Investigating the temperature dependence of the specific shear viscosity of QCD matter with dilepton radiation

This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $\eta /s\left(T\right)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $\eta /s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.

Figure 1

Linear (a) and quadratic (b) temperature dependence of $\eta /s$.

Figure 2

Relative size of the envelope of the viscous correction relative to the (ideal) isotropic rate in the local rest frame.

Figure 3

Yield of thermal dileptons (a) and pions (b) for various values of $\eta /s\left(T\right)$. All results are in the 20–40% centrality class.

Figure 4

Elliptic flow of charged hadrons (a) and thermal dileptons (b) with different slopes of $\eta /s\left(T\right)$. Each colored band represents the statistical error associated with the 200 events run. All results are in the 20–40% centrality class.

Figure 5

Elliptic flow $v_2\left(M\right)$ (a) and ${\nu }_2\left(M\right)$ (b) of QGP dileptons for different slopes of $\eta /s\left(T\right)$ using the constant cross section $\delta R$. The definition of ${\nu }_2\left(M\right)$ is in Eq. (18). Each colored band represents the statistical error associated with the 200 events generated. All results are in the 20–40% centrality class.

Figure 6

Elliptic flow $v_2\left(M\right)$ (a) and ${\nu }_2\left(M\right)$ (b) of QGP dileptons for IS $\delta R$ and constant cross section $\delta R$ for both $\eta /s=1/\left(4\pi \right)$ and $\eta /s\left(T\right)$. Each colored band represents the statistical error associated with the 200 events generated. All results are in the 20–40% centrality class.

Figure 7

(a) Momentum anisotropy of the fluid where QGP dilepton rates are used. The meaning of ideal/full $T^{\mu \nu }$ is explained in the text. The development of ${\pi }^{\mu \nu }/(\varepsilon +P)$ in the local rest frame at $(x,y,{\eta }_s)=(0,0,0)$ is shown in (b) where an average over 200 events was performed.

Figure 8

$v_2\left(M\right)$ of HM dileptons under the influence of a $\eta /s\left(T\right)$ is shown in (a), while the hydrodynamic momentum anisotropy evolution in the HM is displayed in (b). All results shown are within the 20–40% centrality class.

Figure 9

(a) The hydrodynamical momentum anisotropy evolution on the freeze-out surface using the full $T^{\mu \nu }$. (b) Presents the same quantity as (a) except only the inviscid part of $T^{\mu \nu }$ is being used to compute the hydrodynamical momentum anisotropy. All results shown are within the 20–40% centrality class.

Figure 10

Event-averaged temperature for the cell $(x,y,{\eta }_s)=(0,0,0)$ during the first fm/$c$ of evolution (a) and at later stages (b) and (c). Event-averaged expansion rate $\theta$ during the first fm/$c$ of evolution (d) and at later stages (e) and (f). Entropy production rate ${\partial }_{\mu }{S}^{\mu }$ rescaled by $\tau$ during the first fm/$c$ of evolution (g) and at later stages (h) and (i).

Figure 11

Event-averaged ${\beta }_T$ during the first fm/$c$ of evolution (a) and at later stages (b),(c).

Figure 12

Event-averaged temperature in the transverse plane at $z=0$ at $(\tau -{\tau }_0)=5.25$ fm/$c$ for $\frac{\eta }{s}=\frac{1}{4\pi }$ (a) and $\frac{\eta }{s}=0.4513\left(\frac{T}{T_{tr}}-1\right)+\frac{1}{4\pi }$ (b). The constant temperature contours ranging from 163 MeV for the inner most contour all the way down to $T_{F0}=145$ MeV, are separated by 3 MeV intervals.

Figure 13

Elliptic (a) and triangular (b) flow of thermal dileptons for a linearly dependent $\eta /s\left(T\right)$.

Figure 14

Yield of thermal dileptons (a) and pions (b) for various values of $\eta /s\left(T\right)$.

Figure 15

Elliptic flow of charged hadrons (a) and thermal dileptons (b) with different values for $a$ in Eq. (3). (c) $v_2/v_3$ ratio for linear and quadratic $\eta /s\left(T\right)$.

Figure 16

A comparison of $v_2$ (a), $v_3$ (b), and $v_4$ (c) of thermal dileptons using linear and quadratic $\eta /s\left(T\right)$ at an intermediate invariant mass. The uncertainties associated with the 200 events generated were removed to improve visual clarity.

Figure 17

A comparison of $v_3$ (a) and $v_4$ (b) of thermal dileptons using linear and quadratic $\eta /s\left(T\right)$ at low invariant mass. The uncertainties associated with the 200 events generated were removed to improve visual clarity.

Figure 18

The size of the viscous contribution to the dilepton yield in the QGP relative to its ideal (inviscid) dilepton production for a medium with constant $\eta /s=1/\left(4\pi \right)$. Left column: $\delta N/N_0$ using the IS $\delta R$. Right column: $\delta N/N_0$ using the constant cross section $\delta R$.

Figure 19

The size of the viscous contribution to the dilepton yield in the QGP relative to its ideal (inviscid) dilepton production for a medium with constant $\eta /s=1/\left(4\pi \right)$. Left column: $\delta N/N_0$ using the IS $\delta R$. Right column: $\delta N/N_0$ using the constant cross section $\delta R$.

Figure 20

The size of the viscous contribution to the dilepton yield in the QGP relative to its ideal (inviscid) dilepton production using the constant cross section $\delta R$ for a medium with linear $\eta /s\left(T\right)$ and slope $m=0.5516$. The left column plots $\delta N/N_0$ for $M=0.3$ GeV whereas the right column plots the same quantity at $M=1.5$ GeV.