Method for comparing finite temperature field theory results with lattice data

The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one (${T}_{c}$), they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying two specific Pad\'e-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop $\overline{\mathrm{MS}}$ beta function for ${\ensuremath{\alpha}}_{s}$ by its Borel-Pad\'e resummation, thus eliminating the unphysical Landau singularities of ${\ensuremath{\alpha}}_{s}$. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results\char22{}for the pressure $p$, the chemical potential contribution $\ensuremath{\Delta}p$ to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to ${T}_{c}$.