechanics, to the EoS. Event-by-event (E-by-E) fluctuations are reconstructed using a novel probabilistic approach based on Fuzzy Logic, which effectively circumvents the limitations imposed by incomplete E-by-E particle identification in experimental data. Several strategies for efficiency correction are discussed, and a data-driven event-mixing technique is employed to account for volume (centrality) fluctuations. The fully corrected normalized factorial cumulants of the proton multiplicity distribution, including their acceptance dependence in rapidity, are presented and compared with canonical ensemble baseline calculations that incorporate correlations arising from local attractive interactions. The HADES results extend the trends observed by the STAR experiment toward lower collision energies for the measured cumulant ratios.

Inclusive e$^+$e$^-$ production has been studied with HADES in $\pi^-$ + p, $\pi^-$ + C and $\pi^- + \mathrm{CH}_2$ reactions, using the GSI pion beam at $\sqrt{s_{\pi p}}$ = 1.49 GeV. Invariant mass and transverse momentum distributions have been measured and reveal contributions from Dalitz decays of $\pi^0$, $\eta$ mesons and baryon resonances. The transverse momentum distributions are very sensitive to the underlying kinematics of the various processes. The baryon contribution exhibits a deviation up to a factor seven from the QED reference expected for the dielectron decay of a hypothetical point-like baryon with the production cross section constrained from the inverse $\gamma$ n$\rightarrow \pi^-$ p reaction. The enhancement is attributed to a strong four-momentum squared dependence of the time-like electromagnetic transition form factors as suggested by Vector Meson Dominance (VMD). Two versions of the VMD, that differ in the photon-baryon coupling, have been applied in simulations and compared to data. VMD1 (or two-component VMD) assumes a coupling via the $\rho$ meson and a direct coupling of the photon, while in VMD2 (or strict VMD) the coupling is only mediated via the $\rho$ meson. The VMD2 model, frequently used in transport calculations for dilepton decays, is found to overestimate the measured dielectron yields, while a good description of the data can be obtained with the VMD1 model assuming no phase difference between the two amplitudes. Similar descriptions have also been obtained using a time-like baryon transition form factor model where the pion cloud plays the major role.

MIMOSIS is a CMOS Monolithic Active Pixel Sensor developed to equip the Micro Vertex Detector of the Compressed Baryonic Matter (CBM) experiment at FAIR/GSI. The sensor will combine an excellent spatial precision of 5 µm with a time resolution of ∼5 µs and provide a peak hit rate capability of ∼ 80 MHz/cm 2 . To fulfill its task, MIMOSIS will have to withstand ionising radiation doses of ∼ 5 MRad and fluences of ∼ 7 × 10 13 n eq /cm 2 . This paper introduces the reticle size full feature sensor prototype MIMOSIS-2.1, which was improved with respect to earlier prototypes by adding on-chip grouping circuits and by improving the analog power grid. Moreover, it features for a first time a 50 μm epitaxial layer, which is found to improve the performances of the non-irradiated device significantly. We discuss the in beam sensor performances as measured during beam tests at the CERN-SPS.

The Micro Vertex Detector (MVD) is the most upstream detector of the fixed-target Compressed Baryonic Matter Experiment (CBM) at the future Facility for Antiproton and Ion Research (FAIR). It enables high-precision low-momentum tracking in direct proximity of the target. Reaching the stringent requirements for the MVD, a material budget of 0.3–0.5% X 0 per layer, operating the dedicated CMOS MAPS ('MIMOSIS') in the target vacuum, the strong magnetic dipole field, and a harsh radiation environment (5 Mrad, 7×10 13 n eq /cm 2 per CBM year), poses an unprecedented integration challenge. In this paper, the integration concept of the detector will be outlined, elaborating on the selection and preparation of materials, assembly procedures, and quality assessment steps in the ongoing preparation of pre-series production and detector commissioning in 2028.

