Hadronic Matter Is Soft

The stiffness of the hadronic equation of state has been extracted from the production rate of K mesons in heavy-ion collisions around 1 AGeV incident energy. The data are best described with a compression modulus K around 200 MeV, a value which is usually called ''soft.'' This is concluded from a detailed comparison of the results of transport theories with the experimental data using two different procedures: (i) the energy dependence of the ratio of K from Au Au and C C collisions and (ii) the centrality dependence of the K multiplicities. It is demonstrated that input quantities of these transport theories which are not precisely known, such as the kaon-nucleon potential, the N ! NK cross section, or the lifetime of the in matter, do not modify this conclusion. DOI: 10.1103/PhysRevLett.96.012302 PACS numbers: 25.75.Dw, 21.65.+f For many years one of the most important challenges in nuclear physics has been to determine E=A; T, the energy/nucleon in nuclear matter in thermal equilibrium as a function of the density and the temperature T. Only at equilibrium density, 0 , do we know the energy per nucleon E=A 0 ; T 0 ÿ16 MeV by extrapolating the Weizsäcker mass formula to infinite matter. This quest has been dubbed ''search for the nuclear equation of state (EoS).'' Modeling of neutron stars or supernovae has not yet constrained the nuclear equation of state [1]; therefore, the most promising approach in extracting E=A; T is to use heavy-ion reactions in which the density of the colliding nuclei changes significantly. Three principal experimental observables have been suggested in the course of this quest which carry -according to theoretical calculations -information on the nuclear EoS: (i) the strength distribution of the giant isoscalar monopole resonances (i) The study of monopole vibrations has been very successful, but the variation in density is minute; therefore, giant monopole resonances are sensitive to the energy which is necessary to change the density of a cold nucleus close to the equilibrium point 0 . According to theory the vibration frequency depends directly on the force that counteracts any deviation from the equilibrium and therefore the potential energy. The careful analysis of the isoscalar monopole strength in nonrelativistic [2] and relativistic mean field models has recently converged which measures the curvature of E=A; T at the equilibrium point. is the compressibility. The values found are around K 240 MeV and therefore close to what has been dubbed a ''soft equation of state.'' (ii) If the overlap zone of projectile and target becomes considerably compressed in semicentral heavy-ion collisions, an in-plane flow is created due to the transverse pressure on the baryons outside of the interaction region with this flow being proportional to the transverse pressure. In order to obtain a noticeable compression, the beam energy has to be large compared to the Fermi energy of the nucleons inside the nuclei and hence a beam energy of at least 100 AMeV is necessary. Compression goes along with excitation and therefore the compressional energy of excited nuclear matter is encoded in the in-plane flow. It has recently been demonstrated [6] that transport theories do not agree quantitatively yet and therefore conclusions (iii) The third method is most promising for the study of nuclear matter at high densities and is the subject of this Letter. K mesons produced far below the NN threshold cannot be created in first-chance collisions between projectile and target nucleons. They do not provide sufficient energy even if one includes the Fermi motion. The effective energy for the production of a K meson in the NN center of mass system is 671 MeV as, in addition to the mass of the kaon, a nucleon has to be converted into a to conserve strangeness. Before nucleons can create a K at these subthreshold energies, they have to accumulate en-PRL 96

K^-/K^+ ratio at GSI in hot and dense matter

The $K^-/K^+$ ratio in heavy-ion collisions at GSI energies is studied including the properties of the participating hadrons in hot and dense matter. The determination of the temperature and chemical potential at freeze-out conditions compatible with the ratio $K^-/K^+$ is very delicate, and depends on the approach adopted for the antikaon self-energy. Three approaches for the $K^-$ self-energy are considered: non-interacting $K^-$, on-shell self-energy and single-particle spectral density. With respect to the on-shell approach, the use of an energy dependent $\bar{K}$ spectral density, including both s- and p-wave components of the $\bar{K}N$ interaction, lowers considerably the freeze-out temperature and gives rise to the "broad-band equilibration" advocated by Brown, Rho and Song.Comment: 8 pages, 5 figures, talk given at the Strange Quark Matter Conference, Atlantic Beach, North Carolina, March 12-17, 200

