Data for QCD and electroweak equations of state (2006)

Mikko Laine and York Schröder

The files below contain data shown in figs. 3,4 of hep-ph/0603048, with minor updates as discussed below.

General comments

We normally used the data by loading it into memory and then calling some interpolating routine (e.g. spline) for the temperature needed. This allows to be prepared for future improvements that will come from lattice simulations, particularly in the 'grey zones' of our figures.

If the data is inspected very carefully, a small difference with respect to the plots in the paper can be noticed. The reason is that there was a minor bug in the program at the time of producing those figures.

Electroweak sector

Now that the Higgs mass is known, it is possible to significantly reduce the uncertainties in the grey zone corresponding to electroweak crossover (such results have more recently been added here). The current file refers to mH = 150 GeV, however it should be noted that the error from the Higgs mass is smaller than the theoretical uncertainty from higher-order radiative corrections (probably several percent).

A peculiar qualitative feature may be noticed above the electroweak crossover: the number of effective degrees of freedom appears to decrease slightly with increasing temperature. The reason is probably related to the Higgs field: it is essentially massless around the crossover but then again massive at higher T due to thermal mass corrections, so there is an intermediate range in which its effective mass increases and its influence might decrease. (However the effect is so small that it's certainly below theoretical errors from higher-order radiative corrections.)

In the cosmological context, the treatment of the regime T < 2 MeV requires care, as neutrinos fall out of thermal equilibrium. This issue has been rectified in the updated data set available here.

Notation

The file names indicate whether the QCD part (fig.3) or the full Standard Model (fig.4) is shown. The file qcd_widerange.dat has the same parameters as qcd_Nf4.dat but a wider temperature range (the same as in standardmodel.dat). The columns of the files are:

1: T / MeV
2: p / T^4
3: e / T^4
4: s / T^3
5: c / T^3
6: w = p / e
7: c_s^2 = s / c
8: g_eff
9: h_eff
10: i_eff

Here are the files: