In-medium Potential Research Articles

Complex-valued in-medium potential between heavy impurities in ultracold atoms

Complex-valued in-medium potential between heavy impurities in ultracold atoms

Momentum dependence of in-medium potentials: A solution to the hyperon puzzle in neutron stars

Momentum dependence of in-medium potentials: A solution to the hyperon puzzle in neutron stars

Investigating color screening in proton-nucleus collisions with complex potentials* *Supported by the National Natural Science Foundation of China (NSFC) (12175165, 11705125); S.S. acknowledges support from U.S. Department of Energy, Office of Science, Office of Nuclear Physics, (DE-FG88ER40388); X.D acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the CRC-TR 211 'Strong-interaction matter under extreme conditions’– project number 315477589

Color screening and parton inelastic scattering modify the heavy-quark antiquark potential in mediums consisting of particles from quantum chromodynamics (QCD), leading to the suppression of quarkonium production in relativistic heavy-ion collisions. Owing to the small charm/anti-charm () pair production number in proton-nucleus (pA) collisions, the correlation between different pairs is negligible, which makes the Schrödinger equation viable for tracking the evolution of only one pair. We employ the time-dependent Schrödinger equation with an in-medium potential to study the evolution of charmonium wave functions in a hydrodynamic-like QCD medium produced in pA collisions. We explore different parametrizations of real and imaginary parts of the potential and calculate the nuclear modification factors () of and in TeV energy p-Pb collisions at the Large Hadron Collider (LHC). Comparing strong and weak screening scenarios with experimental data in this approach, we arrive at the conclusion that color screening is weak at temperatures close to the deconfined phase transition. Moreover, the imaginary part of the potential is crucial in describing the experimental data, which is consistent with widely studied semi-classical approaches, where dissociation rates are essential.

In-medium $$\Delta (1232)$$ potential, pion production in heavy-ion collisions and the symmetry energy

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $\Delta$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_\Delta \approx$ 0.45. For the isovector component only a constraint between the potential's strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the $\Delta$(1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. This region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10$\%$. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5$\%$.

Formation and dynamics of exotic hypernuclei in heavy-ion collisions

The dynamics of exotic hypernuclei in heavy-ion collisions has been investigated thoroughly with a microscopic transport model. All possible channels on hyperon ($\Lambda$, $\Sigma$ and $\Xi$) production near threshold energies are implemented in the transport model. The light complex fragments (Z$\leq$2) are constructed with the Wigner-function method. The classical phase-space coalescence is used for recognizing heavy nuclear and hyperfragments and the statistical model is taken for describing the decay process. The nuclear fragmentation reactions of the available experimental data from the ALADIN collaboration are well reproduced by the combined approach. It is found that the in-medium potentials of strange particles influence the strangeness production and fragment formation. The hyperfragments are mainly created in the projectile or target-like rapidity region and the yields are reduced about the 3-order magnitude in comparison to the nuclear fragments. The hypernuclear dynamics of HypHI data is well described with the model. The possible experiments for producing the neutron-rich hyperfragments at the high-intensity heavy-ion accelerator facility (HIAF) are discussed.

Heavy quarkonia in a bulk viscous medium

We study the properties of heavy quarkonia in a quark gluon plasma in the presence of bulk viscous effects. Within the hard thermal loop approximation at one-loop, the dielectric permittivity of a quark gluon plasma is computed, where the bulk viscous effect enters through the deformation of the distribution functions of thermal quarks and gluons. Based on the modified dielectric permittivity, we compute the in-medium heavy quark potential, that includes non-pertubative string-like terms as well as the perturbative Coulombic term. We discuss how the bulk viscous effect modify the real and imaginary parts of the in-medium potential. Several prescriptions are examined as to how to include the string-like non-perturbative potentials. Using the deformed potential, we compute the wave functions, binding energies, and decay widths of heavy quarkonia in a bulk viscous medium, and study their sensitivity to the strength of the bulk viscous effect. An estimate of the melting temperatures is given.

Extraction of the heavy-quark potential from bottomonium observables in heavy-ion collisions

The in-medium color potential is a fundamental quantity for understanding the properties of the strongly coupled quark-gluon plasma (sQGP). Open and hidden heavy-flavor (HF) production in ultrarelativistic heavy-ion collisions (URHICs) has been found to be a sensitive probe of this potential. Here we utilize a previously developed quarkonium transport approach in combination with insights from open HF diffusion to extract the color-singlet potential from experimental results on ϒ production in URHICs. Starting from a parameterized trial potential, we evaluate the ϒ transport parameters and conduct systematic fits to available data for the centrality dependence of ground and excited states at RHIC and the LHC. The best fits and their statistical significance are converted into a temperature dependent potential. Including nonperturbative effects in the dissociation rate guided from open HF phenomenology, we extract a rather strongly coupled potential with substantial remnants of the long-range confining force in the QGP.

