Evolution of the ρ meson's spin alignment in a pion gas

We study the evolution of the spin alignment of neutral ρ mesons in a pion gas using spin kinetic or Boltzmann equations. The ρππ coupling is given by the chiral effective theory. The collision terms at the leading and next-to-leading order in spin Boltzmann equations are derived. The evolution of the spin density matrix of the neutral ρ meson is simulated with different initial conditions. The numerical results show that the interaction of pions and neutral ρ mesons creates very small spin alignment in the central rapidity region if there is no ρ meson in the system at the initial time. Such a small spin alignment in the central rapidity region will decay rapidly toward zero in later time. If there are ρ mesons with a sizable spin alignment at the initial time the spin alignment will also decrease rapidly. We studied the effect on ρ₀₀ from the elliptic flow of pions in the blast wave model. With vanishing spin alignment at the initial time, the deviation of ρ₀₀ from 1/3 is positive but very small. The effect of tensor polarizations of ρ mesons on γ correlator observables for CME has also been investigated.