The QCD equation of state at nonzero densities: lattice result

Abstract

In this letter we give the equation of state of QCD at finite temperatures and densities. The recently proposed overlap improving multi-parameter reweighting technique is used to determine observables at nonvanishing chemical potentials. Our results are obtained by studying n_f=2+1 dynamical staggered quarks with semi-realistic masses on N_t=4 lattices.

Figures (6)

• Figure 1: The best weight lines on the $\mu$--$\beta$ plane, along which reweighting is performed. In the middle we indicate the transition line. Its first dotted part is the crossover region. The blob represents the critical endpoint, after which the transition is of first order. Below the transition line the system is in the hadronic phase, above the transition line we find the QGP. The integration paths used to calculate the pressure are shown by the arrows along the $\mu=0$ axis and the best weight lines.
• Figure 2: The pressure normalised by $T^4$ as a function of $T/T_c$ at $\mu=0$ (to help the continuum interpretation the raw lattice result is multiplied with $c_p$). The continuum SB limit is also shown.
• Figure 3: $\Delta p=p(\mu\neq 0,T)-p(\mu=0,T)$ normalised by $T^4$ as a function of $T/T_c$ for $\mu_B$=100,210,330,410 MeV and $\mu_B$=530 MeV (from top to bottom; to help the continuum interpretation the raw lattice result is multiplied with $c_\mu$).
• Figure 4: $\Delta p$ of the interacting QCD plasma normalised by $\Delta p$ of the free gas (SB) as a function of $T/T_c$ for $\mu_B$=100,210,330,410 MeV and $\mu_B$=530 MeV. The result is essentially $\mu$-independent.
• Figure 5: $(\epsilon-3p)/T^4$ at $\mu_B$=0,210,410 MeV and $\mu_B$=530 MeV as a function of $T/T_c$ (from bottom to top; to help the continuum interpretation the raw lattice result is multiplied with $c_p$)