The Facility for Antiproton and Ion Research (FAIR) is in its final construction stage next to the campus of the Gesellschaft fur Schwerionenforschung Helmholtzzentrum for heavy-ion research in Darmstadt, Germany. Once it starts its operation, it will be the main nuclear physics research facility in many basic sciences and their applications in Europe for the coming decades. Owing to the ability of the new fragment separator, Super-FRagment Separator, to produce high-intensity radioactive ion beams in the energy range up to about 2 GeV/nucleon, these can be used in various nuclear reactions. This opens a unique opportunity for various nuclear structure studies across a range of fields and scales: from low-energy physics via the investigation of multi-neutron systems and halos to high-density nuclear matter and the equation of state, following heavy-ion collisions, fission and study of short-range correlations in nuclei and hypernuclei. The newly developed reactions with relativistic radioactive beams ((RB)-B-3) set up at FAIR would be the most suitable and versatile for such studies. An overview of highlighted physics cases foreseen at (RB)-B-3 is given, along with possible future opportunities, at FAIR. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

We generalize and extend the recently proposed method [1] to account for contributions of system size (or volume/participant) fluctuations to the experimentally measured moments of particle multiplicity distributions. We find that in the general case there are additional biases which are not directly accessible to experiment. These biases are, however, parametrically suppressed if the multiplicity of the particles of interest is small compared to the total charged-particle multiplicity, e.g., in the case of proton number fluctuations at top RHIC and LHC energies. They are also small if the multiplicity distribution of charged particles per wounded nucleon is close to the Poissonian limit, which is the case at low energy nuclear collisions, e.g., at GSI/SIS18. We further find that mixed events are not necessarily needed to extract the correction for volume fluctuations. We provide the formulas to correct pure and mixed cumulants of particle multiplicity distributions up to any order together with their associated biases.

The ultra-thin and highly granular CMOS Monolithic Active Pixel Sensors (MAPS) are typically optimized for high rate high precision tracking, which implies the use of a very thin active medium and digital readout. Both features hamper using the devices for identifying low momentum particles by means of dE/dx. Still, MAPS feature charge sharing and typically clusters of more than one fired pixel per impinging particles are formed. It was previously shown that the number of fired pixels per cluster scales with the dE/dx, which allowed identifying highly ionizing nuclear fragments [1]. Assuming a sufficiently strong response to different dE/dx, this approach could also be considered for distinguishing minimum ionizing particles (MIP) from light fragments like alpha particles in tracking detectors. In this work, we study this response with particle beams with a dE/dx of up to four times the ones of MIPs, for non-irradiated and irradiated chips, with different sensing nodes as implemented in the MIMOSIS-1 prototype used for the vertex detector of the CBM experiment.

Hadron production ( π ^± , proton, Λ , K_S^0 , K^± ) in π ^- + C and π ^- + W collisions is investigated at an incident pion beam momentum of 1.7 GeV/c . This comprehensive set of data measured with HADES at SIS18/GSI significantly extends the existing world data on hadron production in pion induced reactions and provides a new reference for models that are commonly used for the interpretation of heavy-ion collisions. The measured inclusive differential production cross-sections are compared with state-of-the-art transport model (GiBUU, SMASH) calculations. The (semi-) exclusive channel π ^- + A →Λ + K_S^0 +X , in which the kinematics of the strange hadrons are correlated, is also investigated and compared to a model calculation. Agreement and remaining tensions between data and the current version of the considered transport models are discussed.

The central tracking system of the HADES detector, installed at the SIS-18 synchrotron at GSI/Darmstadt (Germany), employs large-area, low-mass drift chambers, featuring Aluminum potential wires and small cell sizes. The chambers in front of the magnetic field, closest to the interaction point, have developed significant self-sustained currents and discharges during operation, most probably triggered by isobutane-based gas mixtures. Only both, (i) replacing isobutane by CO2 and (ii) adding 1000 to 3500 ppmv of water into the Ar/CO2 counting gas mixture, individually optimized for a given chamber, allowed to recover the chambers, enabling stable operation in several production runs since then, e.g. with high-intensity heavy-ion induced reactions. The origin of the instability was found to be deposits on the cathode wires, provoking the Malter-like effects, by visual inspection and energy-dispersive X-ray spectroscopy. The charge on the wires accumulated during their lifetime does not point to so-called classical aging, but presumably the interaction of isobutane with materials in the gas flow, residual impurities, and reaction products formed in plasma, e.g., built by discharges.