Quarkonium Phenomenology from a Generalised Gauss Law

We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass m D . Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the Ψ ′ / J / Ψ ratio in heavy-ion collisions at different beam energies.

Quantum dynamical dissociation of quarkonia by wave function decoherence in quark-gluon plasma

In this study, we investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in an improved QCD based stochastic potential model. This model describes the quarkonium dynamics in terms of a Schrödinger equation with an in-medium potential and two noise terms encoding the residual interaction between the heavy quarks and the medium. The time evolution described by this equation is unitary, since the effective potential term is real-valued. At a glance this is at odds with lattice results, but we explain why it is actually not the case.We discuss the time evolution of the admixtures of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualitatively consistent with the experimental data in relativistic heavy-ion collisions. The other is that the noise plays an important role in order to describe quarkonium dynamics in medium, in particular it causes decoherence of the quarkonium wave function.

Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations

We present our first results on a direct computation of the complex in-medium heavy quark potential from realistic lattice QCD simulations. Ensembles with Nτ = 12 from the HotQCD and TUMQCD collaboration offer unprecedented high statistics, those with Nτ = 16 unprecedented time resolution, making possible a robust extraction of the real part from the spectral functions of Wilson line correlators. To this end we deploy a combination of a Bayesian reconstruction (BR method), as well as a Padé-like approximation. We corroborate findings made on less realistic lattices that Re[V] smoothly transitions from a confining to a screened behavior at high temperatures and its values lie close to the color singlet free energies. A finite value of the Im[V] is observed in the quark-gluon-plasma phase.

From in-Medium Color Forces to Transport Properties of QGP

A thermodynamic quantum many-body T-matrix approach is employed to study the spectral and transport properties of the quark-gluon plasma at moderate temperatures where nonperturbative effects are essential. For the partonic two-body interaction we utilize a QCD-inspired Hamiltonian whose color forces are motivated by the heavy-quark (HQ) limit including remnants of the confining force, and augmented by relativistic corrections. We solve the in-medium parton propagators and T-matrices selfconsistently and resum the skeleton diagrams for the equation of state (EoS) to all orders thereby accounting for the dynamical formation of two-body bound states. Two types solutions for the in-medium potential are found in when fitting to lattice-QCD data for the EoS, HQ free energy and quarkonium correlators: a weakly-coupled scenario (WCS) with a (real part of the) potential close to the free energy, resulting in moderately broadened spectral functions and weak bound states near Tc, and a strongly-coupled scenario (SCS), with a much stronger potential which produces large imaginary parts (“melting” the parton spectral functions) and generates strong bound states near Tc. We calculate pertinent transport coefficients (specific shear viscosity and HQ diffusion coefficient) and argue that their constraints from heavy-ion phenomenology unambiguously favor the strongly-coupled scenario.

Effect of the K+ in-medium potential on K+ production in heavy ion collisions

K+ meson productions in nucleus-nucleus collisions at energies near the kaon production threshold energy were investigated within the quantum molecular dynamics (QMD) model based on the covariant kaon dynamics. We analyzed the rapidity dependence of the direct flow v1 and the elliptic flow v2 of K+ meson, and the transverse momentum (pT) dependence of v1 for the K+ meson in Ni + Ni collisions at 1.91 AGeV, and compared the results with the FOPI data. We observed that the kaon in-medium potential obviously affects the K+ production in nucleus-nucleus collisions. After taking into account the K+ in-medium potential and using the soft equation of state, the theoretical results are in good agreement with the experimental data.

T -matrix approach to quark-gluon plasma

A selfconsistent thermodynamic $T$-matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly-coupled solution (WCS) which features color-potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near $T_{\rm c}$, and a strongly-coupled solution (SCS) with a strong color potential (much larger than the free energy) resulting in broad non-quasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching $T_{\rm c}$.

Dynamical dissociation of quarkonia by wave function decoherence

We investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in one dimension using an improved QCD based stochastic potential model. This model describes the quarkonium dynamics in terms of a Schr\"odinger equation with an in-medium potential and two noise terms encoding the residual interactions between the heavy quarks and the medium. The probabilities of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma are discussed. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualitatively consistent with the experimental data in relativistic heavy-ion collisions. The other is that the noise plays an important role in order to describe quarkonium dynamics in medium, in particular it causes decoherence of the quarkonium wave function. The effectiveness of decoherence is controlled by a new length scale $l_{\rm corr}$. It represents the noise correlation length and its effect has not been included in existing phenomenological studies.

