We study fluctuations and correlations of conserved charges in QCD using a string-based description of the hadronic mass spectrum. Mesons and baryons are modeled as open relativistic strings with quark-antiquark and quark-diquark endpoints, respectively, leading to an exponential Hagedorn growth of states with a limiting temperature fixed by the string tension. We find that continuous Hagedorn spectra constrained by experimentally established hadrons underestimate net-baryon number fluctuations obtained in lattice QCD (LQCD) calculations. By extracting the Hagedorn string spectrum directly from lattice QCD through a fit to the second-order net-baryon number susceptibility, we obtain a consistent description of a broad set of fluctuations of conserved charges from LQCD with the Hagedorn temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>T</mi><mi>H</mi></msub><mo>≃</mo><mn>323</mn><mspace width="0.16em"></mspace><mi>MeV</mi></mrow></math>, without introducing additional free parameters. Our results provide thermodynamic evidence in support of a string quark-diquark picture of baryons in the confined phase of QCD.

Poland

Japan

Michał Marczenko

Krzysztof Redlich

Evidence for quark-diquark structure of baryons from fluctuations of conserved charges

An effective chiral model is introduced to illustrate finite-size effects, incorporating the standard zero-mode treatment, momentum-space discretization, and gradient effects modeled via a prescribed finite-volume profile. The fluctuations of the chiral order parameter and the net-baryon number, as well as their scaling properties, are investigated near a critical point and a first-order transition in finite-size systems. The finite-volume effects on the Binder cumulant and the kurtosis are shown along the phase boundary and the approximate freeze-out line, respectively. Phenomenological implications on fluctuation observables are pointed out and explained.

Hungary

Győző Kovács

Pok Man Lo

Chihiro Sasaki

Finite-size effects and scaling properties of chiral and baryon-number fluctuations

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

Anar Rustamov

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

We investigate dilepton production from an isospin-asymmetric hot and dense medium in order to explore the role of isospin imbalance in electromagnetic spectral properties. We focus in particular on modifications of the dilepton production rate associated with the onset of pion condensation, which can occur in the presence of a finite isospin chemical potential. We employ the Nambu–Jona-Lasinio model with isoscalar-vector interaction. We examine the phase structure in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow></math> plane and estimate the vector current correlator-resummed dilepton rate for an effective quark chemical potential. We find that the interplay between isospin asymmetry, pion condensation, and vector interactions leads to nontrivial modifications of the dilepton yield. In particular, we observe two key features of the pion condensed phase: an enhancement at lower invariant mass and a prominent plateaulike structure which also help clearly identify the pion condensed phase from a chirally broken/restored phase. These results highlight the potential sensitivity of dilepton observables to pion-condensed phase of QCD matter, with possible implications for future low-energy heavy-ion collision experiments as well as isospin-rich environments such as neutron star matter.

Romania

Aritra Bandyopadhyay

India

Chowdhury Aminul Islam

Dilepton production as a probe of pion condensation in hot and dense QCD matter

We investigate the thermodynamic properties of fermionic excitations in heavy-quark QCD on the lattice with Wilson fermions. The grand potential is calculated analytically in the hopping parameter expansion (HPE) on the basis of the cumulant expansion. Using the grand potential, we compute the quark number susceptibilities and their ratios up to next-to-leading order in the HPE. The ratio of fourth- to second-order susceptibilities is shown to be unity (nine) in the deconfined (confined) phase at the leading order. Excitation properties of baryonic and quark modes in each phase are also investigated utilizing the Boltzmann statistics. We obtain an analytic formula for the quark excitation energy in the deconfined phase, while that for baryonic excitations in the confined phase is decomposed into flavor multiplets.

Kei Tohme

Takahiro M. Doi

Masakiyo Kitazawa

Thermodynamics of fermionic excitations in heavy-quark QCD

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired corresponding to a physical spatial dimension, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>3</mn></math>. We show that the physical mass spectrum of massive mesons—in both the strange and nonstrange sectors separately—is reasonably well described and extended by the exponential mass spectrum of open strings, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo stretchy="false">(</mo><mi>m</mi><mo stretchy="false">)</mo></math>, characterized by a unique Hagedorn temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>H</mi></msub><mo>=</mo><msqrt><mrow><mn>3</mn><mi>σ</mi><mo>/</mo><mn>2</mn><mi>π</mi></mrow></msqrt></math>, expressed by the string tension <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>. This <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>H</mi></msub></math> is the value appropriate for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>3</mn></math> spatial dimensions and is of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>∼</mo><mrow><mn>300</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></mrow></math> for typical values of the string tension. It is much larger than the values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>H</mi></msub></math> which have been phenomenologically extracted so far to describe the meson spectrum. Glueball states in pure gauge theory, modeled by closed strings, exhibit a similarly large Hagedorn temperature, highlighting a universal feature of the exponential spectrum. We further analyze the thermodynamic properties of the equation of state at finite temperature and demonstrate that, in the confined phase, the string models agree with lattice QCD results. This lends further support to the recent interpretation of the QCD phase diagram that incorporates strings as relevant degrees of freedom.

