#
Low-Shear QCD Plasma from Perturbation Theory^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## Acknowledgments

## References

- Aamodt, K.; Quintana, A.A.; Adamova, D.; Adare, A.M.; Aggarwal, M.M.; Rinella, G.A.; Agocs, A.G.; Agostinelli, A.; Salazar, S.A.; Ahammed, Z.; et al. Rapidity and transverse momentum dependence of inclusive J/ψ production in pp collisions at $\sqrt{s}$ = 7 TeV. Phys. Lett. B
**2011**, 704, 442, Adare, A.; Afanasiev, S.; Aidala, C.; Ajitanand, N.N.; Akiba, Y.; Al-Bataineh, H.; Alexander, J.; Al-Jamel, A.; Aoki, K.; Aphecetche, L.; et al. Heavy Quark Production in p + p and Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at $\sqrt{{s}_{\mathrm{NN}}}$ = 200 GeV. Phys. Rev. C**2011**, 84, 044905. [Google Scholar] [CrossRef] - Kovtun, P.; Son, D.T.; Starinets, A.O. Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett.
**2005**, 94, 111601. [Google Scholar] [CrossRef] - Meyer, H.B. A Calculation of the bulk viscosity in SU(3) gluodynamics. Phys. Rev. Lett.
**2008**, 100, 162001, Transport properties of the quark-gluon plasma from lattice QCD. Nucl. Phys. A**2009**, 830, 641C; Mages, S.W.; Borsányi, S.; Fodor, Z.; Schäfer, A.; Szabó, K. Shear Viscosity from Lattice QCD. PoS LATTICE**2015**, 2014, 232; Astrakhantsev, N.; Braguta, V.; Kotov, A. Temperature dependence of shear viscosity of SU(3)–gluodynamics within lattice simulation. JHEP**2017**, 1704, 101. [Google Scholar] [CrossRef] [PubMed] - Arnold, P.B.; Moore, G.D.; Yaffe, L.G. Transport coefficients in high temperature gauge theories. 1. Leading log results. JHEP
**2000**, 0011, 001, Transport coefficients in high temperature gauge theories. 2. Beyond leading log. ibid.**2003**, 0305, 051. [Google Scholar] [CrossRef] - Baym, G.; Monien, H.; Pethick, C.; Ravenhall, D. Transverse Interactions and Transport in Relativistic Quark-Gluon and Electromagnetic Plasmas. Phys. Rev. Lett.
**1990**, 64, 1867. [Google Scholar] [CrossRef] [PubMed] - Jackson, G.; Peshier, A. Re-running the QCD shear viscosity. J. Phys. G
**2018**, 45, 095001. [Google Scholar] [CrossRef] - Borsanyi, S.; Endrodi, G.; Fodor, Z.; Katz, S.D.; Szabo, K.K. Precision SU(3) lattice thermodynamics for a large temperature range. JHEP
**2012**, 1207, 056, Full result for the QCD equation of state with 2+1 flavors. Phys. Lett. B**2014**, 730, 99. [Google Scholar] [CrossRef] - Cutler, R.; Sivers, D.W. Quantum Chromodynamic Gluon Contributions to Large-p
_{T}Reactions. Phys. Rev. D**1978**, 17, 196. [Google Scholar] [CrossRef] - Grozin, A. Asymptotic freedom: History and interpretation. arXiv
**2008**, arXiv:0803.2589. [Google Scholar] - Peshier, A. The QCD collisional energy loss revised. Phys. Rev. Lett.
**2006**, 97, 212301. [Google Scholar] [CrossRef] [PubMed] - Bernhard, J.E.; Moreland, J.S.; Bass, S.A.; Liu, J.; Heinz, U. Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium. Phys. Rev. C
**2016**, 94, 024907. [Google Scholar] [CrossRef]

**Figure 1.**The viscosity, for ${n}_{\phantom{\rule{-0.166667em}{0ex}}f}=0$, to LO and NLL accuracy, and from our estimate (5). To illustrate that ${\eta}_{{}_{\mathrm{NLL}}}$ cannot explain $\eta /s\precsim 0.5$ (but ${\eta}_{{}_{\mathrm{LO}}}$ may), we also show the constraint for the entropy, $4{T}^{3}\le s\le {s}_{0}$ for $T>1.2{T}_{c}$ (see main text). Near the deconfinement temperature ${T}_{c}$ the entropy of the QGP is notably smaller than ${s}_{0}\phantom{\rule{0.166667em}{0ex}}$.

**Figure 2.**The viscosity in units of the entropy [7]; full lines show our result with running coupling, the bands give the uncertainty from ${t}^{\u2605}\in [\frac{1}{2},2]{T}^{2}$, see text. The left panel, for the quenched limit, shows lattice results [3], and by the dashed line the LO result with ${Q}_{T}=2\pi T$ in running coupling. Overlayed on the right, for ${n}_{\phantom{\rule{-0.166667em}{0ex}}f}=3\phantom{\rule{0.166667em}{0ex}}$, are estimates from hydrodynamics [11]. Hatched region: $\eta /s\le 1/\left(4\pi \right)$.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jackson, G.; Peshier, A.
Low-Shear QCD Plasma from Perturbation Theory. *Proceedings* **2019**, *10*, 7.
https://doi.org/10.3390/proceedings2019010007

**AMA Style**

Jackson G, Peshier A.
Low-Shear QCD Plasma from Perturbation Theory. *Proceedings*. 2019; 10(1):7.
https://doi.org/10.3390/proceedings2019010007

**Chicago/Turabian Style**

Jackson, Greg, and Andre Peshier.
2019. "Low-Shear QCD Plasma from Perturbation Theory" *Proceedings* 10, no. 1: 7.
https://doi.org/10.3390/proceedings2019010007