We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness based on the results of lattice QCD simulations and the hadron resonance gas model. The situation of strangeness neutrality and a fixed charge-to-baryon ratio, which resembles that of heavy nuclei, is considered for the application to relativistic heavy-ion collisions. This increases the values of baryon chemical potential compared to the case of vanishing strangeness and electric charge chemical potentials, modifying the fireball trajectory in the phase diagram. We perform viscous hydrodynamic simulations and demonstrate the importance of multiple chemical potentials for identified particle production in heavy-ion collisions at the RHIC and SPS beam energy scan energies.
An attempt is made to interpret, in the framework of QCD, the likeness between the shapes of the neutron-neutron strong and electrostatic interactions at the distances $\sim 1÷3$ fm.
We provide a concise review on recent theory advancements towards full-fledged (3+1)D dynamical descriptions of relativistic nuclear collisions at finite baryon density. Heavy-ion collisions at different collision energies produce strongly-coupled matter and probe the QCD phase transition at the crossover, critical point, and first-order phase transition regions. Dynamical frameworks provide a quantitative tool to extract properties of hot QCD matter and map fireballs to the QCD phase diagram. Outstanding challenges are highlighted when confronting current theoretical frameworks with current a…
We review the equation of state of QCD matter at finite densities. We discuss the construction of the equation of state with net baryon number, electric charge, and strangeness using the results of lattice QCD simulations and hadron resonance gas models. Its application to the hydrodynamic analyses of relativistic nuclear collisions suggests that the interplay of multiple conserved charges is important in the quantitative understanding of the dense nuclear matter created at lower beam energies. Several different models of the QCD equation of state are discussed for comparison.
We construct the QCD equation of state at finite chemical potentials including net baryon, electric charge, and strangeness, based on the conserved charge susceptibilities determined from lattice QCD simulations and the equation of state of the hadron resonance gas model. For the application to relativistic heavy ion collisions we consider the situation of strangeness neutrality and matter with a fixed electric charge-to-baryon ratio, resembling that of heavy nuclei. The importance of finite electric charge and strangeness chemical potentials for particle production in heavy ion collisions is …
We investigated the transverse charge densities in the nucleon in nuclear matter within the framework of the in-medium modified Skyrme model. The medium modification of the nucleon electromagnetic form factors are first discussed. The results show that the form factors in nuclear matter fall off faster than those in free space, as the momentum transfer increases. As a result, the charge radii of the nucleon become larger, as the nuclear matter density increases. The transverse charge densities in the nucleon indicate that the size of the nucleon tends to bulge out in nuclear matter. This salie…
Abstract (abridged edition): Properties of the relativistic nucleon self-energy decomposition of the symmetry energy as well as the equation of state (EOS) of pure neutron matter (PNM) are explored systematically within the QCD sum rules (QCDSR). Our results in the present work have demonstrated that the QCDSR approach can be used to explore the properties of asymmetric nuclear matter (ANM) in a quantitative manner, at least in lower density region. The QCDSR approach establishes a bridge connecting the EOS of ANM and the non-perturbative QCD vacuum, and thus provides a useful way to understan…
Within the interacting Fermi gas model for isospin asymmetric nuclear matter, effects of the in-medium three-body interaction and the two-body short-range tensor force due to the $ρ$ meson exchange as well as the short-range nucleon correlation on the high-density behavior of the nuclear symmetry energy are demonstrated respectively in a transparent way. Possible physics origins of the extremely uncertain nuclear symmetry energy at supra-saturation densities are discussed.
We have presented a strategy to study nuclei and nuclear matters from first principles, namely, from QCD. We first compute nucleon-nucleon potentials numerically in lattice QCD, and then use them to investigate properties of nuclei and nuclear matter by various methods developed in nuclear physics. As a demonstration that this strategy works, mass and structure of ^4^He, ^16^O and ^40^Ca, and equation of state of nuclear matters are determined with the lattice QCD induced two-nucleon potentials in a heavy quark region as an input. We have found that these nuclei and the symmetric nuclear matte…
Extending previous work we study the constraints of QCD sum rules on mass and width of light vector and axial-vector mesons in vacuum and in a medium with finite nuclear density. For the latter case especially the effect of nuclear pions leading to vector-axial-vector mixing is included in the analysis.
