Estimation from quantized Gaussian measurements: when and how to use dither

Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/K^0.930 for the number of measurements K > 20, estimators we present are more efficient than the midrange.https://arxiv.org/abs/1811.06856Accepted manuscrip

Medium Modifications of the Rho Meson at CERN/SPS Energies

Rho meson propagation in hot hadronic matter is studied in a model with coupling to $\pi\pi$ states. Medium modifications are induced by a change of the pion dispersion relation through collisions with nucleons and $\Delta's$ in the fireball. Maintaining gauge invariance dilepton production is calculated and compared to the recent data of the CERES collaboration in central S+Au collisions at 200 GeV/u. The observed enhancement of the rate below the rho meson mass can be largely accounted for.Comment: 10 pages RevTeX and 2 figures (uuencoded .ps-files

Low-mass dielectrons from the PHENIX experiment at RHIC

The production of the low-mass dielectrons is considered to be a powerful tool to study the properties of the hot and dense matter created in the ultra-relativistic heavy-ion collisions. We present the preliminary results on the first measurements of the low-mass dielectron continuum in Au+Au collisions and the phi meson production measured in Au+Au and d+Au collisions at sqrt{s_NN} = 200 GeV performed by the PHENIX experiment.Comment: 6 pages, 12 figures, conference proceedings for QNP06 (5-10 June, 2006, Madrid

Photon production in relativistic nuclear collisions at SPS and RHIC energies

Chiral Lagrangians are used to compute the production rate of photons from the hadronic phase of relativistic nuclear collisions. Special attention is paid to the role of the pseudovector a_1 meson. Calculations that include reactions with strange mesons, hadronic form factors and vector spectral densities consistent with dilepton production, as well as the emission from a quark-gluon plasma and primordial nucleon-nucleon collisions, reproduce the photon spectra measured at the Super Proton Synchrotron (SPS). Predictions for the Relativistic Heavy Ion Collider (RHIC) are made.Comment: Work presented at the 26th annual Montreal-Rochester-Syracuse-Toronto conference (MRST 2004) on high energy physics, Montreal, QC, Canada, 12-14 May 2004. 8 pages, 3 figure

A chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole ('$\sigma$') channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $\mu_q\simeq 0.4$ GeV (or 4 times nuclear saturation density), we find the 'chiral crystal phase' to be competitive with the color superconductor.Comment: 14 pages ReVTeX, including 11 ps-/eps-figure

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

Chiral Disorder and QCD at Finite Chemical Potential

We investigate the effects of a finite chemical potential $\mu$ in QCD viewed as a disordered medium. In the quenched approximation, $A_4=i\mu$ induces a complex electric Aharonov-Bohm effect that causes the diagonal contribution to the quark return probability to vanish at $\mu=m_{\pi}/2$ (half the pion mass). In two-color QCD, the weak-localization contribution to the quark return probability remains unaffected causing a mutation in the spectral statistics. In full QCD, the complex electric flux is screened and the light quarks are shown to diffuse asymmetrically with a substantial decrease in the conductivity along the `spatial' directions. Mean-field arguments suggest that a d=1 percolation transition may take place in the range $1.5\rho_0<\rho<3\rho_0$, where $\rho_0$ is nuclear matter density.Comment: 4 page

Correlations of Heavy Quarks Produced at Large Hadron Collider

We study the correlations of heavy quarks produced in relativistic heavy ion collisions and find them to be quite sensitive to the effects of the medium and the production mechanisms. In order to put this on a quantitative footing, as a first step, we analyze the azimuthal, transverse momentum, and rapidity correlations of heavy quark-anti quark ($Q\overline{Q}$) pairs in $pp$ collisions at $\cal{O}$($\alpha_{s}^{3}$). This sets the stage for the identification and study of medium modification of similar correlations in relativistic collision of heavy nuclei at the Large Hadron Collider. Next we study the additional production of charm quarks in heavy ion collisions due to multiple scatterings, {\it viz.}, jet-jet collisions, jet-thermal collisions, and thermal interactions. We find that these give rise to azimuthal correlations which are quite different from those arising from prompt initial production at leading order and at next to leading order.Comment: 26 pages, 15 figures. Three new figures added, comparison to experimental data included, abstract and discussion expande