Relativistic Heavy Ion Collider experiments exhibit correlations peaked in relative azimuthal angle and extended in rapidity. Called the ridge, this peak occurs both with and without a jet trigger. We argue that the untriggered ridge arises when particles formed by flux tubes in an early glasma stage later manifest transverse flow. Combining a blast wave model of flow fixed by single-particle spectra with a simple description of the glasma, we find excellent agreement with current data.
Nuclear collisions exhibit long-range rapidity correlations not present in proton-proton collisions. Because the correlation structure is wide in relative pseudorapidity and narrow in relative azimuthal angle, it is known as the ridge. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) as well as correlations without a trigger (the soft ridge). Earlier we argued that the soft ridge arises when particles formed in an early Glasma stage later manifest transverse flow. We extend this study to address new soft ridge measurements. We th…
A multi-task learning (MTL) framework, called gradient kernel ridge regression, for nuclear masses and separation energies is developed by introducing gradient kernel functions to the kernel ridge regression (KRR) approach. By taking the WS4 mass model as an example, the gradient KRR network is trained with the mass model residuals, i.e., deviations between experimental and theoretical values of masses and one-nucleon separation energies, to improve the accuracy of theoretical predictions. Significant improvements are achieved by the gradient KRR approach in both the interpolation and the extr…
Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.
We briefly comment on the ridge-like structure origin in the nuclear and hadronic reactions emphasizing that this structure in the two-particle correlation function can result from the rotation of the transient state of matter.
The azimuthal angular dependence of the nuclear modification factor R_{AA}(p_T, phi,N_{part}) recently obtained by PHENIX is related at low p_T to the trigger phi dependence of the ridge yield as measured by STAR in a framework in which the azimuthal anisotropy is driven by semihard scattering near the surface. Careful consideration of the initial geometry leads to the determination of a surface segment in which the production of semihard partons are responsible for the phi dependence of the inclusive distribution on the one hand, and for the angular correlation in ridge phenomenology on the o…
Correlation measurements indicate that excess two particle correlations extend over causally disconnected rapidity ranges. Although, this enhancement is broad in relative rapidity $η=η_1 - η_2$, it is focused in a narrow region in relative azimuthal angle $ϕ=ϕ_1 - ϕ_2$. The resulting structure looks like a ridge centered at $η= ϕ=0$. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) and in correlations without a trigger (the soft ridge). The long range rapidity behavior requires that the correlation originates in the earliest stag…
It is shown that the soft mechanism of multiparticle production by Lund hadronic strings formed by colliding constituent degrees of freedom generates a shape of angular correlations similar to the ridge structure observed in the pp collisions at 7 TeV at the LHC.
The kernel ridge regression (KRR) method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$ formulae, and their improved versions by considering the isospin dependence are adopted as examples. The parameters in these six formulae are refitted using the Levenberg-Marquardt method, which give better results than the previous ones. The radius for each nucleus is predicted with the KRR network, which is trained with the deviations between experimental and calculated nuclear ch…
An $η$-elongated same-side 2D peak ("soft ridge") in minimum-bias angular correlations from heavy ion collisions has been attributed both to jet formation and to initial-state geometry structure coupled to radial flow. We consider evidence for both interpretations.
The kernel ridge regression (KRR) approach is extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function without introducing new weight parameters and inputs in the training network. By taking the WS4 mass model as an example, the mass for each nucleus in the nuclear chart is predicted with the extended KRR network, which is trained with the mass model residuals, i.e., deviations between experimental and calculated masses, of other nuclei with known masses. The resultant root-mean-square mass deviation from the available experimental data for the 2…
In this paper, we give an account of the peripheral-tube model, which has been developed to give an intuitive and dynamical description of the so-called ridge effect in two-particle correlations in high-energy nuclear collisions. Starting from a realistic event-by-event fluctuating hydrodynamical model calculation, we first show the emergence of ridge + shoulders in the so-called two-particle long-range correlations, reproducing the data. In contrast to the commonly used geometric picture of the origin of the anisotropic flow, we can explain such a structure dynamically in terms of the presenc…
The formation of ridges induced by semihard scattering in nuclear collisions is included in the description of single-particle distributions for both pion and proton at low transverse momenta. The ridge component is characterized by an azimuthal dependent factor that is derived in the study of the ridge structure in two-particle correlation distributions involving triggers. It is shown that the inclusive ridge can reproduce the observed data on $v_2(p_T)$ if the base component underlying the ridge has no azimuthal dependence. A common description of pion and proton spectra is given in the reco…
We attribute the phenomenon known as "the ridge" to long range initial state correlations from Color Glass Condensate flux tubes and later stage radial flow. We show that this description can explain the amplitude and azimuthal width of the soft ridge and nearly explain that of the hard ridge, suggesting that the two are essentially the same phenomenon.
