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We analyze the behavior of cumulants of conserved charges in a subvolume of a thermal system with exact global conservation laws by extending a recently developed subensemble acceptance method (SAM) [1] to multiple conserved charges. Explicit expressions for all diagonal and off-diagonal cumulants up to sixth order that relate them to the grand canonical susceptibilities are obtained. The derivation is presented for an arbitrary equation of state with an arbitrary number of different conserved charges. The global conservation effects cancel out in any ratio of two second order cumulants, in any ratio of two third order cumulants, as well as in a ratio of strongly intensive measures Σ and ∆ involving any two conserved charges, making all these quantities particularly suitable for theory-to-experiment comparisons in heavy-ion collisions. We also show that the same cancellation occurs in correlators of a conserved charge, like the electric charge, with any non-conserved quantity such as net proton or net kaon number. The main results of the SAM are illustrated in the framework of the hadron resonance gas model. We also elucidate how net-proton and net-Λ fluctuations are affected by conservation of electric charge and strangeness in addition to baryon number.
The quantum van der Waals (QvdW) extension of the ideal hadron resonance gas (HRG) model which includes the attractive and repulsive interactions between baryons – the QvdW-HRG model – is applied to study the behavior of the baryon number related susceptibilities in the crossover temperature region. Inclusion of the QvdW interactions leads to a qualitatively different behavior of susceptibilities, in many cases resembling lattice QCD simulations. It is shown that for some observables, in particular for χBQ11/χB2, effects of the QvdW interactions essentially cancel out. It is found that the inclusion of the finite resonance widths leads to an improved description of χB2, but it also leads to a worse description of χBQ11/χB2, as compared to the lattice data. On the other hand, inclusion of the extra, unconfirmed baryons into the hadron list leads to a simultaneous improvement in the description of both observables.
We use 4stout improved staggered lattice data at imaginary chemical potentials to calculate fugacity expansion coefficients in finite temperature QCD. We discuss the phenomenological interpretation of our results within the hadron resonance gas (HRG) model, and the hints they give us about the hadron spectrum. We also discuss features of the higher order coefficients that are not captured by the HRG. This conference contribution is based on our recent papers [1, 2].
We develop a framework to relate proton number cumulants measured in heavy-ion collisions within a momentum space acceptance to the susceptibilities of baryon number, assuming that particles are emitted from a fireball with uniform distribution of temperature and baryochemical potential, superimposed on a hydrodynamic flow velocity profile. The rapidity acceptance dependence of proton cumulants measured by the HADES Collaboration in √sNN = 2.4 GeV Au-Au appears to be consistent with thermal emission of nucleons from a grand-canonical heat bath, with the extracted baryon number susceptibilities exhibiting an hierarchy χB 4 >> −χB 3 >> χB 2 >> χB 1 . Naively, this could indicate large nonGaussian fluctuations that might point to the presence of the QCD critical point close to the chemical freeze-out at T ∼ 70 MeV and μB ∼ 850 − 900 MeV. However, the description of the experimental data at large rapidity acceptances becomes challenging once the effect of exact baryon number conservation is incorporated, suggesting that more theoretical and experimental studies are needed to reach a firm conclusion.
The thermal fit to preliminary HADES data of Au+Au collisions at sNN=2.4 GeV shows two degenerate solutions at T≈50 MeV and T≈70 MeV. The analysis of the same particle yields in a transport simulation of the UrQMD model yields the same features, i.e. two distinct temperatures for the chemical freeze-out. While both solutions yield the same number of hadrons after resonance decays, the feeddown contribution is very different for both cases. This highlights that two systems with different chemical composition can yield the same multiplicities after resonance decays. The nature of these two minima is further investigated by studying the time-dependent particle yields and extracted thermodynamic properties of the UrQMD model. It is confirmed, that the evolution of the high temperature solution resembles cooling and expansion of a hot and dense fireball. The low temperature solution displays an unphysical evolution: heating and compression of matter with a decrease of entropy. These results imply that the thermal model analysis of systems produced in low energy nuclear collisions is ambiguous but can be interpreted by taking also the time evolution and resonance contributions into account.
The creation of loosely bound objects in heavy ion collisions, e.g. light clusters, near the phase transition temperature () has been a puzzling observation that seems to be at odds with Big Bang nucleosynthesis suggesting that deuterons and other clusters are formed only below a temperature . We solve this puzzle by showing that the light cluster abundancies in heavy ion reactions stay approximately constant from chemical freeze-out to kinetic freeze-out. To this aim we develop an extensive network of coupled reaction rate equations including stable hadrons and hadronic resonances to describe the temporal evolution of the abundancies of light (anti-)(hyper-)nuclei in the late hadronic environment of an ultrarelativistic heavy ion collision. It is demonstrated that the chemical equilibration of the light nuclei occurs on a very short timescale as a consequence of the strong production and dissociation processes. However, because of the partial chemical equilibrium of the stable hadrons, including the nucleon feeding from Δ resonances, the abundancies of the light nuclei stay nearly constant during the evolution and cooling of the hadronic phase. This solves the longstanding contradiction between the thermal fits and the late stage coalescence (and the Big Bang nucleosynthesis) and explains why the observed light cluster yields are compatible with both a high chemical production temperature and a late state emission as modeled by coalescence. We also note in passing that the abundancies of the light clusters in the present approach are in excellent agreement with those measured by ALICE at LHC.
We derive the relation between cumulants of a conserved charge measured in a subvolume of a thermal system and the corresponding grand-canonical susceptibilities, taking into account exact global conservation of that charge. The derivation is presented for an arbitrary equation of state, with the assumption that the subvolume is sufficiently large to be close to the thermodynamic limit. Our framework – the subensemble acceptance method (SAM) – quantifies the effect of global conservation laws and is an important step toward a direct comparison between cumulants of conserved charges measured in central heavy ion collisions and theoretical calculations of grand-canonical susceptibilities, such as lattice QCD. As an example, we apply our formalism to net-baryon fluctuations at vanishing baryon chemical potentials as encountered in collisions at the LHC and RHIC.
We estimate the feeddown contributions from decays of unstable A=4 and A=5 nuclei to the final yields of protons, deuterons, tritons, 3He, and 4He produced in relativistic heavy-ion collisions at sNN>2.4 GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, 3He, and 4He at sNN≲10 GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable (>10%) effects for deuteron yields are observed at sNN≲4 GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the T-μB plane itself is affected significantly by the light nuclei at high baryochemical potential.
We study the correlation between the distributions of the net-charge, net-kaon, net-baryon and net-proton number at hadronization and after the final hadronic decoupling by simulating ultra relativistic heavy ion collisions with the hybrid version of the ultrarelativistic quantum molecular dynamics (UrQMD) model. We find that due to the hadronic rescattering these distributions are not strongly correlated. The calculated change of the correlation, during the hadronic expansion stage, does not support the recent paradigm, namely that the measured final moments of the experimentally observed distributions do give directly the values of those distributions at earlier times, when the system had been closer to the QCD crossover.
The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the netbaryon density at imaginary baryochemical potential – corresponding to the fugacity or virial expansion at real chemical potential – are calculated within this model, and compared with the Nt = 12 lattice data. The lattice QCD behavior of the first four Fourier coefficients up to T 185 MeV is described fairly well by an interacting HRG with a single baryon–baryon eigenvolume interaction parameter b 1 fm3, while the available lattice data on the difference χB 2 − χB 4 of baryon number susceptibilities is reproduced up to T 175 MeV.