The medium modifications in the properties of QCD cascades are considered. In particular, the changes in the intrajet rapidity distributions due to medium-induced decoherence, collisional losses of cascade gluons and those of final prehadrons are analyzed.
Basis Representation for Nuclear Densities from Principal Component Analysis
Fuzhou University（福州大学）；Beihang University（北京航空航天大学）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Kyoto University（京都大学）；RIKEN Nishina Center for Accelerator-based Science, RIKEN（理化学研究所筑波加速器科学研究中心）
Vector mesons show up in the electromagnetic current-current correlator. QCD sum rules provide a constraint on hadronic models for this correlator. This constraint is discussed for the case of finite nuclear density concerning the longitudinal as well as the transverse part of the current-current correlator at finite three-momentum.
In this letter we give the equation of state of QCD at finite temperatures and densities. The recently proposed overlap improving multi-parameter reweighting technique is used to determine observables at nonvanishing chemical potentials. Our results are obtained by studying n_f=2+1 dynamical staggered quarks with semi-realistic masses on N_t=4 lattices.
Pairing correlations have a strong influence on nuclear level densities. Empirical descriptions and theoretical models have been developed to take these effects into account. The present article discusses cases, where descriptions of nuclear level densities are inconsistent or in conflict with the present understanding of nuclear properties. Phenomenological approaches consider a back-shift parameter. However, the absolute magnitude of the back-shift, which actually corresponds to the pairing condensation energy, is generally not compatible with the observation that stable pairing correlations…
The symmetry energy coefficients for nuclei with mass number A=20~250 are extracted from more than 2000 measured nuclear masses. With the semi-empirical connection between the symmetry energy coefficients of finite nuclei and the nuclear symmetry energy at reference densities, we investigate the density dependence of symmetry energy of nuclear matter at subnormal densities. The obtained results are compared with those extracted from other methods.
The nuclear symmetry energy determines the birth of neutron stars and the elementary nucleosynthesis in the universe. To constrain the nuclear symmetry energy, besides the studies in astrophysics, many terrestrial nuclear experiments are being carried out using a wide variety of advanced new facilities. In this paper, by cross-checking two unrelated experimental measurements using the newly updated transport model, we obtained a slightly soft symmetry energy at supra-saturation nuclear densities. While extrapolating to low nuclear densities, this result is compatible with the recent finding by…
Lattice QCD is progressing toward being able to impact our understanding of nuclei and nuclear processes. I discuss areas of nuclear physics that are becoming possible to explore with lattice QCD, the techniques that are currently available and the status of numerical explorations.
We calculate the nucleon self-energies in isospin-asymmetric nuclear matter using QCD sum rules. Taking the difference of these for the neutron and proton enables us to express the potential part of the nuclear symmetry energy in terms of local operators. We find that the scalar (vector) self-energy part gives a negative (positive) contribution to the nuclear symmetry energy which is consistent with the results from relativistic mean-field theories. Moreover, we find that an important contribution to the negative contribution of the scalar self-energy comes from the twist-4 matrix elements, wh…
I review recent progress in the development of Lattice QCD into a calculational tool for nuclear physics. Lattice QCD is currently the only known way of solving QCD in the low-energy regime, and it promises to provide a solid foundation for the structure and interactions of nuclei directly from QCD.
We compute the spectral densities of $T^{μν}$ and $J^μ$ in high temperature QCD plasmas at small frequency and momentum,\, $ω,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a…
We calculate and resum a perturbative expansion of nuclear enhanced power corrections to the structure functions measured in deeply inelastic scattering of leptons on a nuclear target. Our results for the Bjorken $x$-, $Q^2$- and $A$-dependence of nuclear shadowing in $F_2^A(x,Q^2)$ and the nuclear modifications to $F_L^A(x,Q^2)$, obtained in terms of the QCD factorization approach, are consistent with the existing data. We demonstrate that the low-$Q^2$ behavior of these data and the measured large longitudinal structure function point to a critical role for the power corrections when compare…
Within an isospin- and momentum-dependent hadronic transport model it is shown that the recent FOPI data on the $π^-/π^+$ ratio in central heavy-ion collisions at SIS/GSI energies (Willy Reisdorf {\it et al.}, NPA {\bf 781}, 459 (2007)) provide circumstantial evidence suggesting a rather soft nuclear symmetry energy \esym at $ρ\geq 2ρ_0$ compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.
