Strongly-interacting Matter Research Articles

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.

Probing Dense Nuclear Matter in the Laboratory: Experiments at FAIR and NICA

The poorly known properties of high-density strongly-interacting matter govern the structure of neutron stars and the dynamics of neutron star mergers. New insight has been and will be gained by astronomical observations, such as the measurement of mass and radius of neutron stars, and the detection of gravitational waves emitted from neutron star mergers. Alternatively, information on the Nuclear Matter Equation-of-State (EOS) and on a possible phase transition from hadronic to quark matter at high baryon densities can be obtained from laboratory experiments investigating heavy-ion collisions. Detector systems dedicated to such experiments are under construction at the “Facility for Antiproton and Ion Research” (FAIR) in Darmstadt, Germany, and at the “Nuclotron-based Ion Collider fAcility” (NICA) in Dubna, Russia. In heavy-ion collisions at these accelerator centers, one expects the creation of baryon densities of up to 10 times saturation density, where quark degrees-of-freedom should emerge. This article reviews the most promising observables in heavy-ion collisions, which are used to probe the high-density EOS and possible phase transition from hadronic to quark matter. Finally, the facilities and the experimental setups will be briefly described.

Particle production in AgAg collisions at EKin=1.58A GeV within a hadronic transport approach

Heavy-ion collisions at low beam energies explore the high density regime of strongly-interacting matter. The dynamical evolution of these collisions can be successfully described by hadronic transport approaches. In March 2019, the HADES collaboration has taken data for AgAg collisions at $E_{\rm Kin}=1.58A$ GeV and in this work, we provide predictions for particle production and spectra within the Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) approach. The multiplicities and spectra of strange and non-strange particles follow the expected trends as a function of system size. In particular, in AuAu collisions, much higher yields of double-strange baryons were observed experimentally than expected from a thermal model. Therefore, we incorporate a previously suggested mechanism to produce $\Xi$ baryons via rare decays of high mass $N^*$ resonances and predict the multiplicities. In addition, we predict the invariant mass spectrum for dilepton emission and explore the most important sources of dileptons above 1 GeV, that are expected to indicate the temperature of the medium. Interestingly, the overall dilepton emission is very similar to the one in AuAu collisions at $1.23 A$ GeV, a hint that the smaller system at a higher energy behaves very similar to the larger system at lower beam energy.

Thermodynamics from the quark condensate

We present a method to compute thermodynamic quantities within functional continuum frameworks that is independent of the employed truncation. As a proof of principle, we first apply it to a Nambu-Jona-Lasinio model in mean-field approximation. Then, we use the method with solutions obtained from a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of ($2+1$)-flavor quantum chromodynamics in Landau gauge to obtain the pressure, entropy density, energy density, and interaction measure across the phase diagram of strong-interaction matter. We also discuss the limitation of the proposed method.

Strong-Interaction Matter under Extreme Conditions from Chiral Quark Models with Nonlocal Separable Interactions

We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions. The analysis includes the predictions for various hadron properties in vacuum, as well as the study of the features of deconfinement and chiral restoration phase transitions for systems at finite temperature and/or density. We also address other related subjects, such as the study of phase transitions for imaginary chemical potentials, the possible existence of inhomogeneous phase regions, the presence of color superconductivity, the effects produced by strong external magnetic fields and the application to the description of compact stellar objects.

On the stability of two-flavor and three-flavor quark matter in quark stars within the framework of NJL model

Following our recently proposed self-consistent mean field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli–Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.

SmallestSU(N)hadrons

If new physics contains new, heavy strongly-interacting particles belonging to irreducible representations of SU(3) different from the adjoint or the (anti)fundamental, it is a non-trivial question to calculate what is the minimum number of quarks/antiquarks/gluons needed to form a color-singlet bound state ("hadron"), or, perturbatively, to form a gauge-invariant operator, with the new particle. Here, I prove that for an SU(3) irreducible representation with Dynkin label $(p,q)$, the minimal number of quarks needed to form a product that includes the (0,0) representation is $2p+q$. I generalize this result to SU($N$), with $N>3$. I also calculate the minimal total number of quarks/antiquarks/gluons that, bound to a new particle in the $(p,q)$ representation, give a color-singlet state, or, equivalently, the smallest-dimensional gauge-invariant operator that includes quark/antiquark/gluon fields and the new strongly-interacting matter field. Finally, I list all possible values of the electric charge of the smallest hadrons containing the new exotic particles, and discuss constraints from asymptotic freedom both for QCD and for grand unification embeddings thereof.

