We study the N/Z and N/A dependence of balance energy (E$_{bal}$) for isotopic series of Ca having N/Z (N/A) varying from 1.0 to 2.0 (0.5 to 0.67). We show that the N/Z (N/A) dependence of E$_{bal}$ is sensitive to symmetry energy and its density dependence at densities higher than saturation density and is insensitive towards the isospin dependence of nucleon-nucleon (nn) cross section and Coulomb repulsion. We also study the effect of momentum dependent interactions (MDI) on the N/Z (N/A) dependence of E$_{bal}$. We find that although MDI influences the E$_{bal}$ drastically, the N/Z (N/A) dependence of E$_{bal}$ remains unchanged on inclusion of MDI.
The widths of charge balance function in high energy hadron-hadron and relativistic heavy ion collisions are studied using the Monte Carlo generators PYTHIA and AMPT, respectively. The narrowing of balance function as the increase of multiplicity is found in both cases. The mean parton-freeze-out time of a heavy-ion-collision event is used as the characteristic hadronization time of the event. It turns out that for a fixed multiplicity interval the width of balance function is consistent with being independent of hadronization time.
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isobaric systems with N/A = 0.5 and 0.58. Our fndings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
A novel state of matter has been hypothesized to exist during the early stage of relativistic heavy ion collisions, with normal hadrons not appearing until several fm/c after the start of the reaction. To test this hypothesis, correlations between charges and their associated anticharges are evaluated with the use of balance functions. It is shown that late-stage hadronization is characterized by tightly correlated charge/anticharge pairs when measured as a function of relative rapidity.
We study the N/Z dependence of balance energy (E$_{bal}$) for isotopic series of Ca having N/Z varying from 1.0 to 2.0. We show that the N/Z dependence of E$_{bal}$ is sensitive to symmetry energy and its density dependence at densities higher than saturation density and is insensitive towards the isospin dependence of nucleon-nucleon cross section
Based on the isospin-dependent quantum molecular dynamics (IQMD) picture, we attempt to understand the nature of transverse flow in $_{28}Ni^{58}+_{28}Ni^{58}$ and $_{26}Fe^{58}+_{26}Fe^{58}$ systems at wide range of energies and impact parameters. The isospin dependence of balance energy in transverse flow is clearly visible. The results are compared with the experimental data available.
An introductory overview of electromagnetic probes in ultra-relativistic heavy-ion collisions is provided. Experimental evidence supporting the production of thermal photons and dileptons in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are reviewed. Thermal electromagnetic emission evaluated from hydrodynamical models of collisions is discussed.
Heavy-ion collisions at the LHC provide the conditions to investigate regions of quark-gluon plasma that reach higher temperatures and that persist for longer periods of time compared to collisions at the Relativistic Heavy Ion Collider. This extended duration allows correlations from charge conservation to better separate during the quark-gluon plasma phase, and thus be better distinguished from correlations that develop during the hadron phase or during hadronization. In this study charge balance functions binned by relative rapidity and azimuthal angle and indexed by species are considered.…
We calculate the charge balance function of the bulk quark system before hadronization and those for the directly produced and the final hadron system in high energy heavy ion collisions. We use the covariance coefficient to describe the strength of the correlation between the momentum of the quark and that of the anti-quark if they are produced in a pair and fix the parameter by comparing the results for hadrons with the available data. We study the hadronization effects and decay contributions by comparing the results for hadrons with those for the bulk quark system. Our results show that wh…
The current status of photon and dilepton emission in ultra-relativistic heavy ion collisions is reviewed, and recent developments are highlighted. The importance of emissions at early, intermediate and late times is emphasized.
We present here the system size dependence of balance energy for semi-central and peripheral collisions using quantum molecular dynamics model. For this study, the reactions of $Ne^{20}+Ne^{20}$, $Ca^{40}+Ca^{40}$, $Ni^{58}+Ni^{58}$, $Nb^{93}+Nb^{93}$, $Xe^{131}+Xe^{131}$ and $Au^{197}+Au^{197}$ are simulated at different incident energies and impact parameters. A hard equation of state along with nucleon-nucleon cross-sections between 40 - 55 mb explains the data nicely. Interestingly, balance energy follows a power law $\propto{A^τ}$ for the mass dependence at all colliding geometries. The p…
A strong differential transverse collective flow is predicted for the first time to occur in heavy-ion collisions at balance energies. We also give a novel explanation for the disappearance of the total transverse collective flow at the balance energies. It is further shown that the differential flow especially at high transverse momenta is a useful microscope capable of resolving the balance energy's dual sensitivity to both the nuclear equation of state and in-medium nucleon-nucleon cross sections in the reaction dynamics.