The properties of open strange meson $K_1^\pm$ in nuclear matter are estimated in the QCD sum rule approach. We obtain a relation between the in-medium mass and width of $K_1^-$ ($K_1^+$) in nuclear matter, and show that the upper limit of the mass shift is as large as -249 (-35) MeV. The spectral modification of the $K_1$ meson is possible to be probed by using kaon beams at J-PARC. Such measurement together with that of $K^*$ will shed light on how chiral symmetry is partially restored in nuclear matter.
We investigate the medium modification of the generalized vector form factors of the nucleon, which include the electromagnetic and energy-momentum tensor form factors, based on an in-medium modified $π$-$ρ$-$ω$ soliton model. We find that the vector form factors of the nucleon in nuclear matter fall off faster than those in free space, which implies that the charge radii of the nucleon become larger in nuclear medium than in free space. We also compute the corresponding transverse charge densities of the nucleon in nuclear matter, which clearly reveal the increasing of the nucleon size in nuc…
We study single-particle potential of Lambda, Sigma, and Xi hyperons in nucleonic matter starting from the fundamental theory of the strong interaction, QCD. First we carry out a lattice QCD numerical simulation, and extract baryon-baryon interactions from QCD by means of the HAL QCD method. We employ a full QCD gauge configuration ensemble at almost physical point so that we can study the physical world, hence mass of hadrons are nearly physical, for example, pion mass is 146 MeV, kaon mass is 525 MeV, and nucleon mass is 958 MeV. Then, we apply the obtained hyperon interactions to the Brueck…
We propose a new method to determine the spatially or impact-parameter dependent nuclear parton distribution functions (nPDFs) using the double parton scattering (DPS) processes in high-energy heavy-ion (proton-nucleus and nucleus-nucleus) collisions. We derive a simple generic DPS formula in nuclear collisions by accommodating both the nuclear collision geometry and the spatially dependent nuclear modification effect, under the assumption that the impact-parameter dependence of nPDFs is only related to the nuclear thickness function. While the geometric effect is widely adopted, the impact of…
This paper scrutinizes the dynamical QCD effects influence on mesons, namely, the mean-square root radius of a pion in the holographic light-front wave function setup, in the context of the AdS/QCD. The nuclear configurational entropy, associated to mesonic holographic light-front wave functions, is shown to have a critical point that optimizes the two parameters of the spin-improved light-front wave function. The mean-square root pion radius and its cross-section, computed upon these derived values, match the exact existing experimental data to the precision of 0.14\%, below the experimental …
We discuss the techniques to extract the electromagnetic Delta form factors in Lattice QCD. We evaluate these form factors using dynamical fermions with smallest pion mass of about 350 MeV. We pay particular attention to the extraction of the electric quadrupole form factor that signals a deformation of the Delta. The magnetic moment of the $Δ$ is extrapolated using a chiral effective field theory. Using the form factors we evaluate the transverse density distributions in the infinite momentum frame showing deformation in the Delta.
We study the two-color QCD matter within two fundamental quark flavors via both chiral perturbation theory and Nambu--Jona-Lasinio model methods. The effective Lagrangian described by low lying meson and baryon, i.e., diquark, is derived, where the excitations locate in the extended $\mathrm{SU}(4)$ flavor symmetry space. We determine the leading order terms on the dependence of the baryon and axial isospin densities. Then, the two-color NJL model is employed to run the numerical simulation and the phase diagram in the plane of $μ-ν_{5}$ is plotted.
The spin and parity dependent nuclear level densities (NLD) are calculated for medium-heavy nuclei using shell model techniques. The NLD are used to calculate cross sections and reaction rates of interest for nuclear astrophysics and nuclear energy applications. We investigate a new approach of describing the shell model NLD via a constant temperature parametrization. This approach provides new information about the effects of symmetries on the temperature of the low-lying nuclear states, and it is shown to be more versatile for applications.
