In-medium Interaction Research Articles

Improving relativistic energy density functionals with tensor couplings

Energy density functionals (EDFs) have been used extensively with great success to calculate properties of nuclei and to predict the equation of state of dense nuclear matter. Besides non-relativistic EDFs, mostly of the Skyrme or Gogny type, relativistic EDFs of different types are in widespread use. In these latter approaches, the effective in-medium interaction is described by an exchange of mesons between nucleons. In most cases, only minimal meson-nucleon couplings are considered. The effects of additional tensor couplings were rarely investigated. In this work, a new relativistic EDF with tensor couplings and density dependent minimal meson-nucleon couplings will be presented. The parameters of the model are determined using a carefully selected set of experimental data with realistic uncertainties that are determined self-consistently. Predictions for various nuclear observables, the nuclear matter equation of state, and properties of neutron stars are discussed.

Isotropization of a longitudinally expanding system of scalar fields in the 2PI formalism

Motivated by isotropization of QCD matter in the initial stages of heavy-ion collisions, we consider a system of scalar fields that undergoes a boost invariant longitudinal expansion. We use the framework of the two-particle irreducible (2PI) effective action, which is close to the underlying quantum field theory, and resum self-energy corrections up to three loops. The resulting 2PI equations of motion are expressed in terms of the Milne coordinates to account for longitudinal expansion. By solving numerically these equations of motion, we can extract the occupation density and the effective mass generated by in-medium interactions. At the largest values of the coupling considered in this study, we observe the onset of isotropization both in the occupation number and in the momentum dependence of the effective mass.

Probing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators.

Energy-energy correlators (EECs) are promising observables to study the dynamics of jet evolution in the quark-gluon plasma (QGP) through its imprint on angular scales in the energy flux of final-state particles. We carry out the first complete calculation of EECs using realistic simulations of high-energy heavy-ion collisions and dissect the different dynamics underlying the final distribution through analyses of jet propagation in a uniform medium. The EECs of γ-jets in heavy-ion collisions are found to be enhanced by the medium response from elastic scatterings instead of induced gluon radiation at large angles. In the meantime, EECs are suppressed at small angles due to energy loss and transverse momentum broadening of jet shower partons. These modifications are further shown to be sensitive to the angular scale of the in-medium interaction, as characterized by the Debye screening mass. Experimental verification and measurement of such modifications will shed light on this scale and the short-distance structure of the QGP in heavy-ion collisions.

Measurement of in-medium modification of energy-space structure of jets via γ and π0 triggered hadrons in Au+Au collisions at RHIC

Since the discovery of the jet quenching at RHIC, the in-medium interaction of hard scattered partons with the nuclear medium created by highenergy heavy-ion collisions has been an excellent tool to understand not only the transport properties of the medium but also its time evolution towards hadronization. The multi-differential measurement of the high momentum twoparticle correlations can probe a particular space-time window as a function of energy transfer. Comparing the correlations with the prompt photon-triggered hadron spectra, one can extract the property of the medium from various aspects and contribute to distinct models. The PHENIX experiment at RHIC has collected its highest statistics of the γ and π0 triggered hadron events in Au+Au collisions at √SNN = 200 GeV in the RHIC Year-2014 run, and measured not only the inclusive spectra of the triggered hadrons but also the angle and energy dependent IAA and DAA. We will discuss the in-medium modification of the energy-space structure of the jets at the RHIC energies with the results obtained.

