arXiv subjects

Ralf Rapp

Publications and source records attributed to Ralf Rapp.

At least 37 records · Page 2Linked to original sources

arXiv2025

Interacting mesons as degrees of freedom in a chiral model

We study the equation of state of hot and dense hadronic matter using an extended Chiral Mean Field (CMF) model framework where the addition is the inclusion of interactions of thermally excited mesons. This is implemented by calculating the in-medium masses of pseudoscalar and vector mesons, obtained through the explicit chiral symmetry-breaking and vector interaction terms in the Lagrangian, respectively, prior to applying the mean-field approximation. As a result, the in-medium meson contributions generate a feedback term to the CMF's equations of motion, which then modifies the equation of state. With this improvement, we quantify the effect on the equation of state of strongly interacting matter through comparisons with state-of-the-art lattice QCD results and other hadronic models like the Hadron Resonance Gas model. We find that the results of the updated hadronic CMF model with an improved meson description (mCMF) provide a better agreement with lattice-QCD data for thermodynamic state variables across a wide range of temperatures and baryon chemical potentials.

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arXiv2025

Hadronization of Heavy Quarks

Heavy-flavor hadrons produced in ultra-relativistic heavy-ion collisions are a sensitive probe for studying hadronization mechanisms of the quark-gluon-plasma. In this work, we survey how different transport models for the simulation of heavy-quark diffusion through a quark-gluon plasma in heavy-ion collisions implement hadronization and how this affects final-state observables. Utilizing the same input charm-quark distribution in all models at the hadronization transition, we find that the transverse-momentum dependence of the nuclear modification factor of various charm hadron species has significant sensitivity to the hadronization scheme. In addition, the charm-hadron elliptic flow exhibits a nontrivial dependence on the elliptic flow of the hadronizing partonic medium.

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arXiv2025

Polarization of Thermal Dilepton Radiation

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 $ρ$-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.

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arXiv2024

Electric Conductivity of QCD Matter and Dilepton Spectra in Heavy-Ion Collisions

The electric conductivity, $σ_{\rm el}$, is a fundamental transport coefficient of QCD matter that can be related to the zero-energy limit of the electromagnetic (EM) spectral function at vanishing 3-momentum in the medium. The EM spectral function is also the central quantity to describe the thermal emission rates and pertinent spectra of photon and dilepton radiation in heavy-ion collisions. Employing a model for dilepton rates that combines hadronic many-body theory with nonperturbative QGP emission constrained by lattice-QCD which describes existing dilepton measurements in heavy-ion collisions, we investigate the sensitivity of low-mass dilepton spectra in Pb-Pb collisions at the LHC to $σ_{\rm el}$. In particular, we disentangle the contributions from QGP and hadronic emission, and identify signatures that can help to extract $σ_{\rm el}$ from high-precision experimental data expected to be attainable with future detector systems at the LHC.

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arXiv2024

Analysis of Static Wilson Line Correlators from Lattice QCD at Finite Temperature with $T$-matrix Approach

We employ a thermodynamic $T$-matrix approach to study Wilson line correlators (WLCs) for a static quark-antiquark pair within the quark-gluon plasma (QGP). By refining earlier determined input parameters, self-consistent $T$-matrix calculations can approximately reproduce the WLCs from 2+1-flavor lattice-QCD (lQCD) computations, while also satisfying constraints on the bulk medium from the QGP equation of state. The main difference from earlier results is a reduced screening in the input potential toward higher temperatures. When elaborating the consequences of this scenario on transport properties we find a more pronounced temperature dependence of the low-momentum relaxation rate of heavy quarks in the QGP. This, in particular, leads to a rather weak increase of the (temperature-scaled) spatial diffusion coefficient, which turns out to be in fair agreement with the most recent pertinent lQCD data.

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arXiv2023

Thermalization of Nuclear Matter in Heavy-Ion Collisions at Fermi-Energies

We analyze the time evolution of the kinetic properties of nuclear matter produced in heavy-ion collisions at Fermi energies. The collision system is simulated using Constrained Molecular Dynamics (CoMD) transport calculations whose output is the isospin, position, and momentum of the nucleons. Focusing on central 35$\,$A$\cdot$MeV $^{40}$Ca+$^{40}$Ca collisions we utilize this information to extract localized momentum distributions in volume elements of 8$\,$fm$^3$ and time steps of 5$\,$fm/$c$. We then parameterize the single-particle momentum distributions with thermally motivated fit functions in the local rest frame of each cell. While the transverse-momentum distributions are well reproduced by thermal ones, the longitudinal ones carry a marked imprint of the initial nuclear motion which we capture by introducing a centroid motion into our fit functions. In particular, we find that Fermi distributions yield significantly better fits than Boltzmann ones, a consequence of the Pauli blocking implemented in CoMD. From the fits we extract the time dependence of the thermodynamic and collective properties of the excited nuclear medium. We find that the transverse temperature gradually rises to about 6$\,$MeV, which is accompanied by a dissipation of the initial centroid motion of the incoming nuclei which vanishes at about 100$\,$fm/$c$ after initial impact. We are therefore able to track the transition of beam energy into random kinetic energy for nucleons, suggesting a three-dimensional equilibration of energy in the late stages of the collision.

