Quark number susceptibilities at high temperatures

We calculate second and fourth order quark number susceptibilities for $2+1$ flavor QCD in the high temperature region. In our study, we use two improved staggered fermion formulations, namely, the highly improved staggered quark formulation and the so-called p4 formulation, as well as several lattice spacings. Second order quark number susceptibilities are calculated using both improved staggered fermion formulations, and we show that in the continuum limit the two formulations give consistent results. The fourth order quark number susceptibilities are studied only using the p4 formulation and at nonzero lattice spacings. We compare our results on quark number susceptibilities with recent weak coupling calculations and find that these agree reasonably well with the lattice calculations within the estimated uncertainties.