United States

Larry McLerran

String-based model with Hagedorn temperature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>H</mi></msub><mo>∼</mo><mn>300</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> describes the spectrum of mesons and glueballs

We present the production systematics of open charm hadron yields in high-energy collisions and their description based on the Statistical Hadronization Model of charm (SHMc). The rapidity density of $\textit{D}$ , $\textit{D}$ , $\textit{D}$ , $$ {D}_s^{+} $$ mesons and $$ {\Lambda}_c^{+} $$ baryons in heavy ion and proton-proton collisions is analyzed for different collision energies and centralities. The SHMc is extended to open charm production in minimum-bias and high-multiplicity pp collisions. In this context, we use the link established in [1, 2], between the rapidity density of open charm hadron yields, $\textit{dN}$ /$\textit{dy}$, and the rapidity density of charm-anticharm quark pairs, $$ d{N}_{c\overline{c}}/ dy $$ . We demonstrate that, in pp, pA and AA collisions, $\textit{dN}$ /$\textit{dy}$ scales in leading order with $$ d{N}_{c\overline{c}}/ d\eta $$ and for open charm mesons, $\textit{D}$ , $\textit{D}$ and $\textit{D}$ the slope coefficient is quantified by the appropriate thermal density ratio calculated in the SHMc at the chiral crossover temperature, $\textit{T}$ = 156.5 MeV. The slope coefficient for $$ d{N}_{\Lambda_c^{+}}/ dy $$ differs at $\textit{T}$ by a factor of 1.97 ± 0.14 which is attributed to missing charmed-baryon resonances in the PDG. It is also shown that $\textit{dN}$ /$\textit{dy}$ exhibits power-law scaling with the charged-particle pseudo-rapidity density in high energy collisions and within uncertainties. Furthermore, presently available data on different ratios of open charm rapidity densities in high-energy collisions are independent of collision energy and system size, as expected in the SHMc.

China

Peter Braun-Munzinger

Natasha Sharma

Johanna Stachel

Emergence of new systematics for open charm production in high energy collisions

We discuss the modeling of the hadronic phase of QCD at finite magnetic field in the framework of hadron resonance gas (HRG). We focus on the statistical description of particle yields that include contribution from resonance decays. We demonstrate that the swift increase in the number of protons with magnetic field predicted in the HRG is due to the assumption of structureless resonances. We discuss fluctuations of conserved charges and show that at present the qualitative comparison of the model predictions with the lattice QCD data should be treated with care. We also discuss the principle of detailed balance which allows us to study the magnetic field dependence of neutral resonances.

Michał Szymański

Bithika Karmakar

Pasi Huovinen

Magnetic effects in the hadron resonance gas

We investigate the effect of screening of the four-quarks contact interactions by the ring diagram at finite temperature and density in an effective chiral model inspired by QCD in the Coulomb gauge. As a consequence, a medium-dependent coupling naturally emerges which, in a class of chiral models, brings the chiral crossover temperature down to the value calculated in lattice QCD at low net-baryon density. Furthermore, it implies a stronger divergence of the chiral susceptibility at the critical point compared to the mean-field dynamics. At high densities, the screening induces a substantial instability region and its size depends on the regularization schemes. We discuss the properties of an effective potential for a class of models described by momentum-independent gap equations. In particular, we introduce the method to construct an approximate effective potential from the gap equations to determine the location of the first-order phase transition.

Influence of dynamical screening of four-quarks interaction on the chiral phase diagram

The exploration of critical phenomena in phase transitions of strongly interacting matter governed by quantum chromodynamics (QCD) is one of the goals of present ultrarelativistic heavy-ion collision experiments at BNL and CERN. The key research direction is to locate the putative critical point on the phase diagram of QCD linked to the chiral symmetry restoration at finite temperature and/or density. One of the main theoretical tools used for this purpose is the fluctuations of conserved charges, such as the net-baryon number. However, due to experimental limitations, analyses of heavy-ion collision data suffer from a very doubtful basing of the net-proton number being a proxy for the total net-baryon number fluctuations. In this work, we use the parity doublet model to investigate the fluctuations of the net-baryon number density in hot and dense hadronic matter. The model accounts for chiral criticality within the mean-field approximation. We focus on the qualitative properties and systematics of the first- and second-order susceptibility of the net-baryon number density, and their ratios for nucleons of positive and negative parity, as well as their correlator. We show that the fluctuations of the positive-parity nucleon do not necessarily reflect the fluctuations of the total net-baryon number density at the phase boundary of the chiral phase transition. We also investigate the nontrivial structure of the correlator. Furthermore, we discuss and quantify the differences between the fluctuations of the net-baryon number density in the vicinity of the chiral and liquid-gas phase transition in nuclear matter. We indicate a possible relevance of our results with the interpretation of the experimental data on net-proton number fluctuations in heavy-ion collisions.