Interactions of omega mesons in nuclear matter and with nuclei

In-medium interactions of omega -mesons in infinite nuclear matter and finite nuclei are investigated in a microscopic approach, focused on the particle-hole excitations of the medium involving nucleonic NN^{-1} and N^*N^{-1} modes, where N^* denotes a nucleon resonance. The nuclear polarization tensors include relativistic mean-field dynamics by self–consistent scalar and vector fields. The resulting self-energies are transmitted to finite nuclei in local density approximation. Real and imaginary parts of longitudinal and transversal self-energies are discussed. The relation of the present approach to meson cloud models is addressed and an ambiguity is pointed out. Applications to recent data on the in–medium width of omega mesons scattered on a Niobium target serve to determine unknown N^*Nomega in-medium coupling constants. The data are well described by N^*N^{-1} self–energies containing S–wave and P-wave N^* resonances. Exploratory investigations, however, show that the spectroscopic composition of self-energies depends crucially on the near-threshold properties of the width which at present is known only within large error bars. The calculations predict the prevalence of transversal self–energies, implying that vector current conservation is still maintained in the nuclear medium by slightly more than 90%. Schrödinger-equivalent potentials are derived and scattering lengths and effective range parameters are extracted for the longitudinal and transversal channel. Longitudinal and transversal spectral distributions are discussed and the dependencies on momentum and nuclear density are investigated. Schrödinger-type omega +{}^{93}Nb optical potentials are constructed. Low-energy parameters are determined, are used to study the pole structure of the S-matrix at threshold. The effective range expansion of the omega-nucleus K-matrix led to a omega +{}^{93}Nb bound states with binding energy Re(varepsilon _B)=-448 keV but of width Gamma _B=4445 keV.

Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes* *Supported by the Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2022-sp02, lzujbky-2023-stlt01), the National Natural Science Foundation of China (11875152, 12275111), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000)

The in-medium feature of nuclear force, which includes both nucleon-nucleon () and hyperon-nucleon () interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new effective interaction in the covariant density functional (CDF) theory, namely, DD-LZ1-, is obtained by fitting the experimental data of Λ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of the Λ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei, and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium interactions and core polarization effects.

Nuclear matter effects on jet production at electron-ion colliders

In these proceedings we report recent progress on understanding hadron and jet production in electron-nucleus collisions at the future Electron-Ion Collider [1,2]. These processes will play an essential role in the exploration of the partonic structure of nuclei and the study of parton shower evolution in strongly-interacting matter. We employ the framework of soft-collinear effective theory, generalized to include in-medium interactions, to present the first theoretical results for inclusive hadron and jet cross sections, as well as the jet charge modification in deep inelastic scattering on nuclei. We further demonstrate how to separate initial-state and final-state effects.

Heavy quark potential in the quark-gluon plasma: Deep neural network meets lattice quantum chromodynamics

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real ($V_R(T,r)$) and imaginary ($V_I(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain $V_R(T,r)$ and $V_I(T,r)$ in a model-independent fashion. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-334$~MeV. For $T=151-334$~MeV, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations.

First application of the dispersive optical model to (p,2p) reaction analysis within the distorted-wave impulse approximation framework

Both ($e$,$e'p$) and ($p$,$2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e$,$e'p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy. We apply the DOM wave functions to the traditional ($p$,$2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e$,$e'p$) cross section with the result of the ($p$,$2p$) analysis. Additionally, we make a comparison with a phenomenological single-particle wave function and optical potential. Uncertainty arising from a choice of $p$-$p$ interaction is also investigated. We implement the DOM wave functions to the distorted wave impulse approximation (DWIA) framework for ($p$,$2p$) reactions. DOM + DWIA analysis on $^{40}$Ca($p$,$2p$)$^{39}$K data generates a proton $0d_{3/2}$ spectroscopic factor of 0.560, which is meaningfully smaller than the DOM value of 0.71 shown to be consistent with the ($e$,$e'p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p$-$p$ interaction do not explain this inconsistency. The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p$-$p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.

From lattice QCD to in-medium heavy-quark interactions via deep learning

Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks, which can be characterized by real (VR(T, r)) and imaginary (VI(T, r)) potentials, as functions of temperature and spatial separation. Recently, the masses and thermal widths of up to 3S and 2P bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network (DNN), here, we obtain model-independent results for VR(T, r) and VI(T, r). The temperature dependence of VR(T, r) was found to be very mild between T ≈ 0 − 330 MeV. Meanwhile, VI(T, r) shows rapid increase with T and r, which is much larger than the perturbation theory based expectations.

Static quark anti-quark interactions at non-zero temperature from lattice QCD

We present results on the in-medium interactions of static quark antiquark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles.

Electromagnetic response of hot QCD medium in the presence of background time-varying fields

The response of the hot QCD medium in the presence of external time dependent electromagnetic fields has been studied within the relativistic Boltzmann transport theory. The impact of the time dependence of the electromagnetic fields and collisional aspects of the medium to the induced electric and Hall current densities has been explored. The non-equilibrium momentum distribution of degrees of freedom has been obtained in the presence of space-time varying electromagnetic fields. Further, the analysis has been extended to an anisotropic QCD medium while incorporating the in-medium interaction effects. It is observed that the electric charge transport is sensitive to the inhomogeneity of the fields and the momentum anisotropy of the QCD medium.

