# Crossover-model approach to QCD phase diagram, equation of state and susceptibilities in the 2+1 and 2+1+1 flavor systems

## TL;DR

This paper develops a crossover model for QCD that successfully reproduces lattice QCD data on the equation of state and susceptibilities, and maps the phase diagram for 2+1 and 2+1+1 flavor systems, highlighting flavor independence and transition temperatures.

## Contribution

A simple crossover model based on lattice QCD data that accurately describes the QCD phase diagram and susceptibilities for multiple flavor systems.

## Key findings

- The model reproduces lattice QCD data on EoS and susceptibilities.
- Transition lines are nearly identical in certain chemical potential planes.
- C quark does not influence the 2+1 flavor subsystem.

## Abstract

We construct a simple model for describing the hadron-quark crossover transition by using lattice QCD (LQCD) data in the 2+1 flavor system, and draw the phase diagram in the 2+1 and 2+1+1 flavor systems through analyses of the equation of state (EoS) and the susceptibilities. In the present hadron-quark crossover (HQC) model is successful in reproducing LQCD data on the EoS and the flavor susceptibilities.We define the hadron-quark transition temperature. For the 2+1 flavor system, the transition line thus obtained is almost identical in planes that are created by temperature and the chemical potential for the baryon-number(B), the isospin(I), the hypercharge(Y), when the chemical potentials are smaller than 250 MeV. This BIY approximate equivalence persists also in the 2+1+1 flavor system. We plot the phase diagram also in planes that are created by temperature and the chemical potential for u,d,s quark number in order to investigate flavor dependence of transition lines. In the 2+1+1 flavor system, c quark does not affect the 2+1 flavor subsystem composed of u, d, s. The flavor off-diagonal susceptibilities are good indicators to see how hadrons survive as T increases, since the independent quark model hardly contributes to them.