We study untriggered di-hadron correlations in Pb+Pb at 2.76 TeV, based on an event-by-event simulation of a hydrodynamic expansion starting from flux tube initial conditions. The correlation function shows interesting structures as a function of the pseudorapidity difference $Δη$ and the azimuthal angle difference $Δϕ$, in particular comparing different centralities. We can clearly identify a peak-like nearside structure associated with very low momentum components of jets for peripheral collisions, which disappears towards central collisions. On the other hand, a very broad ridge structure f…
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra …
Ridge formation in near-side correlation in heavy-ion collisions is studied in the framework of a phenomenological model, called Correlated Emission Model (CEM). Successive soft emissions due to jet-medium interaction lead to the enhancement of thermal partons which follow the local flow directions. The correlation between the flow direction and the semihard parton direction is the major factor that causes the ridge formation to depend on the trigger direction relative to the reaction plane. With the use of a few parameters we have been able to reproduce the data on the ridge yields as functio…
An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.
Recombination is a hadronization process that converts partons to hadrons at late time, but the description has no quantitative significance without some meaningful input on the parton distributions at earlier time. Thus observations of particle spectra and correlations have definitive implications on the partonic processes at all transverse momenta. After presenting a general review of the subject at the Workshop, I selected two topics in nuclear collisions for more detailed discussion, which are summarized here. One is on the azimuthal anisotropy at low $p_T$ due to hard or semihard scatteri…
The 2D azimuth & rapidity structure of the two-particle correlations in relativistic A+A collisions is altered significantly by the presence of sharp inhomogeneities in superdense matter formed in such processes. The causality constraints enforce one to associate the long-range longitudinal correlations observed in a narrow angular interval, the so-called (soft) ridge, with peculiarities of the initial conditions of collision process. This study's objective is to analyze whether multiform initial tubular structures, undergoing the subsequent hydrodynamic evolution and gradual decoupling, can f…
We investigate the equation of state (EOS) for nuclear matter, within the framework of the Relativistic Hartree Fock (RHF) theory, with special emphasis on the role of the Pauli coupling of the vector meson $ρ$ to the nucleon vis-a-vis the eventual softening of the EOS as revealed through a substantial reduction of the incompressibility parameter ($K_0$) for symmetric nuclear matter.
Highly compressed nuclear matter created in relativistic heavy collisions is to large extent governed by local non-equilibrium. As an idealised scenario colliding nuclear matter configurations are studied with an effective in-medium interaction based on the microscopic DBHF model. It is found that on top of the repulsive momentum dependence of the nuclear forces kinetic non-equilibrium leads to an effective softening of the equation of state as compared to ground state nuclear matter. The separation of phase space which is the basic feature of such anisotropic configurations has thereby a simi…
Nuclear forces violating parity and time reversal invariance (${\cal P},{\cal T}$-odd) produce ${\cal P},{\cal T}$-odd nuclear moments, for example, the nuclear Schiff moment. In turn, this moment can induce the electric dipole moment in the atom. The nuclear Schiff moment is predicted to be enhanced in nuclei with static quadrupole and octupole deformation. The analogous suggestion of the enhanced contribution to the Schiff moment from the soft collective quadrupole and octupole vibrations in spherical nuclei is tested in this article in the framework of the quasiparticle random phase approxi…
The atomic electric dipole moment (EDM) currently searched by a number of experimental groups requires that both parity and time-reversal invariance be violated. According to current theoretical understanding, the EDM is induced by the nuclear Schiff moment. The enhancement of the Schiff moment by the combination of static quadrupole and octupole deformation was predicted earlier. Here we study a further idea of the possible enhancement in the absence of static deformation but in a nuclear system with soft collective vibrations of two types. Both analytical approximation and numerical solution…
We demonstrate that in the framework of the event-by-event hydrodynamics followed by statistical hadronization, the proper charge conservation in the mechanism of hadron production provides the crucial non-flow component and leads to agreement with the two-dimensional two-particle correlation data in relative azimuthal angle and pseudorapidity at soft transverse momenta (p_T<2GeV). The fall-off of the same-side ridge in relative pseudorapidity follows from the fact that a pair of particles with balanced charges is emitted from the same fluid element, whose collective velocity collimates the mo…
We propose that flow fluctuations have the same origin as transverse momentum fluctuations. The common source of these fluctuations is the spatially inhomogeneous initial state that drives hydrodynamic flow. Longitudinal correlations from an early Glasma stage followed by hydrodynamic flow quantitatively account for many features of multiplicity and $p_t$ fluctuation data. We develop a framework for studying flow and its fluctuations in this picture. We then compute elliptic and triangular flow fluctuations, and study their connections to the ridge.
