We calculate the spin density matrix for neutral $\rho$ mesons from the spectral function and thermal shear tensor by Kubo formula in the linear response theory, which contributes to the $\gamma$ correlator for the CME search. We derive the spectral function of neutral $\rho$ mesons with $\rho\pi\pi$ and $\rho\rho\pi\pi$ interactions using the Dyson-Schwinger equation. The thermal shear tensor contribution is obtained from the Kubo formula in the linear response theory. We numerically calculate $\rho_{ 00}-1/3$ and $\mathrm{ Re}\rho_{ -1,1}$ using the simulation results for the thermal shear tensor by the hydrodynamical model, which are of the order $10^{ -3}\sim10^{ -2}$.
Categories: hep-ph