The production of Σ ^0 hyperons in proton proton collisions at a beam kinetic energy of 3.5 GeV impinging on a liquid hydrogen target was investigated using data collected with the HADES setup. The total production cross section is found to be σ (pK^+Σ ^0) = 17.7 ± 1.7 (stat) ± 1.6 (syst) µb. Differential cross section distributions of the exclusive channel pp → pK^+Σ ^0 were analyzed in the center-of-mass, Gottfried–Jackson and helicity reference frames for the first time at the excess energy of 556 MeV. The data support the interplay between pion and kaon exchange mechanisms and clearly demonstrate the contribution of interfering nucleon resonances decaying to K^+Σ ^0 . The Bonn–Gatchina partial wave analysis was employed to analyse the data. Due to the limited statistics, it was not possible to obtain an unambiguous determination of the relative contribution of intermediate nucleon resonances to the final state. However nucleon resonances with masses around 1.710 GeV/c^2 ( N^*(1710) ) and 1.900 GeV/c^2 ( N^*(1900) or Δ ^*(1900) ) are preferred by the fit.

The unexplained disagreement in the dependence of spectroscopic factors (C2Sexp) on the binding energy obtained by nucleon knockout using different targets is still a puzzle that needs to be addressed. To find an explanation of this riddle through exclusive measurements using different targets. The exclusive measurements were performed by using a Ne17 beam with an energy of 500 MeV/u incident on C and CH2 targets. Through the standard theoretical approach, C2Sexp were derived from the analysis of the experimental data on proton ejection from the proton halo in Ne17 as well as from its core O15. For the C target, proton ejection from the proton halo gave C2Sexp about 37% smaller than for the H target. But when protons are ejected from the core of Ne17, C2Sexp are identical within statistical uncertainties. An explanation for the difference in C2Sexp could be the removal of both halo protons, a more important reaction pathway for the C target. The C2Sexp values obtained by analyzing the proton ejection from the core indicate that it is not affected by the interaction with the halo protons. Published by the American Physical Society 2024

High-precision measurements of flow coefficients v_n ( n = 1 - 4 ) for protons, deuterons and tritons relative to the first-order spectator plane have been performed in Au+Au collisions at √(s__NN)= 2.4 GeV with the High-Acceptance Di-Electron Spectrometer (HADES) at the SIS18/GSI. Flow coefficients are studied as a function of transverse momentum p_t and rapidity y_cm over a large region of phase-space and for several classes of collision centrality. A clear mass hierarchy, as expected by relativistic hydrodynamics, is found for the slope of v_1 , d v_1/d y^'|_y^' = 0 where y^' is the scaled rapidity, and for v_2 at mid-rapidity. Scaling with the number of nucleons is observed for the p_t dependence of v_2 and v_4 at mid-rapidity, which is indicative for nuclear coalescence as the main process responsible for light nuclei formation. v_2 is found to scale with the initial eccentricity ⟨ϵ _2⟩ , while v_4 scales with ⟨ϵ _2⟩ ^2 and ⟨ϵ _4⟩ . The multi-differential high-precision data on v_1 , v_2 , v_3 , and v_4 provides important constraints on the equation-of-state of compressed baryonic matter.

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, α _s(Q^2) , that varies with the energy scale Q^2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of α _s at low momentum transfers limits perturbative calculations to the high-energy region where Q^2≫ _QCD ^2≃ (250 MeV) ^2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large N_c -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected qq̅ mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, W^± or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

MIMOSIS is a CMOS Monolithic Active Pixel Sensor (CPS) developed to equip the Micro Vertex Detector (MVD) of the Compressed Baryonic Matter (CBM) experiment at FAIR/GSI. The sensor will combine a spatial resolution of -5 µm with a time resolution of 5 µs and provide a peak hit rate capability of ∼80 MHz/cm 2 . To fulfil its task, MIMOSIS will have to withstand ionising radiation doses of ∼5 MRad and fluences of ∼7 × 10 13 n eq /cm 2 per year of operation. The paper summarises major requirements of the CBM-MVD and compares them to the detection performances of the first full scale prototype, called MIMOSIS-1, recently evaluated in the laboratory and with particle beams. The tolerance of the sensor to the expected ionising radiation load was evaluated; the paper describes the measurements performed and their outcome.