We review the theory of nuclear collective vibrations evolved over decades from phenomenological quasiclassical picture to sophisticated microscopic approaches. The major focus is put on the underlying microscopic mechanisms of emergent effects, which define the properties of giant resonances and soft modes. The response of atomic nuclei to electromagnetic and weak fields is discussed in detail. Astrophysical implications of the giant resonances and soft modes are outlined.
We evaluate the pion and isobar propagators in cold nuclear matter self consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the pi N Delta vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the Delta resonance at nuclear saturation density. …
Nuclear shadowing corrections are dominated by soft interaction and grow as function of $1/x$ more slowly than the single scattering term, which has an essential contribution from hard interaction. Therefore, we predict vanishing nuclear shadowing at very low $x$ provided that $Q^2$ is high and fixed. At the same time, at medium and low $Q^2$, nuclear shadowing grows with $1/x$ as is well known for soft hadronic interactions.
In this paper, we investigate the ground state properties ($i.e$ binding energy, nuclear radius, radial density distribution and single particle energies) for $^{4}He$ and $^{12}C$ nuclei at equilibrium and at large static compression at zero temperature by using two realistic different potentials namely, Nijmegen and Reid Soft Core (RSC)potentials. We carry out the calculations in No-Core Shell Model space consisting of six major oscillator shells within the framework of the Constrained Spherical Hartree- Fock (CSHF) approximations. We find out that, the computed equilibrium root mean square …
Effects of the density dependence of the nuclear symmetry energy on ground-state properties of superheavy nuclei are studied in the relativistic mean-field theory. It is found that the softening of the symmetry energy plays an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of spherical orbitals in superheavy nuclei. The calculation based on the relativistic mean-field models NL3 and FSUGold supports the double shell closure in $^{292}120$ with the softening of the symmetry energy. In addition, the significant effect of the density dependence of the symmetry energy on th…
Highly compressed nuclear matter created in relativistic heavy collisions is to large extent governed by local non-equilibrium. As an idealized scenario colliding nuclear matter configurations are studied within both, relativistic mean field theory and using more realistic in-medium interactions based on the Dirac-Brueckner T-matrix. The equation of state in anisotropic matter is thereby governed by two competing effects: The enlarged phase space volume in colliding matter tends to soften the internal potential energy of the subsystems whereas the relative motion of the two currents leads to a…
We report the consequences of implementing momentum dependent interactions (MDI) on multifragmentation in heavy-ion reactions over entire collision geometry. The evolution of a single cold nucleus using static soft equation of state and soft momentum dependent equation of state demonstrates that inclusion of momentum dependence increases the emission of free nucleons. However, no heavier fragments are emitted artificially. The calculations performed within the framework of quantum molecular dynamics approach suggest that MDI strongly influence the system size dependence of fragment production.…
An attractive, energy-dependent mean-field potential for baryons is introduced in order to generate a soft region in the nuclear equation-of-state, as suggested by recent lattice QCD calculations of baryon free matter at finite temperature. Based on a hadronic transport model, we find that although this equation-of-state has negligible effects on the inclusive hadronic spectra, it leads to a minimum in the energy dependence of the transverse collective flow and a delayed expansion of the compressed matter. In particular, the transverse flow changes its direction as the colliding system passes …
