Spin density matrix for neutral <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="TIMEQ1"><mml:mrow><mml:mi> </mml:mi><mml:mi>ρ</mml:mi></mml:mrow></mml:math></inline-formula> mesons in a pion gas in linear response theory

We calculate the spin density matrix for neutral $\rho$ mesons fromthe spectral function and thermal shear tensor by Kubo formula inthe linear response theory, which contributes to the $\gamma$ correlatorfor the CME search. We derive the spectral function of neutral $\rho$mesons with $\rho\pi\pi$ and $\rho\rho\pi\pi$ interactions usingthe Dyson-Schwinger equation. The thermal shear tensor contributionis obtained from the Kubo formula in the linear response theory. Wenumerically calculate $\rho_{00}-1/3$ and $\mathrm{Re}\rho_{-1,1}$using the simulation results for the thermal shear tensor by the hydrodynamicalmodel, which are of the order $10^{-3}$-$10^{-2}$.