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Krzysztof Redlich

Publications and source records attributed to Krzysztof Redlich.

At least 19 recordsLinked to original sources
arXiv2026

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

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 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 $T_H \simeq 323~$MeV, 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.

hep-ph↗
arXiv2026

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

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.

hep-ph↗
arXiv2026

Scaling properties of net-baryon number fluctuations at the deconfinement critical point

We investigate the critical behavior of the first four cumulants of the net-baryon number near the deconfinement critical point in QCD in the limit of heavy quarks. By connecting baryon-number fluctuations to Polyakov loop susceptibilities, we analyze their mean-field scaling properties at zero and non-zero baryon chemical potentials. In the mean-field approximation we derive critical exponents via the Landau theory and validate them through explicit numerical calculations in an effective Polyakov loop model. Using a Ginzburg-Landau criterion as a diagnostic of beyond-mean-field effects, we estimate the size of the critical region and find that it shrinks with increasing baryon density. By utilizing the exact scaling function in the 3D Ising model, we estimate critical exponents beyond the mean-field approximation.

hep-ph↗
arXiv2026

Dilepton Production as a Probe of Pion Condensation in Hot and Dense QCD Matter

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 $T-μ_I$ 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 plateau-like 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.

hep-ph↗
arXiv2026

Hadron spectra and thermodynamics for all quark flavors from a universal Hagedorn temperature

We show that hadrons in QCD follow a spectrum determined by string dynamics characterized by a universal Hagedorn temperature linked to the string tension. While this behavior was recently established for light hadrons and glueballs, we demonstrate that the same dynamics describes the heavy-flavor sector. After separating the current quark masses, the resulting spectrum reproduces lattice QCD thermodynamics of charmed hadrons and the observed spectra of hadrons across quark flavors without additional parameters. These results reflect the universal confining dynamics of QCD through the string tension.

hep-ph↗
arXiv2025

Charm Quark Kinetics in Heavy Ion Collisions

We study the evolution of charm $(c)$ quarks in hot QCD matter with $N_f=2+1(+1)$ quark flavors by analyzing the charm production rate and the time dependence of their abundance. Microscopically, the system is described within a quasiparticle model, in which interactions among dynamical quarks and gluons are encoded in their effective masses with the running coupling constrained by lattice QCD data. We investigate $c$-quark kinetics in a longitudinally propagating perfect fluid as well as in a viscous medium undergoing (2+1)D expansion, and find that the charm production rate decreases monotonically across all medium formulations. In the $N_f=2+1+1$ scenario, charm production is systematically suppressed due to the effective mass of heavy quasiparticles. Assuming an initial charm yield given by the Statistical Hadronization Model, we solve the rate equation and compute the total charm abundance in hot QCD medium. For all descriptions considered, the charm quark number remains approximately conserved, consistent with existing experimental evidence.

hep-ph↗
arXiv2025

String-based model with Hagedorn temperature of $T_H\sim 300~$MeV describes the spectrum of mesons and glueballs

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired model, corresponding to a physical spatial dimension, d = 3. We show that the physical mass spectrum of massive mesons--in both the strange and non-strange sectors separately--is reasonably well described and extended by the exponential mass spectrum of open strings, $ρ(m)$, characterized by a unique Hagedorn temperature, $T_H = \sqrt{3σ/2π}$, expressed by the string tension, $σ$. This $T_H$ is the value appropriate for d = 3 spatial dimensions, and is of order $T_H \sim 300~\rm MeV$ for typical values of the string tension. It is much larger than the values of $T_H$, 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.

hep-ph↗
arXiv2025

Baselines for Abelian Charge Fluctuations in Nuclear Collisions:Theory and Comparison with Experimental Data

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.

nucl-th↗
arXiv2025

Thermodynamics of fermionic excitations in heavy-quark QCD

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.

hep-lat↗
arXiv2025

Probing nuclear liquid-gas phase transition with isospin correlations

We investigate the fluctuations of the net-baryon number near the critical point of the liquid-gas phase transition. We use the parity doublet model in the mean-field approximation fixed to the zero-temperature properties of nuclear matter to account for critical behavior. We explicitly calculate the fluctuations of the net-proton and net-neutron numbers as well as their correlations in the isospin-symmetric matter. We focus on the qualitative properties and systematics of the first- to fourth-order susceptibilities and their ratios. We demonstrate that the fluctuations of net-proton number do not reflect the total net-baryon number fluctuations in the vicinity of the nuclear liquid-gas phase transition. We also study the behavior of the baryon and proton number factorial cumulants. We highlight the importance of the non-trivial correlations between protons and neutrons.

nucl-th↗
arXiv2025

The quark-gluon plasma: diagnosis with thermal hadron production from the early history until detailed characterization at high energy colliders