The liquid-gas phase transition in hot asymmetric nuclear matter is studied within density-dependent relativistic mean-field models where the density dependence is introduced according to the Brown-Rho scaling and constrained by available data at low densities and empirical properties of nuclear matter. The critical temperature of the liquid-gas phase transition is obtained to be 15.7 MeV in symmetric nuclear matter falling on the lower edge of the small experimental error bars. In hot asymmetric matter, the boundary of the phase-coexistence region is found to be sensitive to the density depen…
We propose a conceptual distinction between hard and soft realizations of deconfinement from nuclear to quark matter. In the high density region of Hard Deconfinement the repulsive hard cores of baryons overlap each other and bulk thermodynamics is dominated by the core properties that can be experimentally accessed in high-energy scattering experiments. We find that the equation of state estimated from a single baryon core is fairly consistent with those empirically known from neutron star phenomenology. We next discuss a novel concept of Soft Deconfinement, characterized by quantum percolati…
We studied the fragmentation in Au(35 AMeV)+Au collisions at reduced impact parameters in the range b/b_max=0.55 and 0.95 using soft and hard equations of state. The comparison of of QMD simulations at 100 fm/c as a function of reduced impact parameter $b/b_{max}$ with Multics Miniball data showed that soft EoS accurately reproduces the experimental trend of declining fragment multiplicity with impact parameter. The hard EoS on the contrary, seems too explosive to explain the data.
Nuclear forces violating parity and time reversal invariance P,T-odd produce P,T-odd nuclear moments, for example, the nuclear Schiff moment. In turn, this moment can induce the electric dipole moment (EDM) in the atom. The contribution to the Schiff moment from the soft collective quadrupole and octupole vibrations in spherical nuclei is calculated in the framework of the quasiparticle random phase approximation with separable quadrupole and octupole forces. The values of nuclear Schiff moments predicted for odd 217-221Ra and 217-221Ra isotopes indicate a possibility of enhancement by a facto…
Parity and time invariance violating (${\cal P},{\cal T}$-odd) nuclear forces produce ${\cal P},{\cal T}$-odd nuclear moments, for example, the nuclear Schiff moment. In turn, this moment can induce electric dipole moments (EDMs) in atoms. We estimate the contribution to the Schiff moment from the soft collective octupole vibrations existing in many heavy nuclei. Two possible mechanisms are considered, mixing of the ground state of an odd-$A$ nucleus with the octupole phonon state, and ${\cal P},{\cal T}$-odd admixture to the single-particle wave function of the valence nucleon. We found pract…
We discuss the recent constraints on the nuclear equation of state from pulsar mass measurements and from subthreshold production of kaons in heavy-ion collisions. While recent pulsar data points towards a hard equation of state, the analysis of the heavy-ion data allows only for soft equations of state. We resolve the apparent contradiction by considering the different density regimes probed. We argue that future measurements of global properties of low-mass pulsars can serve as an excellent cross-check to heavy-ion data.
Recent astrophysical observations of neutron stars and heavy-ion data are confronted with our present understanding of the equation of state of dense hadronic matter. Emphasis is put on the possible role of the presence of hyperons in the interior of compact stars. We argue that data from low-mass pulsars provide an important cross-check between high-density astrophysics and heavy-ion physics.
We study the implications on compact star properties of a soft nuclear equation of state determined from kaon production at subthreshold energies in heavy-ion collisions. On one hand, we apply these results to study radii and moments of inertia of light neutron stars. Heavy-ion data provides constraints on nuclear matter at densities relevant for those stars and, in particular, to the density dependence of the symmetry energy of nuclear matter. On the other hand, we derive a limit for the highest allowed neutron star mass of three solar masses. For that purpose, we use the information on the n…
Landscape of nuclear deformation softness with spherical quasi-particle random phase approximation
Ho Chi Minh City University of Education（胡志明市教育大学）；Institute for Basic Science (IBS)（韩国基础科学研究院）；San Diego State University（圣地亚哥州立大学）；Tel Aviv University（特拉维夫大学）
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.
