Unstable Hadrons in Hot Hadron Gas in Laboratory and in the Early Universe

We study kinetic master equations for chemical reactions involving the formation and the natural decay of unstable particles in a thermal bath. We consider the decay channel of one into two particles, and the inverse process, fusion of two thermal particles into one. We present the master equations the evolution of the density of the unstable particles in the early Universe. We obtain the thermal invariant reaction rate using as an input the free space (vacuum) decay time and show the medium quantum effects on $\pi+\pi \leftrightarrow \rho$ reaction relaxation time. As another laboratory example we describe the $K+K \leftrightarrow \phi$ process in thermal hadronic gas in heavy-ion collisions. A particularly interesting application of our formalism is the $\pi^{0}\leftrightarrow \gamma +\gamma$ process in the early Universe. We also explore the physics of $\pi^{\pm}$ and $\mu^{\pm}$ freeze-out in the Universe.