The distribution of particles is highly anisotropic in the initial stage of a heavy-ion collision. In this paper we demonstrate that this anisotropy induces a sizable effect on the spin alignment of vector mesons. We study two different production mechanisms for ϕ and K^*0 mesons, on one hand the coalescence of quarks and on the other that of pseudoscalar mesons. In the quark-coalescence picture where ϕ and K^*0 are produced via a bare vector coupling to quarks, a negative δρ_00^y of order 10^-3 is observed. In contrast, when ϕ and K^*0 are produced via quark coalescence with a vertex with spin-orbit coupling, or when they are produced via pseudoscalar-meson coalescence, a positive δρ_00^y emerges. In all cases, the magnitude of the spin alignment is directly proportional to the degree of anisotropy. The sign difference between the cases provides a possibility to clarify the production mechanism for vector mesons.

We present BHAC-QGP, a new numerical code to simulate the evolution of matter created in heavy-ion collisions in the presence of electromagnetic fields. It is derived from the Black Hole Accretion Code (BHAC), which has been designed to model astrophysical processes in a general-relativistic magnetohydrodynamical description. As the original Black Hole Accretion Code, BHAC-QGP benefits from the use of Adaptive Mesh Refinement (AMR), which allows us to dynamically adjust the resolution where necessary, and makes use of time-dependent Milne coordinates and the ultrarelativistic equation of state, P = e/3. We demonstrate that BHAC-QGP accurately passes a number of systematic and rigorous tests.

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy-momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients.

We derive analytical formulas for the equal-time Wigner function in an electromagnetic field of arbitrary strength. While the magnetic field is assumed to be constant, the electric field is assumed to be space independent and oriented parallel to the magnetic field. The Wigner function is first decomposed in terms of the so-called Dirac-Heisenberg-Wigner functions, and then the transverse-momentum dependence is separated using a new set of basis functions which depend on the quantum number n of the Landau levels. Equations for the coefficients are derived and then solved for the case of a constant electric field. The pair production rate for each Landau level is calculated. In the case of finite temperature and chemical potential, the pair-production rate is suppressed by Pauli's exclusion principle.

The present document discusses plans for a compact, next-generation multi-purpose detector at the LHC as a follow-up to the present ALICE experiment. The aim is to build a nearly massless barrel detector consisting of truly cylindrical layers based on curved wafer-scale ultra-thin silicon sensors with MAPS technology, featuring an unprecedented low material budget of 0.05% X$_0$ per layer, with the innermost layers possibly positioned inside the beam pipe. In addition to superior tracking and vertexing capabilities over a wide momentum range down to a few tens of MeV/$c$, the detector will provide particle identification via time-of-flight determination with about 20~ps resolution. In addition, electron and photon identification will be performed in a separate shower detector. The proposed detector is conceived for studies of pp, pA and AA collisions at luminosities a factor of 20 to 50 times higher than possible with the upgraded ALICE detector, enabling a rich physics program ranging from measurements with electromagnetic probes at ultra-low transverse momenta to precision physics in the charm and beauty sector.

1 Introduction 2 QCD and its thermodynamics 3 Equation of state and phase boundaries of strongly interacting matter 4 Model descriptions of strongly interacting matter near deconfinement 5 Summary

Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany Department of Physics, P.O.Box 35, FI-40014 University of Jyväskylä, Finland Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany MTA-KFKI, Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O.Box 49, Hungary

We study the formation of baryons as composed of quarks and diquarks in hot and dense hadronic matter in a Nambu-Jona-Lasinio (NJL)-type model. We first solve the Dyson-Schwinger equation for the diquark propagator and then use this to solve the Dyson-Schwinger equation for the baryon propagator. We find that stable baryon resonances exist only in the phase of broken chiral symmetry. In the chirally symmetric phase, we do not find a pole in the baryon propagator. In the color-superconducting phase, there is a pole, but it has a large decay width. The diquark does not need to be stable in order to form a stable baryon, a feature typical for so-called Borromean states. Varying the strength of the diquark coupling constant, we also find similarities to the properties of an Efimov state. (C) 2011 Elsevier B.V. All rights reserved.