Measurements of kaon production at subthreshold energies in heavy-ion collisions point to a soft nuclear equation-of-state for densities up to 2-3 times nuclear matter saturation density. We apply these results to study the implications on compact star properties, especially in the context of the recent measurement of the two solar mass pulsar PSR J1614-2230. The implications are two-fold: Firstly, the heavy-ion results constrain nuclear matter at densities relevant to light neutron stars. Hence, a radius measurement could provide information about the density dependence of the symmetry energy…
In the framework of soft-collinear effective theory with Glauber gluons, results and predictions for inclusive hadron suppression, based upon in-medium parton shower evolution, are presented for Au+Au and Pb+Pb collisions at RHIC and LHC energies $\sqrt{s}=200$ AGeV and $\sqrt{s}=2.76, \, 5.1$ ATeV, respectively. The $\rm SCET_G$ medium-induced splitting kernels are further implemented to evaluate the attenuation of reconstructed jet cross in such reactions and to examine their centrality and radius $R$ dependence. Building upon a previously developed method to systematically resum the jet sha…
Motivated by a schematic model of multiple parton scattering within the Glauber formalism, the transverse momentum spectra in $pA$ and $AA$ collisions are analyzed in terms of a nuclear modification factor with respect to $pp$ collisions. The existing data at the CERN Super Proton Synchrotron (SPS) energies are shown to be consistent with the picture of Glauber multiple scattering in which the interplay between soft and hard processes and the effect of absorptive processes lead to nontrivial nuclear modification of the particle spectra. Relative to the additive model of incoherent hard scatter…
We study single jet production in electron-nucleus collisions e^- + N_A -> J + X, using the 1-jettiness (τ_1) global event shape. It inclusively quantifies the pattern of radiation in the final state, gives enhanced sensitivity to soft radiation at wide angles from the nuclear beam and final-state jet, and facilitates the resummation of large Sudakov logarithms associated with the veto on additional jets. Through their effect on the observed pattern of radiation, 1-jettiness can be a useful probe of nuclear PDFs and power corrections from dynamical effects in the nuclear medium. This formalism…
The parity-odd effect in the Standard Model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the $ΔI=1$ channel with the parity-odd pion-nucleon coupling constant $h_π^1$. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well-understood. In this Letter we derive a soft-pion theorem relating $h_π^1$ and the neutron-proton mass-splitting induced by an artificial parity-even counterpart of the $ΔI=1$ weak Lagrangian, and demonstrate that the theorem still holds exact …
More than twenty years ago, it was predicted that nuclei can adopt interesting shapes, such as rods or slabs, etc., in the cores of supernovae and the crusts of neutron stars. These non-spherical nuclei are referred to as nuclear "pasta". In recent years, we have been studying the dynamics of the pasta phases using a method called quantum molecular dynamics (QMD) and have opened up a new aspect of study for this system. Our findings include: dynamical formation of the pasta phases by cooling down the hot uniform nuclear matter; phase diagrams in the density versus temperature plane; structural…
Quantum phase transitions between competing equilibrium shapes of nuclei with an odd number of nucleons are explored using a microscopic framework of nuclear energy density functionals and a particle-boson core coupling model. The boson Hamiltonian for the even-even core nucleus, as well as the spherical single-particle energies and occupation probabilities of unpaired nucleons, are completely determined by a constrained self-consistent mean-field calculation for a specific choice of the energy density functional and pairing interaction. Only the strength parameters of the particle-core coupli…
Impact of soft versus hard equations of state on hybrid stars
Université Paris-Saclay（巴黎萨克雷大学）；CNRS/IN2P3, IJCLab（法国国家科学研究中心/法国核物理与粒子物理研究所，IJCLab）；Physics Department, Yildiz Technical University（伊斯坦布尔技术大学物理系）；Faculty of Engineering and Architecture, Istanbul Esenyurt University（伊斯坦布尔埃森尤特大学工程与建筑学院）；Institut Universitaire de France (IUF)（法兰西学院）；International Research Laboratory on Nuclear Physics and Astrophysics, Michigan State University and CNRS（密歇根州立大学与中国国家科学研究中心核物理与天体物理学国际研究实验室）
We formulate a Lattice Hamiltonian approach for the modeling of intermediate energy heavy ion collisions. After verifying stationary ground state solutions, we implement this in a calculation of nuclear stopping power and compare our results with experimental data. Our findings support a relatively soft nuclear equation of state, with a momentum-dependent self-consistent mean field.