The equation of gluodynamics with modified integral kernel is solved up to 2NLO (next-to-next-to-leading order) and 3NLO (next-to-next-to-next-to-leading order) in perturbative QCD. A relationship between the nuclear factor Ns and the ratio of the cumulant and factorial moments of the multiplicity distribution is examined. A comparison of theoretical results and experimental data in p-Pb and Pb-Pb collisions at 200A GeV and 546A GeV is carried out.
Critical examination is made on the relation between the mass shift of vector mesons in nuclear medium and the vector-meson $-$ nucleon scattering length. We give detailed comparison between the QCD sum rule approach by two of the present authors (Phys. Rev. {\bf C46} (1992) R34) and the scattering-length approach by Koike (Phys. Rev. {\bf C51} (1995) 1488). It is shown that the latter approach is mortally flawed both technically and conceptually.
We compute the longitudinal hydrodynamic flow in ultrarelativistic heavy ion collisions at $\sqrt{s}$ = 5500 GeV by using boost non-invariant initial conditions following from perturbative QCD. The transfer of entropy and energy from the central region to larger rapidities caused by boost non-invariance is determined and the associated decrease in the lifetime of the system is estimated.
We study the properties of rho mesons in nuclear matter by means of QCD sum rules at finite density. For increased sensitivity, we subtract out the vacuum contributions. With the spectral function as estimated in the literature, these subtracted sum rules are found to be not well satisfied. We suppose that Landau singularities from higher resonance states in the nearby region in this channel are the cause for this failure.
We investigate QCD sum rules for vector currents in the rho meson channel in the nuclear medium. For increased sensitivity, we subtract out the vacuum contributions. With a saturation scheme often considered in the literature, we find these subtracted sum rules to be unstable. It indicates the importance of other contributions neglected in the saturation scheme. These include more Landau singularities at low energy, additional operators in the medium, and possibly the in-medium width of the rho meson.
We establish the interrelation between the QCD scalar response of the nuclear medium and its response to a scalar probe coupled to nucleons, such as the scalar meson responsible for the nuclear binding. The relation that we derive applies at the nucleonic as well as at the nuclear levels. Non trivial consequences follow. One concerns the scalar QCD susceptibility of the nucleon. The other opens the possibility of relating medium effects in the scalar meson exchange of nuclear physics to QCD lattice studies of the nucleon mass.
I discuss highlights in the progress that is being made toward calculating processes of importance in nuclear physics from QCD using high performance computing. As exa-scale computing resources are expected to become available around 2017, I present current estimates of the computational resources required to accomplish central goals of nuclear physics.
We report on the application of a cascade + viscous hydro + cascade model for heavy ion collisions in the RHIC Beam Energy Scan range, $\sqrt{s_{\rm NN}}=6.3\dots200$ GeV. By constraining model parameters to reproduce the data we find that the effective(average) value of the shear viscosity over entropy density ratio $η/s$ decreases from 0.2 to 0.08 when collision energy grows from $\sqrt{s_{\rm NN}}\approx7$ to 39 GeV.
We extract the mass-dependent symmetry energy coefficients $a_{\text{sym}}({A})$ with the nuclear mass differences reducing the uncertainties as far as possible. The estimated $a_{\text{sym}}({A})$ of $^{208}\text{Pb}$ is $22.4\pm 0.3 $ MeV, which is further used to analyze the density-dependent nuclear matter symmetry energy at subsaturation densities. The slope parameter of the symmetry energy at the saturation density $ρ_{0}$ is $L=50.0\pm15.5$ MeV. Furthermore, it is found that, at the density of $ρ=0.69ρ_{0}=0.11$fm$^{-3}$, the symmetry energy $S(ρ=0.11\text{fm}^{-3})=25.98\pm0.01$ MeV an…
We study a chiral relativistic theory of nuclear matter aimed at the desciption of both the binding and saturation properties and the QCD properties, quark condensate and QCD susceptibilities. For this purpose the nucleon scalar response of the quark-meson coupling model is introduced in the linear sigma model. The consequences for the nuclear and the QCD scalar susceptibilities are discussed.
