Quark Number Susceptibility, Thermodynamic Sum Rule, and Hard Thermal Loop Approximation

The quark number susceptibility, associated with the conserved quark number density, is closely related to the baryon and charge fluctuations in the quark-gluon plasma, which might serve as signature for the quark-gluon plasma formation in ultrarelativistic heavy-ion collisions. Beside QCD lattice simulations, the quark number susceptibility has been calculated recently using a resummed perturbation theory (Hard Thermal Loop resummation). In the present work we show, based on general arguments, that the computation of this quantity neglecting Hard Thermal Loop vertices contradicts the Ward identity and violates the thermodynamic sum rule following from the quark number conservation. We further show that the Hard Thermal Loop perturbation theory is consistent with the thermodynamic sum rule.