The proton elliptic flow in collisions of Ca on Ca at energies from 30 to 100 MeV/nucleon is studied in an isospin-dependent transport model. With increasing incident energy, the elliptic flow shows a transition from positive to negative flow. Its magnitude depends on both the nuclear equation of state (EOS) and the nucleon-nucleon scattering cross section. Different elliptic flows are obtained for a stiff EOS with free nucleon-nucleon cross sections and a soft EOS with reduced nucleon-nucleon cross sections, although both lead to vanishing in-plane transverse flow at the same balance energy. …
Using an isospin-dependent quantum molecular dynamics, nuclear stopping in intermediate heavy ion collisions has been studied. The calculation has been done for colliding systems with different neutron-proton ratios in beam energy ranging from 15MeV/u to 150MeV/u. It is found that, in the energy region from above Fermi energy to 150MeV/u, nuclear stopping is very sensitive to the isospin dependence of in-medium nucleon-nucleon cross section, but insensitive to symmetry potential. From this investigation, we propose that nuclear stopping can be used as a new probe to extract the information on …
We investigate J/psi transverse momentum distribution in a transport approach. While the nuclear modification factor R_{AA}(N_p) at RHIC is almost the same as at SPS, the averaged transverse momentum square <p_t^2> and R_{AA}(p_t) are very different at SPS, RHIC and LHC and can be used to differentiate from the J/psi production mechanisms in high energy nuclear collisions.
We study the propogation and diffusion of electric charge fluctuations in high energy heavy ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1 dimensional Bjorken hydrodynamical model. Limiting the speed of propagation of charge fluctuations increases the height and reduces the wid…
The dependence of $K^+$ production on the nuclear equation of state is investigated in heavy ion collisions. An increase of the excitation function of $K^+$ multiplicities obtained in heavy ($Au+Au$) over light ($C+C$) systems when going far below threshold which has been observed by the KaoS Collaboration strongly favours a soft equation of state. This observation holds despite of the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental $K^+$ yields. Phase space effects are discussed with respect to the $K^+$ excitation…
Dilepton and photon production in heavy-ion collisions at SPS energies are studied in the relativistic transport model that incorporates self-consistently the change of hadron masses in dense matter. It is found that the dilepton spectra in proton-nucleus reactions can be well described by the conventional mechanism of Dalitz decay and direct vector meson decay. However, to provide a quantitative explanation of the observed dilepton spectra in central heavy-ion collisions requires contributions other than these direct decays and also various medium effects. Introducing a decrease of vector mes…
The dependence of K+ production on the nuclear equation of state is investigated in heavy ion collisions. An increase of the excitation function of K+ multiplicities obtained in heavy (Au+Au) over light (C+C) systems when going far below threshold which has been observed by the KaoS Collaboration strongly favours a soft equation of state. This observation holds despite of the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental K+ yields. Phase space effects are discussed with respect to the K+ excitation function.
We review essential elements in using the $J^P=1^-$ channel as a probe for hot and dense matter as produced in (ultra-) relativistic collisions of heavy nuclei. The uniqueness of the vector channel resides in the fact that it directly couples to photons, both real and virtual (dileptons), enabling the study of thermal radiation and in-medium effects on both light ($ρ, ω, ϕ$) and heavy ($Ψ, Υ$) vector mesons. We emphasize the importance of interrelations between photons and dileptons, and characterize relevant energy/mass regimes through connections to Quark-Gluon-Plasma emission and chiral sym…
In collisions between heavy ions at ultra-relativistic energies the participating protons lose energy, which is converted into new particles. As the protons slow down, they emit bremsstrahlung radiation. The yield and angular distribution of the emitted radiation are sensitive probes of how much energy the incoming protons have lost. In this paper, the spectrum of bremsstrahlung radiation is calculated for different stopping scenarios, and the results are compared with the expected yield of photons from hadronic interactions.
In conjunction with models, the experimental observable total multiplicity can be used to check if the data contain the signature of phase transition and if it is first order. Two of the models reach similar conclusions. The third one is quite different.