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arXiv2023

$T$-matrix Analysis of Static Wilson Line Correlators from Lattice QCD at Finite Temperature

We utilize a previously constructed thermodynamic $T$-matrix approach to the quark-gluon plasma (QGP) to calculate Wilson line correlators (WLCs) of a static quark-antiquark pair and apply them to the results from 2+1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent $T$-matrix results, which include constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of the input parameters are implemented. In particular, the input potential requires less screening than used in previous $T$-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks which turns out to have a rather weak temperature dependence, in approximate agreement with recent lQCD results.

hep-lat↗

arXiv2023

Spin-Dependent Interactions and Heavy-Quark Transport in the QGP

We extend a previously constructed T-matrix approach to the quark-gluon plasma (QGP) to include the effects of spin-dependent interactions between partons. Following earlier work within the relativistic quark model, the spin-dependent interactions figure as relativistic corrections to the Cornell potential. When applied to the vacuum spectroscopy of quarkonia, in particular their mass splittings in S- and P-wave states, the issue of the Lorentz structure of the confining potential arises. We confirm that a significant admixture of a vector interaction (to the previously assumed scalar interaction) improves the description of the experimental mass splittings. The temperature corrections to the in-medium potential are constrained by results from thermal lattice-QCD for the equation of state (EoS) and heavy-quark (HQ) free energy in a selfconsistent set-up for heavy- and light-parton spectral functions in the QGP. We then deploy the refined in-medium heavy-light T-matrix to compute the charm-quark transport coefficients in the QGP. The vector component of the confining potential, through its relativistic corrections, enhances the friction coefficient for charm quarks in the QGP over previous calculations by tens of percent at low momenta and temperatures, and more at higher momenta. Our results are promising for improving the current phenomenology of open heavy-flavor observables at Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC).

hep-ph↗

arXiv2023

Spin-Induced Interactions and Heavy-Quark Transport in the QGP

A previously constructed $T$-matrix approach for studying the quark-gluon plasma (QGP) is improved by incorporating spin-dependent interactions between partons. These interactions arise from the relativistic corrections to the Cornell potential. We first study the vacuum spectroscopy of quarkonia with this potential and find that a significant admixture of a vector component in the confining potential (rather than the previously considered scalar interaction) improves the description of the experimental mass splittings in $S$- and $P$-wave states. The in-medium potential containing the vector component in the confining interaction is constrained by fitting lattice-QCD results for heavy-quark (HQ) free energies and the equation of state (EoS) computed within in the selfconsistent $T$-matrix framework. We subsequently extract the transport coefficients for charm quarks in the QGP with the improved in-medium potentials. The relativistic corrections to the vector component of the confining potential cause a notable increase in the thermal relaxation rate of charm quarks in the QGP in comparison to previous calculations, especially at high momenta. These results are expected to have significant ramifications for the phenomenology of open heavy-flavor observables at RHIC and the LHC.

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arXiv2023

Bottom hadro-chemistry in high-energy hadronic collisions

The hadro-chemistry of bottom quarks ($b$) produced in hadronic collisions encodes valuable information on the mechanism of color-neutralization in these reactions. Since the $b$-quark mass is much larger than the typical hadronic scale of $\sim$1\,GeV, $b\bar b$ pair production is expected to be well separated from subsequent hadronization processes. A significantly larger fraction of $b$ baryons has been observed in proton-proton ($pp$) and proton-antiproton ($p\bar{p}$) reactions relative to $e^+e^-$ collisions, challenging theoretical descriptions. We address this problem by employing a statistical hadronization approach with an augmented set of $b$-hadron states beyond currently measured ones, guided by the relativistic quark model and lattice-QCD computations. Assuming {\it relative} chemical equilibrium between different $b$-hadron yields, thermal densities are used as fragmentation weights of $b$-quarks into various hadron species. With quark model estimates of the decay patterns of excited states, the fragmentation fractions of weakly-decaying $b$ hadrons are computed and found to agree with measurements in $p\bar{p}$ collisions at the Tevatron. By combining transverse-momentum ($p_T$) distributions of $b$-quarks from perturbative QCD with thermal weights and independent fragmentation toward high $p_T$, a fair description of the $p_T$-dependent $\bar{B}_s^0/B^-$ and $Λ_b^0/B^-$ ratios measured in $pp$ collisions at the LHC is obtained. Finally, we implement the hadro-chemistry into a strongly-coupled transport approach for $b$-quarks in heavy-ion collisions, utilizing previously determined $b$-quark transport coefficients in the Quark-Gluon Plasma, to highlight the modifications of hadro-chemistry and collective behavior of $b$ hadrons in Pb-Pb collisions at the LHC.

