We investigate fluctuations in the canonical ensemble of an Abelian charge, such as baryon number. Our focus is on cumulants and factorial cumulants of baryon and antibaryon multiplicity distributions, including their sum and difference, in both the full phase space and subsystems. In particular, we establish a correlation between net-baryon number fluctuations within a subsystem, which is pertinent for fluctuation analyses in nucleus-nucleus collisions, and fluctuations of baryon and antibaryon numbers in the total system. We derive analytical expressions for factorial cumulants of arbitrary order and present concise results in terms of the cumulants of the total baryon number. To account for dynamics beyond global conservation, we introduce local attractive and repulsive multi-particle interactions within a phenomenological framework. A comparison of calculated and generated cumulants with STAR and HADES data indicates that multiparticle interactions play a decisive role in the description of observed fluctuation patterns. At high collision energies, the data are well-reproduced by incorporating repulsive two-proton interactions, while at lower energies, attractive three-particle interactions become essential. Furthermore, our framework facilitates realistic event generation, enabling a direct comparison with experimental measurements.

Germany

Bengt Friman

Poland

Krzysztof Redlich

Anar Rustamov

Baselines for Abelian charge fluctuations in nuclear collisions:theory and comparison with experimental data

The invariant mass spectra of dileptons radiated from the fireballs formed in high-energy heavy-ion collisions have been successfully used to investigate the properties of hot and dense QCD matter. Using a realistic model for the in-medium electromagnetic spectral function, we predict polarization observables and compare them to experiment. This allows, for the first time, independent tests of the longitudinal and transverse components of the virtual photon's selfenergy. While the low- and high-mass regions exhibit the expected limits of transverse and unpolarized photons, respectively, baryon-driven medium effects in the <italic>&#961;</italic>-meson mass region create a marked longitudinal polarization that transits into a largely unpolarized emission from the quark-gluon plasma, thus providing a sensitive test of microscopic emission processes in QCD matter. Applications to available data from the HADES and NA60 experiments at SIS and SPS energies, respectively, are consistent with our predictions and set the stage for quantitative polarization studies at FAIR and collider energies.

Florian Seck

Tetyana Galatyuk

Hendrik van Hees

United States

Ralf Rapp

Enrico Speranza

Jochen Wambach

Polarization of thermal dilepton radiation

We study the Fourier coefficients <math><msub><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math> of the net baryon number density in strongly interacting matter at finite temperature. We show that singularities in the complex chemical potential plane connected with phase transitions are reflected in the asymptotic behavior of the coefficients at large k. We derive the scaling properties of <math><msub><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math> near a second order phase transition in the <math><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> and <math><mi>Z</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> universality classes. The impact of first order and crossover transitions is also examined. The scaling properties of <math><msub><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math> are linked to the QCD phase diagram in the temperature and complex chemical potential plane.

Hungary

Gábor András Almási

Japan

Kenji Morita

Fourier coefficients of the net baryon number density and their scaling properties near a phase transition

We investigate the Fourier coefficients <math><msub><mi>b</mi><mi>k</mi></msub><mo>(</mo><mi>T</mi><mo>)</mo></math> of the net baryon number density in strongly interacting matter at nonzero temperature and density. The asymptotic behavior of the coefficients at large <math><mi>k</mi></math> is determined by the singularities of the partition function in the complex chemical potential plane. Within a QCD-like effective chiral model, we show that the chiral and deconfinement properties at nonzero baryon chemical potential are reflected in characteristic <math><mi>k</mi></math>- and <math><mi>T</mi></math>-dependencies of the Fourier coefficients. We also discuss the influence of the Roberge-Weiss transition on these coefficients. Our results indicate that the Fourier expansion approach can provide interesting insights into the criticality of QCD matter.