At high energies a quark-gluon plasma is expected to be formed in heavy ion collisions at RHIC and LHC. The theoretical description of these processes is directly associated to a complete knowledge of the details of medium effects in the nuclear gluon distribution. In this paper we analyze the possibility to constraint the behavior of this distribution considering peripheral heavy ion collisions. We reanalyze the photoproduction of heavy quarks for the deduction of the in-medium gluon distribution using three current parameterizations for this parton distribution. Moreover, we show that the el…
We present an overview of the current state of understanding of the early time dynamics of high-energy heavy-ion collisions, emphasizing recent developments and connections between the physics of the initial state and that of hard probes in heavy-ion collisions. Based on a weak-coupling description, we first establish a microscopic picture of the early time dynamics and equilibration process and subsequently discuss their macroscopic manifestations along with a novel macroscopic description of the pre-equilibrium phase. Some phenomenological consequences concerning the role of the pre-equilibr…
Hard QCD processes in ultrarelativistic heavy-ion collisions become increasingly relevant and they can be used as probes of the dense matter formed during the violent scatterings. We will discuss how one can use these hard probes to study the properties of the dense matter and the associated phenomenologies. In particular, we study the effect of jet quenching due to medium-induced energy loss on inclusive particle $p_T$ distributions and investigate how one can improve the measurement of parton energy loss in direct photon events
In this paper a pair of observables are proposed as alternative ways, by examining the fluctuation of net momentum-ordering of charged pairs, to study the charge separation induced by the Chiral Magnetic Effect (CME) in relativistic heavy ion collisions. They are, the out-of-plane to in-plane ratio of fluctuation of the difference between signed balance functions measured in pair's rest frame, and the ratio of it to similar measurement made in the laboratory frame. Both observables have been studied with simulations including flow-related backgrounds, and for the first time, backgrounds that a…
At the early stage of heavy ion collisions, non-trivial topologies of the gauge fields can be created resulting in an imbalance of axial charge density and eventually separation of electric charges along the direction of the magnetic field produced in such collisions. This process is called the chiral magnetic effect (CME). In this work we implement such a charge separation at the partonic level in AMPT for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV to study its consequence on experimental observables. We present the effects on the pion elliptic flow ($v_2$) and the charged particle balance…
The effect of shadowing on the early state of ultrarelativistic heavy ion collisions is investigated along with transverse energy and hard process production, specifically Drell-Yan, $J/ψ$, and $Υ$ production. We choose several parton distributions and parameterizations of nuclear shadowing, as well as the spatial dependence of shadowing, to study the influence of shadowing on relevant observables. Results are presented for Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV and Pb+Pb collisions at $\sqrt{s_{NN}} = 5.5$ TeV.
Due to their penetrating nature, electromagnetic probes, i.e., lepton-antilepton pairs (dileptons) and photons are unique tools to gain insight into the nature of the hot and dense medium of strongly-interacting particles created in relativistic heavy-ion collisions, including hints to the nature of the restoration of chiral symmetry of QCD. Of particular interest are the spectral properties of the electromagnetic current-correlation function of these particles within the dense and/or hot medium. The related theoretical investigations of the in-medium properties of the involved particles in bo…
This manuscript is the outcome of the subgroup ``PDFs, shadowing and $pA$ collisions'' from the CERN workshop ``Hard Probes in Heavy Ion Collisions at the LHC''. In addition to the experimental parameters for $pA$ collisions at the LHC, the issues discussed are factorization in nuclear collisions, nuclear parton distributions (nPDFs), hard probes as the benchmark tests of factorization in $pA$ collisions at the LHC, and semi-hard probes as observables with potentially large nuclear effects. Also, novel QCD phenomena in $pA$ collisions at the LHC are considered. The importance of the $pA$ progr…
Fluctuation and correlation observables are often measured using multi-particle correlation methods and therefore mutually probe the origins of genuine correlations present in multi-particle distribution functions. We investigate the common influence of correlations arising from the spatially inhomogeneous initial state on multiplicity and momentum fluctuations as well as flow fluctuations. Although these observables reflect different aspects of the initial state, taken together, they can constrain a correlation scale set at the earliest moments of the collision. We calculate both the correlat…
We discuss the prospects of using jets as precision probes in electron-nucleus collisions at the future Electron-Ion Collider. Jets produced in deep-inelastic scattering can be calibrated by a measurement of the scattered electron. Such electron-jet "tag and probe" measurements call for an approach that is orthogonal to most HERA jet measurements as well as previous studies of jets at the future EIC. We present observables such as the electron-jet momentum balance, azimuthal correlations and jet substructure, which can provide constraints on the parton transport coefficient in nuclei. We compa…