The primary focus of our work has been the research of vacuum properties of the low-lying scalar, pseudoscalar, vector and axial-vector mesons (with the energies up to approximately 1.5 GeV) within a linear sigma model with global chiral invariance. As a first approximation of a large r study, we have taken into account only the mesons contain- ing u and d quarks. All mesons in our model are quark- antiquark states due to their behaviour in the limit of large number of colours (e.g., no qqq¯ q states for now). Their as- signment to the physical fields is straightforward in the cas e of pseudsosclars: pion and N (the latter is the non-strange contribution to the physical meson); vectors: !(782) and (770); axial-vectors: f1(1285) and a1(1260). The scalar mesons can be assigned in at least two ways: to f0(600) and a0(980) or to f0(1370) and a0(1450). In Refs. (1, 2) we have presented the case where the scalar mesons are assigned to f0(600) and a0(980). The Lagrangian of the model is discussed and we derive the formulas for the s-wave scattering lengths with isospin zero (scattering length a 0 0 ) and isospin two (scattering length a 2 0) in the coupled channel. We also derive the decay widths for the following processes: → , f1 → a0(980) , a1 → , f0(600) → , a1 → f0(600) and a1 → as well as the decay amplitude in the a0(980) → N channel. We have used the scatter- ing lengths and the decay widths → , f1 → a0(980) and a1 → to calculate the parameters of the model; the decay amplitudea0(980) → N and the decay widths a1 → f0(600) , a1 → and f0(600) → are then the results of the model and can be compared to the exper- imental data. Our calculations have resulted in a perfect agreement with f0(1370)! = 410 MeV formf0(1370) = 1300 MeV and f0(1370)! = 470 MeV for mf0(1370) = 1350 MeV. This result is in accordance with the experimental data from the PDG (4) stating the full width of the f0(1370) be- tween 200 and 500 MeV (and1200 ≤ mf0(1370) ≤ 1500). Therefore, we conclude that the scalar mesons f0(1370) and a0(1450) are (predominantly) q¯

We calculate the pion-nucleon scattering lengths $a_{0}^{(\pm)}$ and the mass parameter $m_{0}$, which describes the nucleon mass in the chiral limit, at tree-level in the framework of a globally symmetric linear sigma model with parity-doubled nucleons. When recent lattice results [Takahashi] are used, we obtain $m_{0}\simeq300-600$ MeV. While $a_{0}^{(-)}$ is in fair agreement with experimental data, $a_{0}^{(+)}$ is too small because of the employed large scalar meson mass. This indicates the need to account for additional scalar degrees of freedom.

S. Gallas1, F. Giacosa1, and D.-H. Rischke1,2 1Institut für Theoretische Physik, Johann Wolfgang Goethe University, Frankfurt, Germany; 2Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt, Germany Understanding the mass of the nucleon is one of the most important issues in modern physics. Neglecting the small contribution of the explicit symmetry breaking, in the classical linear sigma model the mass of the nucleon is generated exclusively through spontaneous breaking of the chiral symmetry, leading to the appearance of a chiral condensate φ ∼ fπ , where fπ = 92.4 MeV is the pion decay constant [1]. The chiral condensate φ can be directly related to the fundamental quark condensate 〈qq〉 as φ ≃ Λ−2 QCD 〈qq〉, where ΛQCD is the QCD Yang-Mills scale. However, not only the quark condensate, but also other condensates, such as the gluon and the tetraquark ones, can contribute to the mass of the nucleon mN and it is not yet settled which is their quantitative role [2]. A possibility to study this problem in the context of a linear sigma model goes via the so called mirror assignment, which was first discussed in Ref. [3] and extensively analyzed in Refs. [4, 5]. In this assignment, the nucleon N and its chiral partner N∗ form a doublet of the chiral group. Then it is possible to introduce a chirally invariant mass term parametrized by m0. This leads to non-vanishing masses of the nucleon and its chiral partner in the chirally restored phase where φ → 0, instead they acquire the same mass m0 6= 0. We show this in Fig. 1. A study of the parameters using the decays N∗ → Nπ and a1 → πγ results in a value of 460 MeV for m0 which denotes the contribution to the mass of the nucleon not stemming from the quark condensate [6]. The viability of our model is tested by studying the decay N∗ → Nη and pion-nucleon scattering at tree level. This can provide useful information to clarify the origin of the nucleon mass and its behavior in the chirally restored phase.

This writeup is a compilation of the predictions for the forthcoming Heavy Ion Program at the Large Hadron Collider, as presented at the CERN Theory Institute 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held from May 14th to June 10th 2007.