Self-consistent mean field approximation and application in three-flavor NJL model

In this study, we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio (NJL) model and compare it with the two-flavor NJL model. The self-consistent mean field approximation introduces a new parameter, , that cannot be fixed in advance by the mean field approach itself. Due to the lack of experimental data, the parameter, , is undetermined. Hence, it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation. affects numerous properties of the chiral phase transitions, such as the position of the phase transition point and the order of phase transition. Additionally, increasing will decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero. Finally, we observed that affects the equation of state (EOS) of the quark matter, and the sound velocity can be calculated to determine the stiffness of the EOS, which provides a good basis for studying the neutron star mass-radius relationship.

Jet charge modification in finite QCD matter

Jet production and jet substructure modification in heavy-ion collisions have played an essential role in revealing the in-medium evolution of parton showers and the determination of the properties of strongly-interacting matter under extreme conditions. It is imperative to extend these studies to include flavor tagging and to devise observables that are sensitive to the partonic origin of jets. The average jet charge, defined as the momentum-weighted sum of the electric charges of particles inside the jet, is a proxy of the electric charge of the quark or gluon that initiates the jet. We demonstrate how the factorization framework of soft-collinear effective theory can be generalized to evaluate the jet charge in a dense strongly-interacting matter environment, such as the one produced in nuclear reactions at collider energies. Observables that can separate the contribution of in-medium branching from the trivial isospin effects are identified and their connection to established jet quenching effects is elucidated. We present predictions for the transverse momentum dependence of the jet charge distribution in nucleus-nucleus collisions and its modification relative to the proton case.

Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions

Collisions between heavy atomic nuclei at ultra-relativistic energies are carried out at particle colliders to produce the quark-gluon plasma, a state of matter where quarks and gluons are not confined into hadrons, and colour degrees of freedom are liberated. This state is thought to be produced as a transient phenomenon before it fragments into thousands of particles that reach the particle detectors. Despite two decades of investigations, one of the big open questions is to obtain an experimental determination of the temperature reached in a heavy-ion collision, and a simultaneous determination of another thermodynamic quantity, such as the entropy density, that would give access to the number of degrees of freedom. Here we obtain the first such determination, utilizing state-of-the-art hydrodynamic simulations. We define an effective temperature, averaged over the space-time evolution of the medium. Then, using experimental data, we determine this temperature, the corresponding entropy density and speed of sound in the matter created in lead-lead collisions at the Large Hadron Collider. Our results agree with first-principles calculations from lattice quantum chromodynamics and confirm that a deconfined phase of matter is indeed produced.

Fierz-complete NJL model study. III. Emergence from quark-gluon dynamics

Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scalar-pseudoscalar interaction channel is dynamically rendered most dominant by the gauge degrees of freedom, indicating the formation of a chiral condensate. Moreover, the inclusion of quark-gluon interactions leaves a significant imprint on the dynamics as measured by the curvature of the finite-temperature phase boundary which we find to be in accordance with lattice QCD results. At large quark chemical potential, we then observe that the dominance pattern of the four-quark couplings is changed by the underlying quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In this regime, the scalar-pseudoscalar interaction channel becomes subleading and the dominance pattern suggests the formation of a chirally symmetric diquark condensate. In particular, our study confirms the importance of explicit $U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at high densities.

Hadronization and Charm-Hadron Ratios in Heavy-Ion Collisions.