Pok Man Lo

Fourier coefficients of the net baryon number density and chiral criticality

We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical mechanics to include pion-nucleon interactions, we reexamine their contribution to the proton yield, taking resonance widths and the presence of nonresonant correlations into account. The effect of multi-pion-nucleon interactions is estimated using lattice QCD results on the baryon-charge susceptibility. We show that a consistent implementation of these features in the statistical hadronization model, leads to a reduction of the predicted proton yield, which then quantitatively matches data of the ALICE collaboration for Pb-Pb collisions at the LHC.

Anton Andronic

China

Peter Braun-Munzinger

Johanna Stachel

The thermal proton yield anomaly in Pb-Pb collisions at the LHC and its resolution

The polarization of virtual photons produced in relativistic nucleus–nucleus collisions provides information on the conditions in the emitting medium. In a hydrodynamic framework, the resulting angular anisotropy of the dilepton final state depends on the flow as well as on the transverse momentum and invariant mass of the photon. We illustrate these effects in dilepton production from quark–antiquark annihilation in the QGP phase and <math><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math> annihilation in the hadronic phase for a static medium in global equilibrium and for a longitudinally expanding system.

India

Amaresh Jaiswal

Virtual photon polarization and dilepton anisotropy in relativistic nucleus–nucleus collisions

We compute the correlation of the net baryon number with the electric charge (<math><msub><mrow><mi>χ</mi></mrow><mrow><mi>B</mi><mi>Q</mi></mrow></msub></math>) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable <math><msub><mrow><mi>χ</mi></mrow><mrow><mi>B</mi><mi>Q</mi></mrow></msub></math> is particularly sensitive to the details of the pion–nucleon interaction, which are consistently incorporated in the current scheme via the empirical scattering phase shifts. Comparing to the recent lattice QCD studies in the <math><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></math>-flavor system, we find that the natural implementation of interactions and the proper treatment of resonances in the S-matrix approach lead to an improved description of the lattice data over that obtained in the hadron resonance gas model.

Chihiro Sasaki

S-matrix analysis of the baryon electric charge correlation

Hadronic polarization and the related anisotropy of the dilepton angular distribution are studied for the reaction πN→Ne+e− . We employ consistent effective interactions for baryon resonances up to spin-5/2, where non-physical degrees of freedom are eliminated, to compute the anisotropy coefficients for isolated intermediate baryon resonances. It is shown that the spin and parity of the intermediate baryon resonance is reflected in the angular dependence of the anisotropy coefficient. We then compute the anisotropy coefficient including the N(1520) and N(1440) resonances, which are essential at the collision energy of the recent data obtained by the HADES Collaboration on this reaction. We conclude that the anisotropy coefficient provides useful constraints for unraveling the resonance contributions to this process.

Miklós Zétényi

Polarization and dilepton anisotropy in pion–nucleon collisions

Starting from the Boltzmann equation in the relaxation time approximation and employing a Chapman–Enskog like expansion for the distribution function close to equilibrium, we derive second-order evolution equations for the shear stress tensor and the dissipative charge current for a system of massless quarks and gluons. The transport coefficients are obtained exactly using quantum statistics for the phase space distribution functions at non-zero chemical potential. We show that, within the relaxation time approximation, the second-order evolution equations for the shear stress tensor and the dissipative charge current can be decoupled. We find that, for large values of the ratio of chemical potential to temperature, the charge conductivity is small compared to the coefficient of shear viscosity. Moreover, we show that in the relaxation-time approximation, the limiting behaviour of the ratio of heat conductivity to shear viscosity is qualitatively similar to that obtained for a strongly coupled conformal plasma.

Relativistic second-order dissipative hydrodynamics at finite chemical potential

We compute the probability distribution P(N) of the net-baryon number at finite temperature and quark-chemical potential, μ , at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For μ/T&lt;1 , the model exhibits the chiral crossover transition which belongs to the universality class of the O(4) spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, P(N) . By considering ratios of P(N) to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to O(4) criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine O(4) criticality in the context of binomial and negative-binomial distributions for the net proton number.