# Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log

## Abstract

We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: $$eB{\sim}{g}^{4}\mathrm{log}(1/g){T}^{2}$$. We work in the assumption that the magnetic field is homogeneous and static, and the electrodynamics is nondynamical in a formal limit $$e{\rightarrow}0$$ while $eB$ is kept fixed. We show that the shear viscosity takes a form $${\eta}=\overline{{\eta}}(\overline{B}){T}^{3}/({g}^{4}\mathrm{log}(1/g))$$ with a dimensionless function $$\overline{{\eta}}(\overline{B})$$ in terms of a dimensionless variable $$\overline{B}=(eB)/({g}^{4}\mathrm{log}(1/g){T}^{2})$$. The variable $$\overline{B}$$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $$\overline{B}{\sim}{l}_{\mathrm{mfp}}/{l}_{\text{cyclo}}$$. We provide a full numerical result for the scaled shear viscosity $$\overline{{\eta}}(\overline{B})$$.

- Authors:

- Univ. of Illinois, Chicago, IL (United States). Dept. of Physics
- Univ. of Illinois, Chicago, IL (United States). Dept. of Physics; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN-BNL Research Center

- Publication Date:

- Research Org.:
- Univ. of Illinois, Chicago, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1430145

- Alternate Identifier(s):
- OSTI ID: 1503833

- Grant/Contract Number:
- SC0018209

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; perturbative QCD; quark-gluon plasma

### Citation Formats

```
Li, Shiyong, and Yee, Ho-Ung. Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log. United States: N. p., 2018.
Web. doi:10.1103/physrevd.97.056024.
```

```
Li, Shiyong, & Yee, Ho-Ung. Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log. United States. doi:10.1103/physrevd.97.056024.
```

```
Li, Shiyong, and Yee, Ho-Ung. Wed .
"Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log". United States. doi:10.1103/physrevd.97.056024.
```

```
@article{osti_1430145,
```

title = {Shear viscosity of the quark-gluon plasma in a weak magnetic field in perturbative QCD: Leading log},

author = {Li, Shiyong and Yee, Ho-Ung},

abstractNote = {We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: $eB{\sim}{g}^{4}\mathrm{log}(1/g){T}^{2}$. We work in the assumption that the magnetic field is homogeneous and static, and the electrodynamics is nondynamical in a formal limit $e{\rightarrow}0$ while $eB$ is kept fixed. We show that the shear viscosity takes a form ${\eta}=\overline{{\eta}}(\overline{B}){T}^{3}/({g}^{4}\mathrm{log}(1/g))$ with a dimensionless function $\overline{{\eta}}(\overline{B})$ in terms of a dimensionless variable $\overline{B}=(eB)/({g}^{4}\mathrm{log}(1/g){T}^{2})$. The variable $\overline{B}$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $\overline{B}{\sim}{l}_{\mathrm{mfp}}/{l}_{\text{cyclo}}$. We provide a full numerical result for the scaled shear viscosity $\overline{{\eta}}(\overline{B})$.},

doi = {10.1103/physrevd.97.056024},

journal = {Physical Review D},

number = 5,

volume = 97,

place = {United States},

year = {2018},

month = {3}

}

DOI: 10.1103/physrevd.97.056024

*Citation information provided by*

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