Thermal Dilepton Rates Research Articles

Testing thermal photon and dilepton rates

We confront the thermal NLO vector spectral function (both the transverse and longitudinal channel with respect to spatial momentum, both above and below the light cone) with continuum-extrapolated lattice data (both quenched and with Nf = 2, at T ∼ 1.2Tc). The perturbative side incorporates new results, whose main features are summarized. The resolution of the lattice data is good enough to constrain the scale choice of αs on the perturbative side. The comparison supports the previous indication that the true spectral function falls below the resummed NLO one in a substantial frequency domain. Our results may help to scrutinize direct spectral reconstruction attempts from lattice QCD.

Thermal dilepton rates and electrical conductivity of the QGP from the lattice

We investigate the temperature dependence of the thermal dilepton rate and the electrical conductivity of the gluon plasma at temperatures of $1.1T_c$, $1.3T_c$ and $1.5T_c$ in quenched QCD. Making use of non-perturbatively clover-improved Wilson valence quarks allows for a clean extrapolation of the vector meson correlation function to the continuum limit. We found that the vector correlation function divided by $T^3$ is almost temperature independent in the current temperature window. The spectral functions are obtained by $\chi^2$ fitting of phenomenologically inspired Ans\"atze for the spectral function to the continuum extrapolated correlator data, where the correlations between the data points have been included. Systematic uncertainties arising from varying the Ans\"atze motivated from strong coupling theory as well as perturbation theory are discussed and estimated. We found that the electrical conductivity of the hot medium, related to the slope of the vector spectral function at zero frequency and momentum, is $0.2C_{em}\lesssim \sigma/T\lesssim0.7C_{em}$ for $T=1.1T_c$ and $0.2C_{em}\lesssim \sigma/T\lesssim0.4C_{em}$ for the higher temperatures. The dilepton rates and soft photon rates, resulting from the obtained spectral functions, show no significant temperature dependence, either.

The thermal dilepton rate at NLO at small and large invariant mass

We report on a recent next-to-leading order perturbative determination of the dilepton rate from a hot QCD plasma for frequency and momentum of the order of the temperature and for much smaller invariant mass M∼gT. We briefly review the calculation, which generalizes the previous one for the photon case (M=0). We then analyze the consequences of the new calculation for the extraction of the photon rate from the small mass dilepton measurements. We then review a recent NLO determination at large M and we show how to match and merge its results with the low-mass ones, resulting in a single rate which is NLO-accurate over the phenomenologically relevant region.

Coarse-graining approach for dilepton production at energies available at the CERN Super Proton Synchrotron

Coarse-grained output from transport calculations is used to determine thermal dilepton emission rates by applying medium-modified spectral functions from thermal quantum field theoretical models. By averaging over an ensemble of events generated with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, we extract the local thermodynamic properties at each time step of the calculation. With an equation of state the temperature $T$ and chemical potential ${\ensuremath{\mu}}_{\mathrm{B}}$ can be determined. The approach goes beyond simplified fireball models of the bulk-medium evolution by treating the full (3+1)-dimensional expansion of the system with realistic time and density profiles. For the calculation of thermal dilepton rates we use the in-medium spectral function of the $\ensuremath{\rho}$ meson developed by Rapp and Wambach and consider thermal quark-gluon plasma (QGP) and multipion contributions as well. The approach is applied to the evaluation of dimuon production in In+In collisions at top CERN Super Proton Synchrotron (SPS) energy. Comparison to the experimental results of the NA60 experiment shows good agreement of this ansatz. We find that the experimentally observed low-mass dilepton excess in the mass region from 0.2 to 0.6 GeV can be explained by a broadening of the $\ensuremath{\rho}$ spectral function with a small mass shift. In contrast, the intermediate-mass region $(M>1.5$ GeV) is dominated by a contribution from the quark-gluon plasma. These findings agree with previous calculations with fireball parametrizations. This agreement, in spite of differences in the reaction dynamics between both approaches, indicates that the time-integrated dilepton spectra are not very sensitive to details of the space-time evolution of the collision.