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arXiv2022

Electric conductivity of hot pion matter

The determination of transport coefficients plays a central role in characterizing hot and dense nuclear matter. Currently, there are significant discrepancies between various calculations of the electric conductivity of hot hadronic matter. In the present work we calculate the electric conductivity of hot pion matter by extracting it from the electromagnetic spectral function, via its zero energy limit at vanishing 3-momentum, within the Vector Dominance Model (VDM). Since within the VDM the photon couples to the hadronic currents primarily through the $ρ$ meson, we use hadronic many-body theory to calculate the $ρ$-meson's self-energy in hot pion matter, by dressing its pion cloud with thermal $π$-$ρ$ and $π$-$σ$ loops including vertex corrections to maintain gauge invariance. In particular, we analyze the low-energy transport peak of the spectral function, extract its behavior with temperature and compare to (the results of) existing approaches in the literature.

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arXiv2022

Charmonium, $B_c$ and X(3872) Transport at the LHC

We deploy a kinetic-rate equation to evaluate the transport of $J/ψ$, $ψ(2S)$, $B_c$ and X(3872) in ultra-relativistic heavy-ion collisions and compare their production yields to experimental data from the Large Hadron Collider. The rate equation has two main transport parameters, i.e., the equilibrium limit and reaction rate for each state. The temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. The reaction rates for charmonia, bottomonia and $B_c$ rely on charm- and bottom-quark masses as well as binding energies from a thermodynamic $T$-matrix approach. For the X(3872) particle, its internal structure information is encoded in reaction rates and initial conditions in the hadronic phase via two different scenarios: a loosely bound hadronic molecule vs. a compact diquark-antidiquark tetraquark.

hep-ph↗

arXiv2022

Dilepton Signature of a First-Order Phase Transition

The search for a first-order phase transition in strongly interacting matter is one of the major objectives in the exploration of the phase diagram of Quantum Chromodynamics (QCD). In the present work we investigate dilepton radiation from the hot and dense fireballs created in Au-Au collisions at projectile energies of 1-2 $A$GeV for potential signatures of a first-order transition. Toward this end, we employ a hydrodynamic simulation with two different equations of state, with and without a phase transition. The latter is constrained by susceptibilities at vanishing chemical potential from lattice-QCD as well as neutron star properties, while the former is implemented via modification of the mean-fields in the quark phase. We find that the latent heat involved in the first-order transition leads to a substantial increase in the low-mass thermal emission signal, by about a factor of two above the cross-over scenario.

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arXiv2022

Non-equilibrium charmonium regeneration in strongly coupled quark-gluon plasma

The evaluation of quarkonium regeneration in ultrarelativistic heavy-ion collisions (URHICs) requires the knowledge of the heavy-quark phase space distributions in the expanding quark-gluon plasma (QGP) fireball. We employ a semi-classical charmonium transport approach where regeneration processes explicitly account for the time-dependent spectra of charm quarks via Langevin simulations of their diffusion. The inelastic charmonium rates and charm-quark transport coefficients are computed from the same charm-medium interaction. The latter is modeled by perturbative rates, augmented with a $K$-factor to represent nonperturbative interaction strength and interference effect. Using central 5.02~TeV Pb-Pb collisions as a test case we find that a good description of the measured $J/ψ$ yield and its transverse-momentum dependence can be achieved if a large $K\gtrsim5$ is employed while smaller values lead to marked discrepancies. This is in line with open-charm phenomenology in URHICs, where nonperturbative interactions of similar strength are required. Our approach establishes a common transport framework for a microscopic description of open and hidden heavy-flavor (HF) observables that incorporates both nonperturbative and non-equilibrium effects, and thus enhances the mutual constraints from experiment on the extraction of transport properties of the QGP.