Thermoelectric response of a weakly magnetized thermal QCD medium

We estimate the thermoelectric response, namely, the Seebeck and Nernst coefficients of a hot and deconfined plasma of quarks and gluons, created post ultrarelativistic heavy ion collisions in the presence of a weak, homogeneous background magnetic field. We employ the kinetic theory framework, wherein we use the relativistic Boltzmann transport equation in the relaxation time approximation. In-medium interactions are taken into account via the quasiparticle masses of the partons extracted from one loop perturbative thermal QCD. We calculate the individual and total Seebeck coefficients in 2 different approaches (1-D and 2-D formulations). In the 1-D analysis, we find that a larger current quark mass has an amplifying effect on the individual Seebeck coefficient in the presence of a weak magnetic field. The temperature sensitivities of the individual Seebeck coefficients increase with increase in the current mass of the quark species in the case of a weak magnetic field whereas the same records a decreasing trend in the presence of a strong magnetic field. The variation of individual and total Seebeck coefficients with temperature, chemical potential and background magnetic field are found to follow similar trends in both the approaches, viz. decrease in magnitude with increasing temperature and increase in magnitude with increase in chemical potential and magnetic field. We also calculate the individual and total Nernst coefficients (in 2-D formulation) which are found to decrease with both temperature and chemical potential and increase with the magnetic field. Further, we find that the sign of the Nernst coefficient is independent of the electric charge of the charge carrier of the medium.

Nuclear Matter Effects on Jet Production at Electron-Ion Colliders.

Jet production and jet substructure in reactions with nuclei at future electron-ion colliders will play a preeminent role in the exploration of nuclear structure and the evolution of parton showers in strongly interacting matter. In the framework of soft-collinear effective theory, generalized to include in-medium interactions, we present the first theoretical study of inclusive jet cross sections and the jet charge at the electron-ion collider. Predictions for the modification of these observables in electron-gold relative to electron-proton collisions reveal how the flexible center-of-mass energies and kinematic coverage at this new facility can be used to enhance the signal and maximize the impact of the electron-nucleus program. Importantly, we demonstrate theoretically how to disentangle the effects from nuclear parton distribution functions and the ones that arise from strong final-state interactions between the jet and the nuclear medium.

Radial profile of bottom quarks in jets in high-energy nuclear collisions * *Supported by the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008), the Science and Technology Program of Guangzhou (2019050001) and the NSFC of China with Project (11935007, 11805167)

Angular correlations between a heavy quark (HQ) and its tagged jet are potentially new tools to gain insight into the in-medium partonic interactions in relativistic heavy-ion collisions. In this work, we present the first theoretical study on the radial profiles of B mesons in jets in Pb+Pb collisions at the Large Hadron Collider (LHC). The initial production of a bottom quark tagged jet in p+p is computed by SHERPA, which matches the next-to-leading order matrix elements with contributions of parton showers, whereas the massive quark traversing the quark-gluon plasma is described by a Monte Carlo model, SHELL, which can simultaneously simulate light and heavy flavor in-medium energy loss within the framework of Langevin evolution. In p+p collisions, we find that at lower the radial profiles of heavy flavors in jets are sensitive to the heavy quark mass. In 0-10% Pb+Pb collisions at TeV, we observe an inverse modification pattern of the B meson radial profiles in jets at GeV compared to those of D mesons: the jet quenching effects narrow the jet radial profiles of B mesons in jets while broadening those of D mesons in jets. We find that in A+A collisions, the contribution dissipated from the higher GeV region naturally has a narrower initial distribution and consequently leads to a narrower modification pattern of the radial profile; however the diffusion nature of the heavy flavor in-medium interactions will give rise to a broader modification pattern of the radial profile. These two effects consequently compete and offset with each other, and the b quarks in jets benefit more from the former and suffer less diffusion effect compared to that of c quarks in jets. These findings can be tested in the future experimental measurements at the LHC to gain better understanding of the mass effect of jet quenching.