Understanding the hadronization of the quark-gluon plasma (QGP) remains a challenging problem in the study of strong-interaction matter as produced in ultrarelativistic heavy-ion collisions (URHICs). The large mass of heavy quarks renders them excellent tracers of the color neutralization process of the QGP when they convert into various heavy-flavor (HF) hadrons. We develop a 4-momentum conserving recombination model for HF mesons and baryons that recovers the thermal and chemical equilibrium limits and accounts for space-momentum correlations (SMCs) of heavy quarks with partons of the hydrodynamically expanding QGP, thereby resolving a long-standing problem in quark coalescence models. The SMCs enhance the recombination of fast-moving heavy quarks with high-flow thermal quarks in the outer regions of the fireball. We also improve the hadrochemistry with "missing" charm-baryon states, previously found to describe the large Λ_{c}/D^{0} ratio observed in proton-proton collisions. Both SMCs and hadrochemistry, as part of our HF hydro-Langevin-recombination model for the strongly coupled QGP, importantly figure in the description of recent data for the Λ_{c}/D^{0} ratio and D-meson elliptic flow in URHICs.

Jet charge in heavy-ion collisions

Jet quenching effects have been widely used to study the properties of strongly-interacting matter, quark-gluon plasma, in heavy-ion collisions. Flavor tagging in heavy-ion collisions plays an important role to reveal the medium parton showers for quark and gluon evolution. Combining with kinematic information, the average jet charge can be used to separate the contribution of different jet flavors, which is defined as the momentum- weighted sum of the charges of hadrons inside a given jet. Using soft-collinear effective theory with medium interactions, we investigate the factorization of the jet charge in QCD medium. We provide predictions for jet charge distributions and their modifications compared to the ones in proton-proton collisions.

Novel self-consistent mean field approximation and its application in strong interaction phase transitions * * Supported in part by the National Natural Science Foundation of China (11690030, 11475085, 11535005) and National Major state Basic Research and Development of China (2016YFE0129300)

We propose a novel self-consistent mean field approximation method by means of a Fierz transformation, taking the Nambu-Jona-Lasinio model as an example. This new self-consistent mean field approximation introduces a new free parameter α to be determined experimentally. When α assumes the value of 0.5, the approximation reduces to the mean field calculation commonly used in the past. Subsequently, we study the influence of the undetermined parameter α on the phase diagram of the two-flavor strong interaction matter. The value of α plays a crucial role in the strong interaction phase diagram, as it not only changes the position of the phase transition point of strong interaction matter, but also affects the order of the phase transition. For example, when α is greater than the critical value , then the strong interaction matter phase diagram no longer has a critical end point. In addition, in the case of zero temperature and finite density, we found that when α > 1.044, the pseudo-critical chemical potential corresponds to ~4–5 times the saturation density of the nuclear matter, which agrees with the expected results from the picture of the hadrons degree of freedom. The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.

Confronting gravitational-wave observations with modern nuclear physics constraints

Multi-messenger observations of neutron star (NS) mergers have the potential to revolutionize nuclear astrophysics. They will improve our understanding of nucleosynthesis, provide insights about the equation of state (EOS) of strongly-interacting matter at high densities, and enable tests of the theory of gravity and of dark matter. Here, we focus on the EOS, where both gravitational waves (GWs) from neutron-star mergers and X-ray observations from space-based detectors such as NICER will provide more stringent constraints on the structure of neutron stars. Furthermore, recent advances in nuclear theory have enabled reliable calculations of the EOS at low densities using effective field theory based Hamiltonians and advanced techniques to solve the quantum many-body problem. In this paper, we address how the first observation of GWs from GW170817 can be combined with modern calculations of the EOS to extract useful insights about the EOS of matter encountered inside neutron stars. We analyze the impact of various uncertainties, the role of phase transitions in the NS core, and discuss how future observations will improve our understanding of dense matter.