In nuclear collisions at relativistic energies, matter is created which resembles closely the matter that filled all space until about 15 microseconds after the big bang. Here we summarize selected aspects of the research that led to the establishment of this new sub-field of physics and briefly describe its current `state of the art' with emphasis on matter creation through thermal particle production. In particular, we will focus on particle production at low transverse momentum and explain how its analysis sheds light on one of the key open questions, i.e. what is the mechanism of hadronization of colored objects such as quarks and gluons.

nucl-th↗
arXiv2025

Emergence of New Systematics for Open Charm Production in High Energy Collisions

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 $D^0, D^+, D^{*+}, D_s^+$ mesons and $Λ_c^+$ 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, $dN_i/dy$, and the rapidity density of charm-anticharm quark pairs, $dN_{c\bar c}/dy$. We demonstrate that, in pp, pA and AA collisions, $dN_i/dy$ scales in leading order with $dN_{c\bar c}/dη$ and for open charm mesons, $D^0,D^+$ and $D^{*+}$ the slope coefficient is quantified by the appropriate thermal density ratio calculated in the SHMc at the chiral crossover temperature, $T_c=156.5$ MeV. The slope coefficient for $dN_{Λ_c^+}/dy$ differs at $T_c$ by a factor of $1.97\pm 0.14$ which is attributed to missing charmed-baryon resonances in the PDG. It is also shown that $dN_i/dy$ 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.

hep-ph↗
arXiv2024

Magnetic effects in the Hadron Resonance Gas

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 ill-defined description of higher-spin states. 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 to study the magnetic field dependence of neutral resonances.

hep-ph↗
arXiv2024

Fluctuations and correlations of baryonic chiral partners

Fluctuations and correlations of the net-baryon number play an important role in exploring critical phenomena in phase transitions of strongly interacting matter governed by Quantum chromodynamics (QCD). 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 non-trivial 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.

hep-ph↗
arXiv2024

Sensitivity of finite size effects to the boundary conditions and the vacuum term

Finite volume effects are studied both with low-momentum cutoff and with momentum discretization in the framework of an (axial)vector meson extended quark-meson model with Polyakov-loop variables. In the momentum cutoff scenario, the CEP moves to lower temperatures and larger quark chemical potentials as the characteristic system size is reduced, however, the treatment of the vacuum term significantly affects its trajectory. The size dependence of the baryon fluctuations is also studied by the kurtosis and the skewness, both of which show moderate dependence on temperature and some dependence on quark chemical potential. The order of the phase transition is also studied near the chiral limit at finite system size and found to be second-order only at vanishing explicit breaking. The implementation of the finite size effect with momentum discretization is more complicated and shows peculiar behavior due to the different modes dropping below the Fermi surface and strong dependence on the type of the boundary condition chosen. We found that both the different boundary conditions and the treatment of the vacuum term cause significant changes in the trajectory of the CEP as the characteristic system size is changed.

hep-ph↗
arXiv2023

The imprint of conservation laws on correlated particle production

The study of event-by-event fluctuations of net-baryon number in a subspace of full phase space is a promising direction for deciphering the structure of strongly interacting matter created in head-on collisions of relativistic heavy nuclei. Such fluctuations are generally suppressed by exact baryon number conservation. Moreover, the suppression is stronger if baryon number is conserved locally. In this report we present a conceptually new approach to quantify correlations in rapidity space between baryon-antibaryon, baryon-baryon, and antibaryon-antibaryon pairs and demonstrate their impact on net-baryon number fluctuations. For the special case of Gaussian rapidity distributions, we use the Cholesky factorization of the covariance matrix, while the general case is introduced by exploiting the well-known Metropolis and Simulated Annealing methods. The approach is based on the use of the canonical ensemble of statistical mechanics for baryon number and can be applied to study correlations between baryons as well as strange and/or charm hadrons. It can also be applied to describe relativistic nuclear collisions leading to the production of multi-particle final states. One application of our method is the search for formation of proton clusters at low collision energies emerging as a harbinger of the anticipated first-order chiral phase transition. In a first step, the results obtained are compared to the recent measurements from the CERN ALICE collaboration. Such investigations are key to explore the phase diagram of strongly interacting matter and baryon production mechanisms at energy scales from several GeV to several TeV.

nucl-th↗
arXiv2023

Interplay of baryonic chiral partners in fluctuations of net-baryon number density

In this contribution, we use the parity doublet model to investigate the fluctuations of the net-baryon number density. We discuss the systematics of the susceptibilities and their ratios for nucleons of positive and negative parity, as well as their correlator. We demonstrate that the fluctuations of positive-parity nucleon do not reflect the fluctuations of the total net-baryon number at the chiral phase transition.

nucl-th↗