Hadron Production in Heavy Ion Collisions

We review hadron production in heavy ion collisions with emphasis on pion and kaon production at energies below 2 AGeV and on partonic collectivity at RHIC energies.Comment: 31 pages, 26 figures, accepted for publication in Landolt-Boernstein Volume 1-23

Recent astrophysical and accelerator based results on the Hadronic Equation of State

In astrophysics as well as in hadron physics progress has recently been made on the determination of the hadronic equation of state (EOS) of compressed matter. The results are contradictory, however. Simulations of heavy ion reactions are now sufficiently robust to predict the stiffness of the (EOS) from (i) the energy dependence of the ratio of $K^+$ from Au+Au and C+C collisions and (ii) the centrality dependence of the $K^+$ multiplicities. The data are best described with a compressibility coefficient at normal nuclear matter density $\kappa$ around 200 MeV, a value which is usually called ``soft'' The recent observation of a neutron star with a mass of twice the solar mass is only compatible with theoretical predictions if the EOS is stiff. We review the present situation.Comment: invited talk Strange Quark Matter Conference SQM06 in Los Angele

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Alignment of the ALICE Inner Tracking System with cosmic-ray tracks

37 pages, 15 figures, revised version, accepted by JINSTALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurements, and the reconstructed tracks from cosmic rays and from proton-proton collisions. The main track-based alignment method uses the Millepede global approach. An iterative local method was developed and used as well. We present the results obtained for the ITS alignment using about 10^5 charged tracks from cosmic rays that have been collected during summer 2008, with the ALICE solenoidal magnet switched off.Peer reviewe

Linear and non-linear flow mode in Pb-Pb collisions at root sNN=2.76 TeV

The second and the third order anisotropic flow, V-2 and V-3, are mostly determined by the corresponding initial spatial anisotropy coefficients, epsilon(2) and epsilon(3), in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn(n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V-n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range |eta| <0.8 and the transverse momentum range 0.2 <p(T)<5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system. (C) 2017 The Author(s). Published by Elsevier B.V.Peer reviewe

D-Meson Azimuthal Anisotropy in Midcentral Pb-Pb Collisions root S-NN=5.02 TeV

The azimuthal anisotropy coefficient v(2) of prompt D-0, D+, D*+, and D-s(+) mesons was measured in midcentral (30%-50% centrality class) Pb-Pb collisions at a center-of-mass energy per nucleon pair root s(NN)=5.02 TeV, with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at midrapidity, |y| < 0.8, in the transverse momentum interval 1 < p(T) < 24 GeV/c. The measured D-meson v(2) has similar values as that of charged pions. The D-s(+) v(2), measured for the first time, is found to be compatible with that of nonstrange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters.Peer reviewe

Production of deuterons, tritons, He-3 nuclei, and their antinuclei in pp collisions at root s=0.9, 2.76, and 7 TeV

Invariant differential yields of deuterons and antideuterons in pp collisions at root s = 0.9, 2.76 and 7 TeV and the yields of tritons, He-3 nuclei, and their antinuclei at root s = 7 TeV have been measured with the ALICE detector at the CERN Large Hadron Collider. The measurements cover a wide transverse momentum (p(T)) range in the rapidity interval vertical bar y vertical bar <0.5, extending both the energy and the pT reach of previous measurements up to 3 GeV/c for A = 2 and 6 GeV/c for A = 3. The coalescence parameters of (anti) deuterons and 3 He nuclei exhibit an increasing trend with pT and are found to be compatible with measurements in pA collisions at low p(T) and lower energies. The integrated yields decrease by a factor of about 1000 for each increase of the mass number with one (anti) nucleon. Furthermore, the deuteron-to-proton ratio is reported as a function of the average charged particle multiplicity at different center-of-mass energies.Peer reviewe

Measuring (KSK +/-)-K-0 interactions using Pb-Pb collisions at root S-NN=2.76 TeV

We present the first ever measurements of femtoscopic correlations between the KS0 and K± particles. The analysis was performed on the data from Pb–Pb collisions at sNN=2.76 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding via the a0(980) resonance. The extracted kaon source radius and correlation strength parameters for KS0K− are found to be equal within the experimental uncertainties to those for KS0K+. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the a0 resonance are tested. Our results are also compatible with the interpretation of the a0 having a tetraquark structure instead of that of a diquark