ar X iv : h ep - l at / 0 20 90 12 v 1 2 S ep 2 00 2 1 The QCD phase transition at high temperature and low density ∗

We study the thermal properties of QCD in the presence of a small quark chemical potential µ. Derivatives of the phase transition point with respect to µ are computed at µ = 0 for 2 and 3 flavors of p-4 improved staggered fermions on a 16 3 ×4 lattice. Moreover we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of µ = 0 on the equation of state, and comment on the screening effect by dynamical quarks and the complex phase of the fermion determinant in QCD with µ = 0. To understand recent heavy-ion collision experiments , theoretical study of the QCD phase transition at high temperature and low density is important. For instance, the interesting regime for RIHC is µ q /T c ∼ 0.1, where µ q = µ/a is a quark chemical potential. However, the Monte-Carlo method is not directly applicable for simulations at µ = 0, which makes the study of finite-density QCD difficult; hence we usually use the reweight-ing method. Using the identity O (β,µ) = OW (β0,0) / W (β0,0) , (1) W = e N f (ln det M(µ)−ln det M(0)) e −Sg(β)+Sg(β0) , the expectation value O at µ = 0 is computed by a simulation at µ = 0. Here M is the fermion matrix, S g the gauge action, and N f the number of flavors. Then, there exists a famous " sign problem ". Because det M is complex at µ = 0, if the complex phase fluctuates rapidly, both numerator and denominator in RHS of eqn.(1) become vanishingly small. For the case of small µ, the complex phase can be written by the odd terms of the Taylor expansion of ln det M [1].