In-Medium Excitations version from December 6, 2008 Convenors: Ralf Rappa1, Burkhard K¨ampferb2 a Cyclotron Institute and Physics Department, Texas A&M University, College Station, Texas 77843-3366, U.S.A. b Forschungszentrum Dresden-Rossendorf, Institut fur¨ Strahlenphysik, D-01314 Dresden, PF 510119, Germany Spectral properties of hadronic excitations are direct probes of the strongly interacting medium as created in energetic collisions of heavy nuclei. In this chapter we discuss the per- tinent theoretical background, recent developments and perspectives for using electromagnetic radiation, as well as strange and charm hadrons, to infer microscopic properties of QCD matter. In the electromagnetic emission sector, our focus is on thermal dileptons and the in-medium modifications of the light vector mesons. We outline their potential for characterizing the QCD phase transition by establishing connections of the electromagnetic correlation function to or- der parameters of chiral symmetry restoration. Complementary information can be obtained from hadronic decays of resonances probing the more dilute stage of a heavy-ion collision. We then turn to in-medium properties of strange and charm quarks and hadrons, which includes charm-quark diffusion in the QGP as well as spectral functions of K and D mesons in hadronic matter. While these quantities are not directly accessible in experiment, a careful study of their production systematics in terms of total abundance, chemistry and collective flow patterns will lead to key insights into the relevant interactions in high-density matter. Finally, we discuss medium effetcs on charmonia in both the QGP and hadronic matter, and how these could manifest themselves in observables. 1Email: [email protected] 2Email: [email protected] Contents 1 Introduction 2 2 Electromagnetic Probes and Light Vector Mesons 6 2.1 Brief Overview of Experimental Status and Interpretation . 6 2.2 Emissivity of Strongly Interacting Matter . 8 2.2.1 Electromagnetic Correlation Function and Thermal Emission Rates . 8 2.2.2 Electromagnetic Spectral Function in Vacuum . 9 2.2.3 Low-Density Expansions and Chiral Mixing . 11 2.3 Sum Rules . 12 2.3.1 QCD Sum Rules . 12 2.3.2 Chiral Sum Rules and Axialvector Spectral Function . 20 2.4 Vector Mesons in Medium: Hadronic Models . 23 2.4.1 ρ Meson . 24 2.4.2 ! Meson . 39 2.4.3 φ Meson . 42 2.5 Thermal Dilepton Rates . 42 2.5.1 Lattice QCD . 42 2.5.2 Hadronic Approaches . 44 2.5.3 RG Approach: Vector Manifestation . 46 2.6 Thermal Photon Rates . 48 2.6.1 Direct Single Photons . 48 2.6.2 Diphotons and In-Medium \σ" . 50 3 Hadronic Resonance Spectroscopy 55 3.1 Meson Resonances . 55 3.2 Baryon Resonances . 58 3.2.1 Chiral Symmetry of Baryons . 58 3.2.2 Baryon Masses and QCD Condensates . 58 3.2.3 Baryon Resonance Decays in Heavy-Ion Collisions . 60 4 Strangeness 63 4.1 Kaons in Dense Matter . 63 4.1.1 Mean Field Dynamics . 64 4.1.2 Effects Non-Linear in Density . 65 4.1.3 Coupled Channel Dynamics . 67 4.1.4 Kaons in Pion Matter . 73 4.1.5 Chiral Symmetry Restoration . 74 4.2 Strange Baryons . 75 2 4.2.1 QCD Sum Rules . 76 4.2.2 Hadronic Models . 76 4.2.3 Exotica . 76 5 Open Charm Probes 78 5.1 Perturbative Calculation of Charm-Quark Production near Threshold . 80 5.1.1 Resummation . 81 5.1.2 Charm-Quark Production in pp Collisions . 82 5.2 Charm-Quark Interactions in the QGP . 86 5.2.1 Energy Loss of Charm Quarks at High Momentum . 86 5.2.2 Charm Diffusion and Nonperturbative Correlations in the QGP . 88 5.2.3 Charm Dilepton Decays . 94 5.3 Charm Chemistry and Thermal Models . 95 5.4 QCD Sum Rules . 97 5.4.1 Open Charm Mesons . 97 5.4.2 Remarks on J= . 100 5.5 Charm Hadrons in Medium . 100 5.5.1 Cold Nuclear Matter . 100 5.5.2 Hot Pion Gas . 102 5.5.3 Hot and Dense Nuclear Matter . 103 5.5.4 Charm Baryons . 106 6 Charmonium 108 6.1 Charmonium in Equilibrium . 108 6.1.1 Color screening and quarkonium . 108 6.1.2 Free Energy of Static Quarks in Lattice QCD . 109 6.1.3 Spectral functions and Euclidean correlators . 111 6.1.4 Charmonium Spectral Functions and Potential Models . 112 6.2 Charm(onium) Production within the Statistical Hadronization Model . 113 6.2.1 Introduction . 113 6.2.2 Assumptions and ingredients of the statistical hadronization model . 114 6.2.3 Energy dependence of charmed hadrons yield . 117 6.2.4 Effects of in-medium modification of charmed hadrons masses . 118 6.2.5 Conclusions . 120 6.3 Charmonium Transport in Hot and Dense Medium . 121 6.3.1 Introduction . 121 6.3.2 Normal and Anomalous Suppression . 122 6.3.3 Regeneration . 127 6.3.4 Transverse-Momentum Distributions . 130 6.3.5 Charmonia in Heavy-Ion Collisions at Low Energies . 132 7 Excitations of Color-Superconducting Matter 135 7.1 Color Superconductivity in the QCD Phase Diagram . 135 7.2 Strong decays of mesonic resonances . 135 7.3 Pre-Critical Phenomena of Color Superconductivity . 