$η/s$ of the Normal Phase of Unitary Fermi Gas from $\varepsilon$ Expansion

Using $\varepsilon$-expansion technique we compute $\eta/s$, where $\eta$ is the shear viscosity, $s$ is the entropy density, of the normal phase of unitary Fermi gas in $d=4-\varepsilon$ dimensions to LO in $\varepsilon$. We use kinetic theory approach and solve transport equations for medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to $\varepsilon^2$ which is LO. The LO result is temperature independent with $\eta/\rm s\simeq (0.11/\varepsilon^2)(\hbar/k_B).$ The $d=3$ prediction for $\eta/\rm s$ exceeds the $\hbar/4 \pi k_B$ bound by a factor of about $1.4.$