Abstract
We present a simple version of hadron-quark hybrid (HQH) model in the $\mu_B$--$T$ plain, where $T$ is temperature and $\mu_{B}$ is the baryon-number chemical potential. The model is composed of the independent-quark model for quark-gluon states and an improved version of excluded-volume hadron resonance gas (EV-HRG) model for hadronic states. In the improved version of EV-HRG, the pressure has charge conjugation and is obtained by a simple analytic form. The switching function from hadron states to quark-gluon states in the present model has no chemical potential dependence. The simple HQH model is successful in reproducing LQCD results on the transition region of chiral crossover and the EoS in $\mu_{B} \leq 400$ MeV. We then predict the chiral-crossover region in $400 \leq \mu_{B} \leq 800$ MeV. We also predict a transition line derived from isentropic trajectories in $0 \leq \mu_{B} \leq 800$ MeV and find that the effect of strangeness neutrality is small there.
Highlights
We present a simple version of hadron-quark hybrid (HQH) model in the μB-T plain, where T is temperature and μB is the baryon-number chemical potential
We find that the fitting of fHðTÞ is good, since the simple HQH (sHQH) result agrees with lattice QCD (LQCD) data [7]
As an interesting result of LQCD simulations for μB 1⁄4 0 [5], the chiral-crossover region determined from dΔl;s=dT agrees with the region from dεðT; μBÞ=dT
Summary
The state-of-art 2 þ 1-flavor lattice QCD (LQCD) simulation of Ref. [1] showed that the transition is “crossover”. The crossover nature means that the transition temperature depends on the choice of observables. Observable-dependent transition temperatures TðcOÞðμBÞ have been discussed in LQCD simulations for zero and small μB; the renormalized chiral condensate O 1⁄4 Δl;sðT; μBÞ, the Polykov loop O 1⁄4 ΦðT; μBÞ, the energy density O 1⁄4 εðT; μBÞ, and the trace anomaly O 1⁄4 IðT; μBÞ are taken in Refs. The location of transition region is essential to determine EoS. For these reasons, a lot of LQCD data have been accumulated [1,2,3,4,5,6,7,8,9,10,11,12,13]
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