Probing the in-medium QCD force by open heavy-flavor observables

The determination of the color force in a quark-gluon plasma (QGP) is a key objective in the investigation of strong-interaction matter. Open and hidden heavy-flavor observables in heavy-ion collisions (HICs) are believed to provide insights into this problem by comparing calculations of heavy-quark (HQ) and quarkonium transport with pertinent experimental data. In this work, we utilize the $T$-matrix formalism to compute charm-quark transport coefficients for various input potentials previously extracted from simultaneous fits to lattice-QCD data for HQ free energies, quarkonium correlators, and the QGP equation of state. We investigate the impact of off-shell effects (spectral functions) in the QGP medium on the HQ transport, and compare to earlier results using the free or internal HQ energies as potential proxies. We then employ the transport coefficients in relativistic Langevin simulations for HICs to test the sensitivity of heavy-flavor observables to the HQ interactions in the QGP. We find that a strongly coupled $T$-matrix solution generates a HQ elliptic flow comparable to the results from the internal energy at low momentum, driven by a long-range remnant of the confining force, while falling off stronger with increasing three-momentum. The weakly coupled $T$-matrix solution, whose underlying potential is close to the free energy, leads to an elliptic flow well below the experimentally observed range.

The quark chemical potential of QCD phase transition and the stochastic background of gravitational waves

The detection of stochastic background of gravitational waves (GWs), produced by cosmological phase transitions (PTs), is of fundamental importance because allows to probe the physics related to PT energy scales. Motivated by the decisive role of non-zero quark chemical potential towards understanding physics in the core of neutron stars, quark stars and heavy-ion collisions, in this paper we qualitatively explore the stochastic background of GW spectrum generated by a cosmological source such as high-density QCD first order PT during the early Universe. Specifically, we calculate the frequency peak fpeak redshifted at today time and the fractional energy density Ωgwh2 in light of equation-of-state improved by the finite quark (baryon) chemical potential (we consider an effective three flavor chiral quarks model of QCD). Our calculations reveal a striking increase in fpeak and Ωgwh2 due to the quark chemical potential, which means to improve the chances of detection, in possible future observations (in particular SKA/PTA experiments), of the stochastic background of GWs from QCD first order PT. Even if the improvements could be weak, by updating the sensitivity of relevant detectors in the future, we can still remain hopeful. Concerning the phenomenological contribution of QCD equation-of-state, and in particular the possibility to detect a stochastic GW signal, we further show that the role of the quark chemical potential is model-dependent. This feature allows to discriminate among possible QCD effective models depending on their capability to shed light on the dynamic of QCD-PT through future observations of primordial GWs. In this perspective, the results are indeed encouraging to employ the GWs to study the QCD PT in high density strong interaction matter.

Strong matter: Rethinking philosophically

Normal condensed matter is merely of electromagnetic interaction. A novel state of strong-interaction matter is revisited.

Fierz-complete NJL model study. II. Toward the fixed-point and phase structure of hot and dense two-flavor QCD

Nambu-Jona-Lasinio-type models are often employed as low-energy models for the theory of the strong interaction to analyze its phase structure at finite temperature and quark chemical potential. In particular at low temperature and large chemical potential, where the application of fully first-principles approaches is currently difficult at best, this class of models still plays a prominent role to guide our understanding of the dynamics of dense strong-interaction matter. In this work, we consider a Fierz-complete version of the Nambu-Jona-Lasinio model with two massless quark flavors and study its renormalization group flow and fixed-point structure at leading order of the derivative expansion of the effective action. Sum rules for the various four-quark couplings then allow us to monitor the strength of the breaking of the axial $U_{\rm A}(1)$ symmetry close to and above the phase boundary. We find that the dynamics in the ten-dimensional Fierz-complete space of four-quark couplings can only be reduced to a one-dimensional space associated with the scalar-pseudoscalar coupling in the strict large-$N_{\rm c}$ limit. Still, the interacting fixed point associated with this one-dimensional subspace appears to govern the dynamics at small quark chemical potential even beyond the large-$N_{\rm c}$ limit. At large chemical potential, corrections beyond the large-$N_{\rm c}$ limit become important and the dynamics is dominated by diquarks, favoring the formation of a chirally symmetric diquark condensate. In this regime, our study suggests that the phase boundary is shifted to higher temperatures when a Fierz-complete set of four-quark interactions is considered.

Low-temperature behavior of the quark-meson model

We revisit the phase diagram of strong-interaction matter for the two-flavor quark-meson model using the Functional Renormalization Group. In contrast to standard mean-field calculations, an unusual phase structure is encountered at low temperatures and large quark chemical potentials. In particular, we identify a regime where the pressure decreases with increasing temperature and discuss possible reasons for this unphysical behavior.