Nucleon knockout experiments using beryllium or carbon targets reveal a strong dependence of the quenching factors, i.e., the ratio ( R_s ) of theoretical to the experimental spectroscopic factors ( C^2S ), on the proton-neutron asymmetry in the nucleus under study. However, this dependence is greatly reduced when a hydrogen target is used. To understand this phenomenon, exclusive ^1H(^17Ne, 2p ^16F) and inclusive ^12C(^17Ne,2p ^16F)X , ^12C(^17Ne, ^16F)X as well as ^1H(^17Ne,^16F)X (X-denotes undetected reaction products) reactions with ^16F in the ground and excited states were analysed. The longitudinal momentum distribution of ^16F and the correlations between the detached protons were studied. In the case of the carbon target, there is a significant deviation from the predictions of the eikonal model. The eikonal approximation was used to extract spectroscopic factor values C^2S . The experimental C^2S value obtained with C target is markedly lower than that for H target. This is interpreted as rescattering due to simultaneous nucleon knockout from both reaction partners, ^17Ne and ^12C .

Being installed as close as 5.5 mm to the beam axis, the Micro Vertex Detector (MVD) of the CBM experiment will be exposed to a sizable flow of heavy beam ions and nuclear fragments. The CMOS Monolithic Active Pixel Sensor for the MVD, MIMOSIS, must resist the related heavy ion impacts without permanent damage or frequent interrupt of operation as caused by single event effects (SEE). We motivate the requirements on the sensor and introduce our concept for protecting the device against SEEs. Moreover, we report the results of a related test campaign carried out with the first full size sensor prototype, MIMOSIS-1, and different heavy ion beams at GSI.

We develop an innovative and unbiased procedure, based on event mixing, to account for unavoidable contributions from volume (or system size) fluctuations to experimentally measured moments of particle multiplicity distributions produced in relativistic nuclear collisions. Within the wounded-nucleon model they are characterized by fluctuations of the number of wounded nucleons, the latter usually referred to as participants. For the first time we extract participant fluctuations directly from the data used for the fluctuation analysis, i.e., without involving model calculations. To achieve this we constructed a dedicated event-mixing algorithm that eliminates all possible correlations between produced particles while preserving the volume fluctuations. The procedure provides direct access to the cumulants of wounded-nucleon distributions, which can be used to account for non-critical contributions to the experimentally measured cumulants of multiplicity distributions.

The double differential production cross sections, $d^2σ/dΩdE$, for hydrogen isotopes and charged pions in the reaction of p + Nb at 3.5 GeV proton beam energy have been measured by the High Acceptance DiElectron Spectrometer (HADES). Thanks to the high acceptance of HADES at forward emission angles and usage of its magnetic field, the measured energy range of hydrogen isotopes could be significantly extended in comparison to the relatively scarce experimental data available in the literature. The data provide information about the development of the intranuclear cascade in the proton-nucleus collisions. They can as well be utilized to study the rate of energy/momentum dissipation in the nuclear systems and the mechanism of elementary and composite particle production in excited nuclear matter at normal density. Data of this type are important also for technological and medical applications. Our results are compared to models developed to describe the processes relevant to nuclear spallation (INCL++) or oriented to probe either the elementary hadronic processes in nuclear matter or the behavior of compressed nuclear matter (GiBUU).

A spheroidal model of the expansion of hadronic matter produced in heavy-ion collisions in the few-GeV energy regime is proposed. It constitutes an extension of the spherically symmetric Siemens-Rasmussen blast-wave model used in our previous works. The spheroidal form of the expansion, combined with a single-freeze-out scenario, allows for a significantly improved description of both the transverse-mass and the rapidity distributions of the produced particles. With the model parameters determined by the hadronic abundances and spectra, we make further predictions of the pion HBT correlation radii that turn out to be in a qualitative agreement with the measured ones. The overall successful description of the data supports the concept of spheroidal symmetry of the produced hadronic systems in this energy range.