In relativistic fermionic systems at high temperature and/or high density, there are two types of fermionic excitations. Besides the ordinary excitation branches of particles and antiparticles, there are additional collective excitations, the so-called plasmino and anti-plasmino [1, 2]. These branches have opposite chirality compared to the ordinary excitation branches [2]. They coincide with the normal fermionic branches for vanishing momenta. For large momenta, they approach the lightcone and their spectral strengths vanish exponentially. The plasmino (anti-plasmino) branch has a minimum (maximum) for small, non-zero momenta. These excitations have been extensively investigated for normal-conducting matter [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], for a review see, for instance, Ref. [19]. With the exception of heavy-ion collisions, in the laboratory it is hard to achieve sufficiently large temperatures and densities such that a relativistic description for fermions becomes necessary, even if they are as light as electrons. On the other hand, there is a plethora of astrophysical situations where fermions have to be treated relativistically. For instance, the core of compact stellar objects could be sufficiently dense to consist of deconfined quark matter. The quark Fermi energy is then of the order of μ ∼ 500 MeV. Thus, at least the light up and down quark flavors have to be considered as relativistic particles, since m ∼ 5 MeV ≪ μ. However, quark matter in compact stellar objects, if sufficiently cold, is not a normal-conducting system, but a color superconductor [20, 21]. In this paper, we therefore investigate whether the plasminos known from normal-conducting systems survive in a superconductor. This is a question of general interest, independent of the specific nature of the superconductor (i.e., ordinary, color, etc.). To our knowledge, this problem has not been considered previously, since electrons can to good approximation be considered as non-relativistic in the condensed-matter context, and plasminos are absent if the temperature is smaller than the mass (at least for zero chemical potential [8]). It is also possible to formulate our expectation regarding the existence of plasminos in superconductors: plasminos are low-momentum excitations which, for large chemical potential μ ≫ p, are buried deep down in the Fermi sea. On the other hand, superconductivity is a Fermi-surface phenomenon. We thus expect that superconductivity should not exert a destructive influence on the presence of the plasmino excitations. Nevertheless, it requires an explicit calculation to prove this, which is the purpose of the present paper. We shall see that our expectations regarding the existence of plasminos in superconductors are confirmed. The outline of this paper is the following. In Sec. II, we consider a normal-conducting system consisting of massless fermions interacting via scalar and vector boson exchange. For the sake of simplicity, we restrict our consideration to zero temperature. This case has been studied before by Blaizot and Ollitrault in Ref. [9]. We largely confirm their results and extend them by computing the spectral density. We then study a superconducting system in Sec. III. Section IV concludes this paper with a summary of our results. Our units are h̄ = c = kB = 1 and the metric tensor is g μν = diag(+,−,−,−). Four-vectors are denoted by capital letters, K ≡ (k0, ~k). Three-vectors have modulus k ≡ |~k| and direction k̂ ≡ ~k/k. Our computations are done in the imaginary-time formalism where space-time integrals are denoted as ∫ X ≡ ∫ 1/T 0 dτ ∫

We consider a phase-space model for particle production in nuclear collisions. Once the multiplicities of the individual particle species are known, single-inclusive momentum spectra can be computed after making simplifying assumptions for the matrix element for multiparticle production. Comparison of the calculated spectra with data for pions and kaons from central Pb+Pb collisions at ELab = 158 AGeV reveals a residual longitudinal phase-space dominance in the final state of the reaction. We account for this by modifying the isotropic, relativistic invariant phase space in a way which retains boost invariance in beam direction but suppresses large transverse momenta. Adjusting a single parameter, we obtain a reasonably good description of transverse momentum and rapidity spectra for both pions and kaons.

We study the gauge field fluctuations in dense quark matter and determine the temperature of the induced first-order phase transition to the color-superconducting phase in weak coupling. We find that the local approximation of the coupling between the gauge potential and the order parameter, employed in the Ginzburg-Landau theory, has to be modified by restoring the full momentum dependence of the polarization function of gluons in the superconducting phase.

It is shown that color-superconducting quark matter, where quarks of the same flavor form Cooper pairs with spin one, exhibits an electromagnetic Meissner effect. This is in contrast to spin-zero color superconductors where Cooper pairs consist of quarks with different flavors.

We consider color superconductivity with two flavors of massless quarks which form Cooper pairs with total spin zero. We solve the gap equation for the color-superconducting gap parameter to subleading order in the QCD coupling constant g at zero temperature, At this order in g, there is also a previously neglected contribution from the real part of the quark self-energy to the gap equation. Including this contribution leads to a reduction of the color-superconducting gap parameter phi(0) by a factor b(0)'=exp[-(pi(2)+4)/8] similar or equal to0.177. On the other hand, the BCS relation T(c)similar or equal to0.57phi(0) between phi(0) and the transition temperature T-c is shown to remain valid after taking into account corrections from the quark self-energy. The resulting value for T-c confirms a result obtained previously with a different method.

We formulate a phenomenological extension of the mean-field theory approach and define a class of thermodynamically self-consistent equations of state for nuclear matter. A new equation of state of this class is suggested and examined in detail.