# Method for comparing finite temperature field theory results with lattice data

## Abstract

The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one (T{sub c}), they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying two specific Pade-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop MS beta function for {alpha}{sub s} by its Borel-Pade resummation, thus eliminating the unphysical Landau singularities of {alpha}{sub s}. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results--for the pressure p, the chemical potential contribution {delta}p to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to T{sub c}.

- Authors:

- Center of Subatomic Studies and Department of Physics, Universidad Tecnica Federico Santa Maria, Valparaiso (Chile)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 21020063

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevD.75.054016; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; LATTICE FIELD THEORY; PADE APPROXIMATION; PERTURBATION THEORY; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARK MATTER; RENORMALIZATION; SINGULARITY

### Citation Formats

```
Cvetic, G., Koegerler, R., and Department of Physics, Universitaet Bielefeld, 33501 Bielefeld.
```*Method for comparing finite temperature field theory results with lattice data*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.054016.

```
Cvetic, G., Koegerler, R., & Department of Physics, Universitaet Bielefeld, 33501 Bielefeld.
```*Method for comparing finite temperature field theory results with lattice data*. United States. doi:10.1103/PHYSREVD.75.054016.

```
Cvetic, G., Koegerler, R., and Department of Physics, Universitaet Bielefeld, 33501 Bielefeld. Thu .
"Method for comparing finite temperature field theory results with lattice data". United States.
doi:10.1103/PHYSREVD.75.054016.
```

```
@article{osti_21020063,
```

title = {Method for comparing finite temperature field theory results with lattice data},

author = {Cvetic, G. and Koegerler, R. and Department of Physics, Universitaet Bielefeld, 33501 Bielefeld},

abstractNote = {The values of the presently available truncated perturbative expressions for the pressure of the quark-gluon plasma at finite temperatures and finite chemical potential are trustworthy only at very large energies. When used down to temperatures close to the critical one (T{sub c}), they suffer from large uncertainties due to the renormalization scale freedom. In order to reduce these uncertainties, we perform resummations of the pressure by applying two specific Pade-related approximants to the available perturbation series for the short-distance and for the long-distance contributions. In the two contributions, we use two different renormalization scales which reflect different energy regions contributing to the different parts. Application of the obtained expressions at low temperatures is made possible by replacing the usual four-loop MS beta function for {alpha}{sub s} by its Borel-Pade resummation, thus eliminating the unphysical Landau singularities of {alpha}{sub s}. The obtained results are remarkably insensitive to the chosen renormalization scale and can be compared with lattice results--for the pressure p, the chemical potential contribution {delta}p to the pressure, and various susceptibilities. A good qualitative agreement with the lattice results is revealed down to temperatures close to T{sub c}.},

doi = {10.1103/PHYSREVD.75.054016},

journal = {Physical Review. D, Particles Fields},

number = 5,

volume = 75,

place = {United States},

year = {Thu Mar 01 00:00:00 EST 2007},

month = {Thu Mar 01 00:00:00 EST 2007}

}