The goal of these lectures, oriented towards the students just entering the field, is to provide an elementary introduction to QCD and the physics of nuclear interactions at high energies. We first introduce the general structure of QCD and discuss its main properties. Then we proceed to Glauber multiple scattering theory which lays the foundation for the theoretical treatment of nuclear interactions at high energies. We introduce the concept of Gribov's inelastic shadowing, crucial for the understanding of quantum formation effects. We outline the problems facing Glauber approach at high ener…
We study numerically the strong coupling limit of lattice QCD with one flavor of massless staggered quarks. We determine the complete phase diagram as a function of temperature and chemical potential, including a tricritical point. We clarify the nature of the low temperature dense phase, which is strongly bound nuclear matter. This strong binding is explained by the nuclear potential, which we measure. Finally, we determine, from this first-principle limiting case of QCD, the masses of atomic nuclei up to A=12 "carbon".
With the aim of understanding the phase structure of nuclear matter created in high-energy nuclear collisions at finite baryon density, a beam energy scan program has been carried out at Relativistic Heavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticality and heavy flavor productions will be discussed. The goal here is to establish the connection between current available data and future heavy-ion collision experiments in a high baryon density region.
We consider a $[ud]^2\bar{s}$ current, in the finite-density QCD sum rule approach, to investigate the scalar and vector self-energies of the recently observed pentaquark state $Θ^+(1540)$, propagating in nuclear mater. We find that, opposite to what was obtained for the nucleon, the vector self-energy is negative, and the scalar self-energy is positive. There is a substantial cancellation between them resulting in an attractive net self-energy of the same order as in the nucleon case.
The baryon self-energies are expressed in terms of the QCD condensates of the lowest dimension in symmetric and asymmetric nuclear matter within the QCD sum-rule approach. The self-energies are shown to satisfy the Gell-Mann--Okubo relations in the linear SU(3) breaking approximation. The results are in qualitative agreement with those obtained by the standard nuclear physics methods.
We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of sign-problems for seniority-conserving nuclear interactions. This technique allows a microscopic calculation of angular momentum and parity projected nuclear level densities. We present results for the $^{55}$Fe, $^{56}$Fe and $^{57}$Fe isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density.
A unified chiral mean field approach is presented for QCD thermodynamics in a wide range of temperatures and densities. The model simultaneously gives a satisfactory description of lattice QCD thermodynamics and fulfills nuclear matter and astrophysical constraints. The resulting equation of state can be incorporated in relativistic fluid-dynamical simulations of heavy-ion collisions and neutron stars mergers. Access to different regions of the QCD phase diagram can be obtained in simulations of heavy-ion data and observations of neutron star mergers.
We establish the interrelation between the QCD scalar response of the nuclear medium and its response to a scalar probe coupled to nucleons, such as the scalar meson responsible for the nuclear binding. The relation that we derive applies at the nucleonic as well as at the nuclear levels. Non trivial consequences follow. In particular it opens the possibility of relating medium effects in the scalar meson exchange or three-body forces of nuclear physics to QCD lattice studies of the nucleon mass
The scalar and vectorial self energies obtained through QCD sum rules are introduced in the Quantum Hadrodynamics (QHD) equations. This QHD and QCD mixing show us that the effect of the density on the coupling constants is very small.
We present an overview of the status of the studies related to the phase diagram of strong interactions through high-energy nuclear collisions. We discuss both the theoretical and experimental status of establishing the various QCD phase structures in the phase diagram, such as, quark-gluon phase, quark-hadron crossover, crossover temperature, phase boundary and critical point.
The nuclear configurational entropy (NCE) is employed to derive two parameters encoding the Pomeron Regge trajectory and the spectrum of closed strings, which are also related to the glueball mass, precisely matching data of the TOTEM collaboration at the LHC. In the Regge regime of holographic QCD, the (Reggeized) glueball propagator and the gravitational form factor of the proton occupy a relevant spot in AdS/QCD. They are used for deriving the cross-sections for the TeV scale proton-proton scattering process, which are the main ingredient for computing the NCE. The nuclear configurational s…
We summarize our current understanding of the connection between the QCD phase line and the chemical freeze-out curve as deduced from thermal analyses of yields of particles produced in central collisions between relativistic nuclei.
Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear r…
