Electric conductivity of a hot hadron gas from a kinetic approach

We calculate the electric conductivity of a gas of relativistic particles with isotropic cross sections using the Boltzmann equation as the starting point. Our analysis is restricted to elastic collisions. We show the perfect agreement with previously published numerical results for a massless quark-gluon plasma, and give results for the electric conductivity of an interacting hadron gas, employing realistic resonance cross sections. These results for the electric conductivity of a hot hadron gas, as created in (ultra)relativistic heavy-ion collisions, are of rich phenomenological as well as theoretical interest and can be compared to, e.g., lattice quantum field theory calculations.

Figure 1

Convergence of the analytical computation for the electric conductivity for a massless quark-gluon gas towards the numerical value obtained by the partonic cascade bamps ([31]).

Figure 2

The mass dependence of the electric conductivity for (three species of) interacting relativistic particles. The cross section was arbitrarily fixed to 10 mb, and the degeneracy ratio of charged/uncharged species is $2/9$, the charges are $\pm 1,0$. On the x-axis we vary the mass ratio of the charged to the uncharged species, and show results for different masses of the charged species.

Figure 3

Results for the electric conductivity from this work and other theories. Parton transport bamps [31], chiral perturbation theory (ChPT) [39], SYM theory [67], a nonconformal holographic model (n-c hm) [46] and lattice [47, 50] calculations are shown for comparison. These theories all require very different effective cross sections when compared to kinetic theory. (a) Interacting pion gas (red squares) in equilibrium for different temperatures. The pions interact via the $\rho$-resonance scattering. (b) The electric conductivity for interacting pions (${\pi }^{+},{\pi }^{-},{\pi }^0$), kaons ($K^0,{\overline{K}}^0,K^{+},K^{-}$) and nucleons ($p,\overline{p},n,\overline{n}$). The cross section ${\sigma }_{\mathrm{tot}}$ is constant and isotropic, and we show results for four different values. Results for a pure pion gas are shown for comparison.

Figure 4

Results for the electric conductivity from this work, including pions, kaons and nucleons, compared to results from parton-hadron-string dynamics (PHSD) [44, 45] and all other theories as before. All constant cross sections (see Table 1) are multiplied with a factor $\kappa$, which we change in the range of $\kappa =0.5$, 1, 1.5 in order to get a feeling for the uncertainty.