Bulk Viscosity and the Conformal Anomaly in the Pion Gas

Fernández-Fraile, D.; Nicola, Á. Gómez

doi:10.1103/physrevlett.102.121601

Cited by 68 publications

(85 citation statements)

References 37 publications

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“…While the Chiral Perturbation Theory based computation of Fernández-Fraile and Gómez Nicola features a clear maximum of ζ associated with the scale-violating pion mass [1], this is absent from earlier studies [2,6] based on empirical phase-shifts, that also differ in the numeric values of ζ.…”

Section: Motivationmentioning

confidence: 68%

“…Where he provides his data, our calculation is numerically similar but somewhat higher. The second computation [1] is a field theory evaluation based on a certain ladder resummation, and is numerically off our result based on the physical phase shifts. However, the qualitative features and saliently the low-temperature limit coincide with our findings.…”

Section: T (Mevmentioning

confidence: 99%

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Bulk viscosity of low-temperature strongly interacting matter

2011

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We study the bulk viscosity of a pion gas in unitarized Chiral Perturbation Theory at low and moderate temperatures, below any phase transition to a quark-gluon plasma phase.We argue that inelastic processes are irrelevant and exponentially suppressed at low temperatures. Since the system falls out of chemical equilibrium upon expansion, a pion chemical potential must be introduced, so we extend the existing theory to include it. We control the zero modes of the collision operator and Landau's conditions of fit when solving the Boltzmann equation with the elastic collision kernel.The dependence of the bulk viscosity with temperature is reminiscent of the findings of Fernández-Fraile and Gómez Nicola [1], while the numerical value is closer to that of Davesne [2]. In the zero-temperature limit we correctly recover the vanishing viscosity associated to a non-relativistic monoatomic gas.Key words: Bulk viscosity, pion gas, inverse amplitude method, heavy ion collisions, elastic pion scattering PACS: , 25.75. Ag, 11.30.Rd, 13.75.Lb, 47.45.Ab, 51.20.+d MotivationBulk viscosity ζ is responsible for the equilibration of a system subject to dilatation or compression perturbations. Although it usually is much smaller than the more common shear viscosity η, it is an interesting probe of the loss of dilatation invariance [3] through the trace anomaly in quantum field theory. In the context of relativistic heavy ion collisions, bulk viscosity can be experimentally accessed for example by means of fluctuations of the two-point correlation of the energy-momentum tensor [4]. It has been computed in the asymptotically high temperature regime of Quantum Chromodynamics [5], and found to be governed there by inelastic processes.However, published investigations concerning bulk-viscosity in the low-energy pion gas (the opposite, lowtemperature limit of strongly interacting matter at zero baryon number) yield contradictory results. While the Chiral Perturbation Theory based computation of Fernández-Fraile and Gómez Nicola features a clear maximum of ζ associated with the scale-violating pion mass [1], this is absent from earlier studies [2,6] based on empirical phase-shifts, that also differ in the numeric values of ζ.Neither of these calculations carefully identifies the zero-modes of the collision operator that might change the temperature counting of the viscosity. A chiral limit calculation has however been reported [7] that studies these zero modes in elastic scattering.Further, none of these works properly emphasizes the role of the Landau-Lifschitz constraint, that is however properly treated in a linear sigma model computation [8].Given the situation, we feel it is worth to settle the issue of the bulk viscosity of a low-temperature pion gas by adopting the best features of the various existent approaches. In this article we provide a Unitarized

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Section: Motivationmentioning

confidence: 68%

Section: T (Mevmentioning

confidence: 99%

Bulk viscosity of low-temperature strongly interacting matter

2011

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“…Nevertheless, the relation connecting the ζ with the trace anomaly requires particular ansatz for the spectral function [43] and a sophisticated technique to rule out the nonthermal contributions [35,44]. Moreover, presently existing results of the T-dependence of the ζ/s are in serious contradiction with each other, e.g., lattice QCD simulations and holographic correspondence methods give concave functions with different features in particular [40,41,45,46], and chiral perturbation theory gives double peak or convex relations [36] or decreasing function at low temperature [47]. Some hadron resonance models and Nambu-Jona-Lasinio model calculations yield convex or concave function [28,31].…”

Section: Introductionmentioning

confidence: 94%

“…[26,[35][36][37][38][39]). However, studies relating the ζ with the trace anomaly suggest [40,41] and explaining recent experiments requires [32,42] a large value.…”

Section: Introductionmentioning

confidence: 99%

Temperature effect on shear and bulk viscosities of QCD matter

Gao

Liu

2018

Phys. Rev. D

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With developing a scheme to determine the thermal width of a pion in a medium, we investigate the shear and bulk viscosities and their ratios to entropy density. We calculate the temperature (T)-dependence of the pion mass and decay constant via the Dyson-Schwinger equations of QCD and get the pion thermal width with the QCD approach. We obtain then the T-dependence of the viscosities, especially a novel feature of the bulk viscosity, via the continuum QCD approach. The novel concavo-convex behavior of the bulk viscosity to entropy density ratio against the temperature is a demonstration of the QCD phase transitions.

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“…If there are significative differences between charged and neutral thermal widths, there could be sizable corrections e.g. to the electrical conductivity, related to the photon spectrum [18] or to the shear and bulk viscosities needed to explain correctly observables such as the elliptic flow or the trace anomaly [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic effects in the pion dispersion relation at finite temperature

Nicola

Andrés

2014

Phys. Rev. D

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We investigate the charged-neutral difference in the pion self-energy at finite temperature T. Within chiral perturbation theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T ¼ 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to OðT 2 Þ ∼ OðM 2 π Þ. Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a 1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being OðT 2 M 2 π =M 2 R Þ with M R the involved resonance masses.

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Bulk Viscosity and the Conformal Anomaly in the Pion Gas

Cited by 68 publications

References 37 publications

Bulk viscosity of low-temperature strongly interacting matter

Bulk viscosity of low-temperature strongly interacting matter

Temperature effect on shear and bulk viscosities of QCD matter

Electromagnetic effects in the pion dispersion relation at finite temperature

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