Δ resonances and charged ρ mesons in neutron stars

We study the equation of state of cold and dense baryon matter within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field. We include Δ(1232) isobars into previously developed models with hyperons and consider the possibility of charged ρ-meson condensation. The Δ-isobars, being included with realistic values of the attractive in-medium potential, do not lead to a strong decrease of the maximum predicted neutron star (NS) mass, and our models thus resolve the “Δ-resonance puzzle”. The charged ρ−-meson condensation leads to a substantial maximum NS mass decrease. However, the observational constraint on the minimal value of the maximum NS mass remains fulfilled in all our models under consideration. The decrease of NS mass can be lowered, if one assumes a limited decrease of the ρ-meson effective mass at high densities.

Density-dependent effective baryon–baryon interaction from chiral three-baryon forces

A density-dependent effective potential for the baryon–baryon interaction in the presence of the (hyper)nuclear medium is constructed, based on the leading (irreducible) three-baryon forces derived within SU(3) chiral effective field theory. We evaluate the contributions from three classes: contact terms, one-pion exchange and two-pion exchange. In the strangeness-zero sector we recover the known result for the in-medium nucleon–nucleon interaction. Explicit expressions for the ΛN in-medium potential in (asymmetric) nuclear matter are presented. Our results are suitable for implementation into calculations of (hyper)nuclear matter. In order to estimate the low-energy constants of the leading three-baryon forces we introduce the decuplet baryons as explicit degrees of freedom and construct the relevant terms in the minimal non-relativistic Lagrangian. With these, the constants are estimated through decuplet saturation. Utilizing this approximation we provide numerical results for the effect of the three-body force in symmetric nuclear matter and pure neutron matter on the ΛN interaction. A moderate repulsion that increases with density is found in comparison to the free ΛN interaction.

In-medium heavy-quarkonium from lattice QCD spectral functions

We discuss recent progress in the study of in-medium heavy quarkonium using first-principles lattice QCD calculations and effective field theory. In particular our focus lies on real-time information carried by QCD spectral functions and we report on a novel strategy for their extraction from Euclidean-time simulations. Combining an effective description for heavy quarks with finite temperature lattice QCD we compute in-medium spectra providing insight in heavy quarkonium melting in a static thermal medium. On the other hand we use spectral information to extract the complex in-medium potential which provides the basis for a dynamical description of quarkonium real-time evolution via the Schrödinger equation.

Reference calculations for subthreshold Ξ production

We present a minimal statistical model designed for the description of rare- hadron multiplicities in nucleus-nucleus collisions at energies below the threshold of the particle production in binary elementary collisions. Differences to more conventional canonical statistical model are explained. The minimal statistical model is applied to the description of multiplicity ratios involving Ξ hyperons, which are measured by the HADES collaboration at GSI-SIS. It is argued that the HADES data cannot be reproduced by the model based on the statistical equilibrium and the strangeness conservation. The data remain underpredicted even when inmedium potentials acting on hadrons are taken into account. This hints to non-equilibrium production of the Ξ hyperons and their continuous freeze-out.

The impact of energy conservation in transport models on the π−/π+ multiplicity ratio in heavy-ion collisions and the symmetry energy

The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state. A comparison of various transport model predictions with existing experimental data has led, however, to contradictory results. Using an upgraded version of the Tübingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. However, pion multiplicities and ratios are proven to be highly sensitive to the yet unknown isovector part of the in-medium Δ(1232) potential which hinders, at present, the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as in-medium pion potentials and retardation effects, are needed for a final verdict on this topic.

Azimuthal emission patterns ofK+and ofK−mesons in Ni + Ni collisions near the strangeness production threshold

Azimuthal emission patterns of $K^\pm$ mesons have been measured in Ni + Ni collisions with the FOPI spectrometer at a beam kinetic energy of 1.91 A GeV. The transverse momentum $p_{T}$ integrated directed and elliptic flow of $K^{+}$ and $K^{-}$ mesons as well as the centrality dependence of $p_{T}$ - differential directed flow of $K^{+}$ mesons are compared to the predictions of HSD and IQMD transport models. The data exhibits different propagation patterns of $K^{+}$ and $K^{-}$ mesons in the compressed and heated nuclear medium and favor the existence of a kaon-nucleon in-medium potential, repulsive for $K^{+}$ mesons and attractive for $K^{-}$ mesons.