Softest Point Research Articles

Speed of sound of a non-equilibrium medium formed at LHC energies

We estimate the squared speed of sound for the hot and dense QCD states formed in ion collisions at very high energies by exploring the implications of small-bounded and geometry effects in the String Percolation Model. The squared sound velocity shows signals of a local minimum (knee point) below the critical temperature consistent with the softest point in the equation of state and the onset of quark deconfinement that characterizes the quark-gluon plasma phase transition.

Searching for Minimum in Dependence of Squared Speed-of-Sound on Collision Energy

Experimental results of the rapidity distributions of negatively charged pions produced in proton-proton (p-p) and beryllium-beryllium (Be-Be) collisions at different beam momentums, measured by the NA61/SHINE Collaboration at the super proton synchrotron (SPS), are described by a revised (three-source) Landau hydrodynamic model. The squared speed-of-sound parametercs2is then extracted from the width of rapidity distribution. There is a local minimum (knee point) which indicates a softest point in the equation of state (EoS) appearing at about40A GeV/c(or 8.8 GeV) incs2excitation function (the dependence ofcs2on incident beam momentum (or center-of-mass energy)). This knee point should be related to the searching for the onset of quark deconfinement and the critical point of quark-gluon plasma (QGP) phase transition.

Cross-over versus first-order phase transition in holographic gravity–single-dilaton models of QCD thermodynamics

A dilaton potential is adjusted to recently confirmed lattice QCD thermodynamics data in the temperature range $(0.7 \ldots 3.5) T_c$ where $T_c = 155 \text{MeV}$ is the pseudo-critical temperature. The employed holographic model is based on a gravity--single-field dilaton dual. We discuss conditions for enforcing (for the pure gluon plasma) or avoiding (for the QCD quark-gluon plasma) a first-order phase transition, but still keeping a softest point (minimum of sound velocity).

Extraction of the sound velocity from rapidity spectra: Evidence for QGP formation at FAIR/RHIC-BES energies

We analyze longitudinal pion spectra from \sqrt{s_{NN}}= 2 GeV to \sqrt {s_{\rm NN}}=20 GeV within Landau's hydrodynamical model and the UrQMD hybrid approach. From the measured data on the widths of the pion rapidity spectra, we extract the sound velocity c_s^2 in the dense stage of the reactions. It is found that the sound velocity has a local minimum (indicating a softest point in the equation of state, EoS) at \sqrt{s_{NN}}= 4-9 GeV, an energy range accessible at the Facility for Antiproton and Ion Research (FAIR) as well as the RHIC-Beam Energy Scan (RHIC-BES). This softening of the EoS is compatible with the formation of a QGP at the onset of deconfinement. The extracted sound velocities are then used to calculate an excitation function for the mean transverse mass of pions from the hybrid model. We find that, above \sqrt{s_{NN}} \approx 10 GeV, even the lowest c_s^{2} gives a considerably larger <m_T> of pions compared to data.

Study on the Microstructure and the Mechanical Properties of TA2

The microstructure and the mechanical properties of welding joint with the material of TA2 have been studied in this paper with the specimens made with the method of argon-arc welding. The microhardness of the welding joint has been compared with the hardness in the same position of the weld joint after annealing. Conclusions have been obtained as follows: The organizations of the welding joint include base material, recrystallization zone, overheated area, fusion zone and the weld zone; the hardness tendency of the weld joint is depicted as M-shape with the softest point located at the center, and the hardest is located at the overheated zone; the annealing treatment can enhance the weld joint hardness mainly at the center, and the hardness of other zones change little.

Connecting Polyakov loops to the thermodynamics ofSU(Nc)gauge theories using the gauge-string duality

We show that in four-dimensional gauge theories dual to five-dimensional Einstein gravity coupled to a single scalar field in the bulk the derivative of the single heavy quark free energy in the deconfined phase is $dF_{Q}(T)/dT \sim -1/c_s^2(T)$, where $c_s(T)$ is the speed of sound. This general result provides a direct link between the softest point in the equation of state of strongly-coupled plasmas and the deconfinement phase transition described by the expectation value of the Polyakov loop. We give an explicit example of a gravity dual with black hole solutions that can reproduce the lattice results for the expectation value of the Polyakov loop and the thermodynamics of SU(3) Yang-Mills theory in the (non-perturbative) temperature range between $T_c$ and $3T_c$.

Ellipsoidal Flows in Relativistic Hydrodynamics of Finite Systems

A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can be utilized for relativistic description of the system evolution in thermodynamic region near the softest point and at the final stage of the hydrodynamic expansion in A+A collisions. The solutions can be used also for testing of numerical hydrodynamic codes solving relativistic hydrodynamic equations for anisotropic expansion of finite systems

Generating new solutions for relativistic transverse flow at the softest point

Using the method of prolongation we generate new stationary solutions from a recently obtained simple particular solution for relativistic transverse flow with cylindrical symmetry in 1+3 dimension. This is an extension of the longitudinal Bjorken flow ansatz and can be applied to situations during a first order phase transition in a fast expanding system. The prolongated solution allows us to trace back the flow profile from any transverse flow conjectured at the end of the phase transition.

Analytic solution for relativistic transverse flow at the softest point

We obtain an extension of Bjorken's 1+1 dimensional scaling relativistic flow solution to relativistic transverse velocities with cylindrical symmetry in 1+3 dimension at constant, homogeneous pressure (vanishing sound velocity). This can be the situation during a first order phase transition converting quark matter into hadron matter in relativistic heavy ion collisions.

Equation of state, flow, fluctuations and J/ψ suppression

Radial flow observed at AGS/SPS energies is very strong, with collective velocities of matter reaching about 0.5c for central collisions of the heaviest ions. The lattice-based Equation of State (EOS) is however rather soft, due to the QCD phase transition. We show that both statements are consistent only if proper kinetic-based treatment of the freeze-out is made. In fact chemical and thermal freeze-out happen at quite different conditions, especially at SPS. Event-by-event fluctuations can shed new light on this problem. We also propose new model of “anomalous” J/ψ suppression found for PbPb collisions, related it to prolonged lifetime of dense matter due the “softest point” of the EOS.

Properties of hot and dense nuclear matter in a mixed phase

The QCD phase transition is treated within a statistical model taking into account the coexistence of interacting quark-gluon and hadron phases. Being in agreement with the recent lattice QCD data, this statistical mixed phase model predicts that the “softest point” of the equation of state, resulting in the longest-lived fireball effect, is atesp ≈ 0.35GeV/fm3. It is shown that this “softest point” is washed out at the baryon densities higher than the normal nuclear density. The approach is extended to include strangeness. Attention is drawn to the study of signatures for forming the mixed quark-hadron phase of nuclear matter in the collision energy rangeElab ≈ 2–10 GeV/A.

Hydrodynamics near the QCD phase transition: Looking for the longest-lived fireball.

We propose a new strategy for the experimental search of the QCD phase transition in heavy ion collisions: One may tune collision energy around the point where the lifetime of the fireball is expected to be longest. We demonstrate that the hydrodynamic evolution of excited nuclear matter does change dramatically as the initial energy density goes through the "softest point" (where the pressure to energy density ratio reaches its minimum). For our choice of equation of state, this corresponds to epsilon_i approx. = 1.5 GeV/fm^3 and collision energy E_lab/A approx. = 30 GeV (for Au+Au). Various observables seem to show distinct changes near the softest point.