Is Rho-Meson Melting Compatible with Chiral Restoration?

Utilizing in-medium vector spectral functions which describe dilepton data in ultra-relativistic heavy-ion collisions, we conduct a comprehensive evaluation of QCD and Weinberg sum rules at finite temperature. The starting point is our recent study in vacuum, where the sum rules have been quantitatively satisfied using phenomenological axial-/vector spectral functions which describe hadronic tau-decay data. In the medium, the temperature dependence of condensates and chiral order parameters is taken from thermal lattice QCD where available, and otherwise estimated from a hadron resonance gas. Since little is known about the in-medium axial-vector spectral function, we model it with a Breit-Wigner ansatz allowing for smooth temperature variations of its width and mass parameters. Our study thus amounts to testing the compatibility of the $\rho$-broadening found in dilepton experiments with (the approach toward) chiral restoration, and thereby searching for viable in-medium axial-vector spectral functions.Comment: 8 pages, 4 figures, updated to be consistent with published versio

Quantitative sum rule analysis of low-temperature spectral functions

We analyze QCD and Weinberg-type sum rules in a low-temperature pion gas using vector and axial-vector spectral functions following from the model-independent chiral-mixing scheme. Toward this end we employ recently constructed vacuum spectral functions with ground and first-excited states in both channels and a universal perturbative continuum; they quantitatively describe hadronic tau-decay data and satisfy vacuum sum rules. These features facilitate the implementation of chiral mixing without further assumptions, and lead to in-medium spectral functions which exhibit a mutual tendency of compensating resonance and dip structures, suggestive for an approach toward structureless distributions. In the sum rule analysis, we account for pion mass corrections, which turn out to be significant. While the Weinberg sum rules remain satisfied even at high temperatures, the numerical evaluation of the QCD sum rules for vector and axial-vector channels reveals significant deviations setting in for temperatures beyond ~140 MeV, suggestive of additional physics beyond low-energy chiral pion dynamics.Comment: 8 pages, 3 figure

Thermal Dileptons from Coarse-Grained Transport as Fireball Probes at SIS Energies

Utilizing a coarse-graining method to convert hadronic transport simulations of Au+Au collisions at SIS energies into local temperature, baryon and pion densities, we compute the pertinent radiation of thermal dileptons based on an in-medium $\rho$ spectral function that describes available spectra at ultrarelativistic collision energies. In particular, we analyze how far the resulting yields and slopes of the invariant-mass spectra can probe the lifetime and temperatures of the fireball. We find that dilepton radiation sets in after the initial overlap phase of the colliding nuclei of about 7 fm/c, and lasts for about 13 fm/c. This duration closely coincides with the development of the transverse collectivity of the baryons, thus establishing a direct correlation between hadronic collective effects and thermal EM radiation, and supporting a near local equilibration of the system. This fireball "lifetime" is substantially smaller than the typical 20-30 fm/c that naive considerations of the density evolution alone would suggest. We furthermore find that the total dilepton yield radiated into the invariant-mass window of $M=0.3-0.7$ GeV/$c^{2}$, normalized to the number of charged pions, follows a relation to the lifetime found earlier in the (ultra-) relativistic regime of heavy-ion collisions, and thus corroborates the versatility of this tool. The spectral slopes of the invariant-mass spectra above the $\phi$ mass provide a thermometer of the hottest phases of the collision, and agree well with the maximal temperatures extracted from the coarse-grained hadron spectra.Comment: 9 pages, 6 figures; v2: extended discussion, matches the version accepted for publicatio

Universal Parametrization of Thermal Photon Rates in Hadronic Matter

Electromagnetic (EM) radiation off strongly interacting matter created in high-energy heavy-ion collisions (HICs) encodes information on the high-temperature phases of nuclear matter. Microscopic calculations of thermal EM emission rates are usually rather involved and not readily accessible to broad applications in models of the fireball evolution which are required to compare to experimental data. An accurate and universal parametrization of the microscopic calculations is thus key to honing the theory behind the EM spectra. Here we provide such a parametrization for photon emission rates from hadronic matter, including the contributions from in-medium rho mesons (which incorporate effects from anti-/baryons), as well as Bremsstrahlung from pi-pi scattering. Individual parametrizations for each contribution are numerically determined through nested fitting functions for photon energies from 0.2 to 5 GeV in chemically equilibrated matter of temperatures 100-180 MeV and baryon chemical potentials 0-400 MeV. Special care is taken to extent the parameterizations to chemical off-equilibrium as encountered in HICs after chemical freezeout. This provides a functional description of thermal photon rates within a 20% variation of the microscopically calculated values.Comment: 4 pages, 3 figures; to be submitted to PRC brief report

Evaluating chiral symmetry restoration through the use of sum rules

We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector and axial-vector channels. We first present an update on constructing quantitative results for pertinent vacuum spectral functions. These spectral functions serve as a basis upon which the in-medium spectral functions can be constructed. A striking feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels. Preliminary results for the finite temperature vector spectral function are presented. Based on a rho spectral function tested in dilepton data which develops a shoulder at low energies, we find that the rho' peak flattens off. The flattening may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.Comment: 9 pages, conference proceedings from Resonance Workshop at UT Austin, March 5-7 201

Universal parametrization of thermal photon rates in hadronic matter

Electromagnetic (EM) radiation off strongly interacting matter created in high-energy heavy-ion collisions (HICs) encodes information on the high-temperature phases of nuclear matter. Microscopic calculations of thermal EM emission rates are usually rather involved and not readily accessible to broad applications in models of the fireball evolution which are required to compare with experimental data. An accurate and universal parametrization of the microscopic calculations is thus key to honing the theory behind the EM spectra. Here we provide such a parametrization for photon emission rates from hadronic matter, including the contributions from in-medium rho mesons (which incorporate effects from baryons and antibaryons), as well as bremsstrahlung from pi pi scattering. Individual parametrizations for each contribution are numerically determined through nested fitting functions for photon energies from 0.2 to 5 GeV in chemically equilibrated matter of temperatures 100-180 MeV and baryon chemical potentials 0-400 MeV. Special care is taken to extent the parametrizations to chemical off-equilibrium as encountered in HICs after chemical freeze-out. This provides a functional description of thermal photon rates within a 20% variation of the microscopically calculated values