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arXiv2022

Collectivity of $J/ψ$ Mesons in Heavy-Ion Collisions

The production of $J/ψ$ mesons in heavy-ion collisions at the Large Hadron Collider is believed to be dominated by the recombination of charm and anti-charm quarks in a hot QCD medium. However, measurements of the elliptic flow ($v_2$) of $J/ψ$ mesons in these reactions are not well described by existing calculations of $J/ψ$ recombination for transverse momenta $p_T\geq$4 GeV. Here, we revisit these calculations in two main aspects. By employing the resonance recombination model, we implement distribution functions of charm quarks transported through the quark-gluon plasma using state-of-the-art Langevin simulations, and we account for the space-momentum correlations of the diffusing charm and anti-charm quarks in the hydrodynamically expanding fireball. These improvements extend the relevance of the recombination processes to substantially larger momenta than before. In addition, we revisit the suppression of the primordially produced $J/ψ$ mesons by propagating them through the same hydrodynamic medium, leading to a marked increase of the $v_2$ of this component over previous estimates. Combining these developments into a calculation of the $p_T$-dependent nuclear modification factor and $v_2$ of inclusive $J/ψ$ production in semi-central Pb-Pb collisions at the LHC, we find a good description of the experimental results by the ALICE collaboration. Our results thus resolve the above-mentioned $v_2$ puzzle and imply the relevance of recombination processes for $p_T$'s of up to $\sim$8 GeV.

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arXiv2022

Heavy-Quark Diffusion in the Quark-Gluon Plasma

The diffusion of heavy quarks through the quark-gluon plasma (QGP) as produced in high-energy heavy-ion collisions has long been recognized as an excellent probe of its transport properties. In addition, the experimentally observed heavy-flavor hadrons carry valuable information about the hadronization process of the transported quarks. Here we review recent progress in the theoretical developments of heavy-quark interactions in the QGP and how they relate to the nonperturbative hadronization process, and discuss the recent status of the pertinent phenomenology in heavy-ion collisions at the RHIC and the LHC. The interactions of heavy quarks in the QGP also constitute a central building block in the description of the heavy quarkonia which controls their transport parameters as well. We will thus focus on theoretical approaches that aim for a unified description of open and hidden heavy-flavor particles in medium, and discuss how they can be constrained by lattice QCD "data" and utilized to deduce fundamental properties of the microscopic interactions and emerging spectral properties of the strongly coupled QGP.

hep-ph↗

arXiv2021

Heavy-Light Susceptibilities in a Strongly Coupled Quark-Gluon Plasma

Quark number susceptibilities as computed in lattice QCD are commonly believed to provide insights into the microscopic structure of QCD matter, in particular its degrees of freedom. We generalize a previously constructed partonic $T$-matrix approach to finite chemical potential to calculate various susceptibilities, in particular for configurations containing a heavy charm quark. At vanishing chemical potential and moderate temperatures, this approach predicts large collisional widths of partons generated by dynamically formed hadronic resonance states which lead to transport parameters characteristic for a strongly coupled system. The quark chemical potential dependence is implemented into the propagators and the in-medium color potential, where two newly introduced parameters for the thermal and screening masses are fixed through a fit to the baryon number susceptibility, $χ^B_2$. With this setup, we calculate heavy-light susceptibilities without further tuning; the results qualitatively agree with the lattice-QCD (lQCD) data for both $χ^{uc}_{11}$ and $χ^{uc}_{22}$. This implies that the lQCD results are compatible with a significant content of broad $D$-meson and charm-light diquark bound states in a moderately hot QGP.

hep-ph↗

arXiv2021

X(3872) Transport in Heavy-Ion Collisions

The production of the $X(3872)$ particle in heavy-ion collisions has been contemplated as an alternative probe of its internal structure. To investigate this conjecture, we perform transport calculations of the $X(3872)$ through the fireball formed in nuclear collisions at the LHC. Within a kinetic-rate equation approach as previously used for charmonia, the formation and dissociation of the $X(3872)$ is controlled by two transport parameters, i.e., its inelastic reaction rate and thermal-equilibrium limit in the evolving hot QCD medium. While the equilibrium limit is controlled by the charm production cross section in primordial nucleon-nucleon collisions (together with the spectra of charm states in the medium), the structure information is encoded in the reaction rate. We study how different scenarios for the rate affect the centrality dependence and transverse-momentum ($p_T$) spectra of the $X(3872)$. Larger reaction rates associated with the loosely bound molecule structure imply that it is formed later in the fireball evolution than the tetraquark and thus its final yields are generally smaller by around a factor of two, which is qualitatively different from most coalescence model calculations to date. The $p_T$ spectra provide further information as the later decoupling time within the molecular scenario leads to harder spectra caused by the blue-shift from the expanding fireball.

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