# The QCD Equation of state and critical end-point estimates at $\mathcal{O}\left({\mu}_{B}^{6}\right)$

## Abstract

Here, we present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μ _{Β}, which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μ _{Β} plane of the QCD phase diagram.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1478422

- Grant/Contract Number:
- [SC001270]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Nuclear Physics. A

- Additional Journal Information:
- [ Journal Volume: 967; Journal Issue: C]; Journal ID: ISSN 0375-9474

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Finite temperature and density Quantum Chromodynamics; Quark-gluon plasma; critical point

### Citation Formats

```
Sharma, Sayantan. The QCD Equation of state and critical end-point estimates at O(μB6). United States: N. p., 2017.
Web. doi:10.1016/j.nuclphysa.2017.05.008.
```

```
Sharma, Sayantan. The QCD Equation of state and critical end-point estimates at O(μB6). United States. doi:10.1016/j.nuclphysa.2017.05.008.
```

```
Sharma, Sayantan. Mon .
"The QCD Equation of state and critical end-point estimates at O(μB6)". United States. doi:10.1016/j.nuclphysa.2017.05.008. https://www.osti.gov/servlets/purl/1478422.
```

```
@article{osti_1478422,
```

title = {The QCD Equation of state and critical end-point estimates at O(μB6)},

author = {Sharma, Sayantan},

abstractNote = {Here, we present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μΒ, which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μΒ plane of the QCD phase diagram.},

doi = {10.1016/j.nuclphysa.2017.05.008},

journal = {Nuclear Physics. A},

number = [C],

volume = [967],

place = {United States},

year = {2017},

month = {9}

}

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