Radial distribution of charm quarks in jets in high-energy heavy-ion collisions

Heavy flavor physics in high-energy heavy-ion collisions is a promising and active area to study the mass dependence of the “jet quenching” effects both at the RHIC and the LHC. In this talk, we present the first theoretical study on the D0 meson radial distributions relative to the jet axis both in p+p and Pb+Pb collisions at sNN=5.02TeV, where a nice agreement of our results with experimental data is observed. The in-medium parton propagations are described by a Monte Carlo transport model which uses the next-to-leading order (NLO) plus parton shower (PS) event generator SHERPA as input and includes elastic (collisional) and inelastic (radiative) in-medium interaction of heavy flavor jet. We find that, at low D0 meson pT, the radial distribution significantly shifts to larger radius indicating a strong diffusion effect, and the diffusion effects decrease quickly with pT, which is consistent with the recent CMS measurements. We demonstrate that the angular deviation of charm quarks is sensitive to Ds but not qˆ, which may provide new constrains on the collisional and radiative heavy quark energy loss.

An Effective Theory of Quarkonia in QCD Matter

The problem of quarkonium production in heavy ion collisions presents a set of unique theoretical challenges – from the relevant production mechanism of J/ψs and ϒs to the relative significance of distinct cold and hot nuclear matter effects in the observed attenuation of quarkonia. In these proceedings we summarize recent work on the generalization of non-relativistic Quantum Chromodynamics (NRQCD) to include Glauber gluon interactions in strongly interacting matter. This new effective theory provides for the first time a universal microscopic description of the in-medium interaction of heavy quarkonia, consistently applicable to a range of phases such as cold nuclear matter, dense hadron gas, and quark-gluon plasma. It is an important step forward in understanding the common trends in proton-nucleus and nucleus-nucleus data on quarkonium suppression. We derive explicitly the lowest order (LO) and next-to-leading order (NLO) interaction terms in the Lagrangian and show the connection of the LO result to existing phenomenology.

Heavy flavor quenching and flow: the roles of initial condition, pre-equilibrium evolution, and in-medium interaction * * Supported by the Natural Science Foundation of China (NSFC) (11805082, 11775095, 11890711, 11935007), a Project of Shandong Province Higher Educational Science and Technology Program (J17KB128), the China Scholarship Council (CSC) (201906775042), the U.S. Department of Energy (DOE) (DE-SC0013460), and the National Science Foundation

Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the in-medium energy loss and hadronization mechanisms of heavy quarks, the evolution profile of the pre-equilibrium stage, the medium flow, and the temperature dependence of heavy quark diffusion coefficients influence the suppression and elliptic flow of heavy mesons at the RHIC and the LHC. Our results show that the different modeling of initial conditions, pre-equilibrium evolution, and in-medium interactions can individually yield uncertainties of approximately 10-40% in D meson suppression and flow at a low transverse momentum. We also find that proper combinations of collisional versus radiative energy loss, coalescence versus fragmentation in hadronization, and the inclusion of medium flow are the most important factors for describing the suppression and elliptic flow of heavy mesons.

Squeezed back-to-back correlation between bosons and antibosons with different in-medium masses in high-energy heavy-ion collisions

We derive the formulas of the squeezed back-to-back correlation (SBBC) between a boson and antiboson with different in-medium masses in high-energy heavy-ion collisions. The influence of the in-medium mass difference between a boson and antiboson on the SBBC is investigated. We calculate the SBBC functions of $D$-meson pairs for the hydrodynamic sources described by the VISH2+1 code for Au+Au collisions at $\sqrt{s_{NN}} =200$~GeV. Our results indicate that the SBBC strengths of $D^+D^-$ and $D^0{\bar D}^0$ are different if there are charge-dependent in-medium interactions.

Heavy Flavor Production, Flow and Energy Loss

An overview of the current status of the heavy quarks as probe of the hot QCD in-medium interaction is presented. Heavy quarks that produced out-of-equilibrium but strongly interacting with the created quark-gluon plasma (QGP) bulk medium offer the unique opportunity to have a probe that thermalize in a time scale comparable with the lifetime of the QGP. Finally, the possible role of heavy quark for probing the initial strong electromagnetic field created in relativistic heavy-ion collisions is discussed.