Prospects for dilepton rates from lattice QCD

We discuss the prospects of computing thermal dilepton rates from first principles lattice QCD. The focus lies in the determination of the meson vector-vector current spectral function to estimate the electrical conductivity, heavy quark diffusion and quarkonium dissociation. We review and compare recent results from continuum-extrapolated, quenched calculations, as well as dynamical two-flavor setups.

In-medium hadron properties from lattice QCD

I review recent results from lattice QCD calculations on the in-medium hadron properties. I discuss the thermal dilepton rates, heavy quarkonium properties as well as the chiral and $U(1)_A$ symmetries at finite temperature.

Electrical conductivity and thermal dilepton rate from quenched lattice QCD

We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cutoff effects on light quark meson correlators at T ≃ 1.45 Tc using clover improved Wilson fermions (Ding et al 2011 Phys. Rev. D 83 034504). We discuss resulting constraints on the electrical conductivity and the thermal dilepton rate in a quark–gluon plasma. In addition, new results at 1.2 and 3.0 Tc will be presented.

Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD

We calculate the vector current correlation function for light valence quarks in the deconfined phase of QCD. The calculations have been performed in quenched lattice QCD at $T\ensuremath{\simeq}1.45{T}_{c}$ for four values of the lattice cutoff on lattices up to size ${128}^{3}\ifmmode\times\else\texttimes\fi{}48$. This allows us to perform a continuum extrapolation of the correlation function in the Euclidean time interval $0.2\ensuremath{\le}\ensuremath{\tau}T\ensuremath{\le}0.5$, which extends to the largest temporal separations possible at finite temperature, to better than 1% accuracy. In this interval, at the value of the temperature investigated, we find that the vector correlation function never deviates from the free correlator for massless quarks by more than 9%. We also determine the first two nonvanishing thermal moments of the vector meson spectral function. The second thermal moment deviates by less than 7% from the free value. With these constraints, we then proceed to extract information on the spectral representation of the vector correlator and discuss resulting consequences for the electrical conductivity and the thermal dilepton rate in the plasma phase.

Comprehensive Interpretation of Thermal Dileptons Measured at the CERN Super Proton Synchrotron

Employing thermal dilepton rates based on a medium-modified electromagnetic correlation function we show that recent dimuon spectra of the NA60 Collaboration in central In-In collisions at the CERN-SPS can be understood in terms of radiation from a hot and dense hadronic medium. Earlier calculated in-medium rho-meson spectral functions provide an accurate description of the data up to dimuon invariant masses of about M approximately or equal to 0.9 GeV, with good sensitivity to the predicted rho-meson line shape, identifying baryon-induced modifications as the prevalent ones. A reliable evaluation of the contribution enables the study of further medium effects: at masses M>0.9 GeV, 4-pion type annihilation accounts for the experimentally observed excess (possibly augmented by effects of "chiral mixing"), while predictions for thermal emission from in-medium omega and phi mesons may be tested in the future.

Hadron correlators, spectral functions and thermal dilepton rates from lattice QCD

We discuss information on thermal modifications of hadron properties which can be extracted from the structure of Euclidean correlation functions of hadronic currents as well as more direct information obtained through the reconstruction of the spectral functions based on the Maximum Entropy Method.

A lattice calculation of thermal dilepton rates

Using clover improved Wilson fermions we calculate thermal vector meson correlation functions above the deconfinement phase transition of quenched QCD. At temperatures 1.5 Tc and 3Tc they are found to differ by less than 15% from that of a freely propagating quark anti-quark pair. This puts severe constraints on the dilepton production rate and in particular rules out a strong divergence of the dilepton rate at low energies. The vector spectral function, which has been reconstructed using the Maximum Entropy Method, yields an enhancement of the dilepton rate over the Born rate of at most a factor two in the energy interval 4 < E/T < 8 and suggests that the spectrum is cut-off at low energies by a thermal mass threshold of about (2-3)T.

Cancellation of infrared and mass singularities in the thermal di-lepton rate

We give a rigorous proof that, at first order in α s, the thermal di-lepton rate is free of infrared and mass singularities. The calculation is performed for massive quarks in the real-time formalism with the n-dimensional regularization scheme. The cancellation is shown to occur within each topology.