138 8 Executive Summary and Relations to Observables 143 1 Chapter 1 Introduction The vacuum of strong interactions is of a rather complex nature giving rise to several funda- mental phenomena, most notably the confinement of quarks and the generation of (the major part of) hadronic masses. The nontrivial vacuum structure is associated with the formation of quark and gluon condensates, which are intimately related to the spontaneous breaking of chiral symmetry and the breaking of scale invariance of Quantum Chromodynamics (QCD). The condensates are, however, not directly observable, and therefore information has to be obtained from excitations of the ground state. At zero temperature and density, the physical excitations are colorless hadrons, whose spin and flavor structure provide a rich laboratory for spectroscopy. At sufficiently high temperature (T ) and/or baryon density, %B (or baryon chemical po- tential, µB), asymptotic freedom of QCD predicts the existence of new phases of matter, in particular the Quark-Gluon Plasma (QGP) at high T and the Color-Superconductor (CSC) at high µB and low T . It is expected that the bulk excitation of the QCD vacuum (thermal or density) induces a \melting" of the condensate structures, accompanied by the restoration of chiral symmetry and deconfinement of color charges. At finite temperature (and vanishing µB) this transition is fairly well established by lattice QCD (lQCD) computations, with a (pseudo-) critical temperature of T = 180 20 MeV. While this is presumably not a phase transition in c the strict sense, lQCD clearly reveals a rapid change in the thermodynamic properties of the system (most notably energy density) over a rather small interval in temperature. The prop- erties of the equation of state and their possible signals in heavy-ion reactions are discussed in detail in Parts [Bulk Properties] and [Observables] of this book. The phase transformation, in turn, implies dramatic changes in the underlying microscopic properties of the strongly interacting medium. Naively, this is realized by a conversion of the degrees of freedom, i.e., from hadrons to quarks and gluons, as roughly reflected in the (de- generacy) coefficient of the equation of state. However, this notion is far from providing an understanding of the mechanisms inducing deconfinement and chiral symmmetry restoration in the medium. More precisely, the microscopic matter properties are characterized by density and temperature dependent changes in hadronic spectral functions1. While medium modifications of hadrons in strongly interacting matter are an interesting and important subject in itself, connections to the underlying condensate structure(s) are essential to meet the challenge of conducting fundamental studies of the QCD phase diagram. Indeed, (approximate) chiral sym- metry alone predicts that (the spectral functions of) chiral partners (i.e. hadronic multiplets 1Note that the (gauge-invariant) concept of a hadronic spectral function is equally valid in the hadronic and QGP phases. 2 that transform into each other under chiral transformations) become (nearly) degenerate in the ∗ symmetric phase. The degeneracy of π and σ channels, ρ and a1, or N and N (1535), obviously implies major changes of the pertinent spectral functions toward the chiral transition. To detect such modifications in heavy-ion experiments, one needs access to the hot and dense phases of the fireball, leading to the notion of \penetrating probes". In general, the latter encompass elec- tromagnetic (photons and dileptons), heavy-quark and high transverse-momentum observables. In the present Part, we will focus on the former two due to their potential of characterizing the matter at relatively soft energy/momentum scales, T; Λ ; 4πf (f =92 MeV: pion decay ∼ QCD π π constant). The modes representing the prevalent degrees of freedom and encoding phase transi- tion properties are expected to operate at these scales. Our goal is to provide a comprehensive presentation of theoretical tools and approaches (with emphasis on recent developments) which are currently available to convert experimental data into meaningful information on spectral and phase-transition properties of QCD matter. The inherently non-perturbative nature of this problem renders a direct solution from first principles difficult. While lattice QCD is well suited to compute the equation of state, its formulation in euclidean space-time makes the evaluation of spectral functions much more de- manding. It is for this reason that effective hadronic (and quark) models are an indispensable tool to provide quantitative predictions that can be tested in experiment. No less important, hadronic models can serve as the main bridge between first principles and experiment, if the following program can be carried out: (a) The interaction Lagrangian is constructed based on essential symmetry principles (chiral, gauge).