Based on an isospin- and momentum-dependent hadronic transport model IBUU04, effects of the nuclear symmetry energy on the single and double pi^{-}/pi^{+}ratios in central reactions of ^{132}Sn+^{124}Sn and ^{112}Sn+^{112}Sn at a beam energy of 400 MeV/nucleon are studied. It is found that around the Coulomb peak of the single pi^{-}/pi^{+} ratio the double pi^{-}/pi^{+} ratio taken from the two isotopic reactions retains about the same sensitivity to the density dependence of nuclear symmetry energy. Because the double pi^{-}/pi^{+}ratio can reduce significantly the systematic errors, it is t…
Modifications of jets in the existence of a hot and dense QCD medium have recently attracted a lot of attentions. In this talk, we demonstrate how jet-medium interactions change the behavior of jets by offering examples of inclusive jet and dijet productions at $ {\cal O}(α_s^3)$ in heavy ion collisions including initial-state cold nuclear effects and especially the final-state parton energy loss effect. The suppression of inclusive jet spectrum varying with jet radii and a flatter dijet momentum imbalance as compared to those in hadron-hadron collisions are observed in high-energy nuclear col…
Flow has emerged as a crucial probe for the properties of the thermalized medium produced in relativistic heavy-ion collisions. The evolution of initial state fluctuations leaves imprints on the power spectrum of flow coefficients. Therefore flow coefficients are a crucial probe of initial state fluctuations arising from the parton distributions of the colliding nuclei. This has a very strong correspondence with the physics of power spectrum of cosmic microwave background radiation (CMBR) anisotropies which directly probes initial inflationary fluctuations. Much work has been done to probe the…
The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve as a probe of the diffusivity of light quarks as well as the evolution of the systems formed in heavy-ion collisions. In this work, we reexamine the formulation of general balance functions and consider how to best define and measure these correlation functions in terms of differences of conditional densities of unlike-sign and like-sign particle pairs. We …
The first collisions of lead nuclei, delivered by the CERN Large Hadron Collider (LHC) at the end of 2010, at a centre-of-mass energy per nucleon pair $\sqrt{s_{NN}}$ = 2.76 TeV, marked the beginning of a new era in ultra-relativistic heavy-ion physics. The study of the properties of the produced hot and dense strongly-interacting matter at these unprecedented energies is currently experimentally pursued by all four big LHC experiments, ALICE, ATLAS, CMS, and LHCb. The more than a factor 10 increase of collision energy at LHC, relative to the previously achieved maximal energy at other collide…
Thermalized matter created in non-central relativistic heavy-ion collisions is expected to be tilted in the reaction plane with respect to the beam axis. The most notable consequence of this forward-backward symmetry breaking is the observation of rapidity-odd directed flow for charged particles. On the other hand, the production points for heavy quarks are forward-backward symmetric and shifted in the transverse plane with respect to the fireball. The drag of heavy quarks from the asymmetrically distributed thermalized matter generates a large directed flow for heavy flavor mesons. We predict…
We predict that the mean transverse momentum of charged hadrons $\langle p_t\rangle$ rises as a function of the charged-particle multiplicity in ultracentral nucleus-nucleus collisions. We explain that this phenomenon has a simple physical origin and represents an unambiguous prediction of the hydrodynamic framework of heavy-ion collisions. We argue that the relative increase of $\langle p_t \rangle$ is proportional to the speed of sound squared $c_s^2$ of the quark-gluon plasma. Based on the value of $c_s^2$ from lattice QCD, we expect $\langle p_t\rangle$ to increase by approximately $18$ Me…
We explore the feasibility of the measurement of charm-jet cross sections in charged-current deep-inelastic scattering at the future Electron-Ion Collider. This channel provides clean sensitivity to the strangeness content of the nucleon in the high-$x$ region. We estimate charm-jet tagging performance with parametrized detector simulations. We show the expected sensitivity to various scenarios for strange parton distribution functions. We argue that this measurement will be key to future QCD global analyses, so it should inform EIC detector designs and luminosity requirements.
The theoretical developments in the study of electromagnetic radiation in relativistic heavy-ion collisions are reviewed. The recent progress in the rates for photon and lepton pair production is discussed. Together with the improvements in the hydrodynamic descriptions of the bulk medium, the combined effort is discussed to resolve the "direct photon flow puzzle" in the RHIC and the LHC experiments. Further prediction of the direct photon production in high multiplicity proton-nucleus collisions at the LHC energy can serve as a signature of the quark gluon plasma formation in these small syst…
Elliptic flow (v_2) of ϕ-meson is shown to be a sensitive probe of the partonic collectivity using A Multi Phase Transport (AMPT) model. Within the ambit of the AMPT model with partonic interactions (string melting version), the ϕ-meson v_2 at midrapidity is found to have negligible contribution from hadronic interactions for Au+Au collisions at 200 GeV per nucleon. Changing the hadron cascade time in the model calculations does not change the ϕ-meson v_2, while it reduces the v_2 of proton at low transverse momentum (pT). These observations indicate that a substantial reduction in ϕ-mesons v_…
