The files below contain data for the vector channel spectral function and the corresponding imaginary-time correlator. In each case two variants are given: a 'vacuum' result which is accurate in the UV domain but represents otherwise an underestimate; and a 'thermal' result which represents our current best estimate from perturbation theory but may still suffer from significant uncertainties. Spatial momentum is denoted by k and frequency by ω.
For vanishing spatial momentum we provide the spectral function ρii and the corresponding imaginary-time correlator Gii. Four temperatures are considered: T = 1.1Tc, 1.2Tc, 1.3Tc, and 1.4Tc. We first consider Tc = 1.25 ΛMS and Nf = 0. The gauge coupling has been evolved with 3-loop running, but we have checked that changes from 4-loop running are small.
As already mentioned, two sets of data are shown. The files (mis)labelled 'vacuum' refer to the LO thermal expression, multiplied by the N4LO correction known for the vacuum spectral function at large ω; the detailed procedure is explained in 1201.1994. This spectral function displays the correct asymptotics at ω >> 3T, but has no transport peak. The corresponding imaginary-time correlator shows a correct behaviour at τ << 0.2/T.
In the second data set, with files labelled 'thermal', the intermediate (ω ~ 3T) and small-frequency domains (ω << T) have been corrected through thermal NLO results extracted from a study by Altherr and Aurenche, as well as a treatment of the infrared regime according to Moore and Robert. There is however an intermediate regime, at around ω ~ T, where no fully consistent computation exists and the result may thus contain a larger uncertainty than elsewhere. In the current data we switch from one regime to another when the curves resulting from the two treatments cross each other, introducing a cusp in a region where the computation is not fully consistent.
The file names indicate rhoT2 (for ρii/T2) or GiiT3 (for Gii/T3); the momentum; T in units of Tc; and whether a 'vacuum' or 'thermal' spectral function has been considered. The columns are specified on the first lines of the files. For the 'vacuum' set we also give the vector correlator GV= Gii - G00 in which a constant mode gets subtracted.
Apart from the quenched results, we also provide data for Nf = 3. In this case we have set Tc = 0.45 ΛMS. The coupling tends to be larger than in the quenched case, so temperatures slightly deeper in the deconfined phase were considered:
For those wishing to test their analytic continuation algorithm, we have prepared mock data corresponding to Nf = 3. These are based on semi-realistic spectral functions at temperatures (1-2)Tc, corresponding to a finite spatial lattice spacing as ~ 0.1fm. Uncorrelated statistical errors (0.5%) and some uncertainty related to the overall renormalization factors have been inserted. The corresponding input spectral functions can be obtained from ML upon request.
The non-zero momenta that can be studied on the lattice are of the form k/T = 2 π (Nτ/Ns) n, where Nτ and Ns are the temporal and spatial extents of the lattice, respectively. If the momenta are taken along one of the axis directions, which guarantees the absence of large discretization effects, then n is an integer.
In some of the existing simulations (cf. 1412.5869), each temperature (T = 1.1Tc, 1.2Tc, 1.3Tc, and 1.4Tc) had a different 'aspect ratio' Ns/Nτ, respectively of 3, 24/7, 24/7, and 4. These are the cases considered below.
Our results concern the full vector spectral function ρV = ρii - ρ00, and the full vector imaginary-time correlator GV. As before, we have assumed Tc = 1.25 ΛMS and Nf = 0, but data for other parameter values can be obtained from the authors upon request.
The 'vacuum' sets refer to the procedure explained in section 5.2 of 1310.0164 which corresponds to the free thermal result multiplied by the N4LO vacuum R-ratio. The 'thermal' data are based on ref. 1410.4203 for ω < 10T and on ref. 1407.7955 for ω > 10T. They go over into the 'vacuum' results at somewhat higher frequencies. For the vacuum part, we also give the 'longitudinal' (G11) and 'transverse' (G2233) correlators (with the direction of k chosen as the x-axis), in accordance with fig. 4 of 1310.0164 .
For T = 1.1Tc, the momenta studied in 1412.5869 were k/T = 2 π (1/3) n, where n=1,2,3.
For T = 1.2Tc, the momenta studied in 1412.5869 were k/T = 2 π (7/24) n, where n=1,2,3.
Given possible uncertainties in the temperature assignment, we also give results for T = 1.3Tc for the same momenta as at T = 1.2Tc.
For T = 1.4Tc, the momenta studied in 1412.5869 were k/T = 2 π (1/4) n, where n=1,2,3.