The pressure of hot QCD has recently been determined to the last perturbatively computable order $g^6\ln g$ by Kajantie et al. using three-dimensional effective theories. A similar method is applied here to the pressure in the presence of small but non-vanishing quark chemical potentials, and the result is used to derive the quark number susceptibilities in the limit $\mu =0.\mathrm{}$ The diagonal quark number susceptibility of QCD with $n_f$ flavors of massless quarks is evaluated to order $g^6\ln g$ and compared with recent lattice simulations. It is observed that the results qualitatively resemble the lattice ones, and that when combined with the fully perturbative but yet undetermined $g^6$ term they may well explain the behavior of the lattice data for a wide range of temperatures.

• Received 23 December 2002

DOI:https://doi.org/10.1103/PhysRevD.67.074032