Collision rates for $\bbox{\rho}$, $\bbox{\omega}$ and $\bbox{\phi}$ mesons at nonzero temperature

The $\omega$ and $\phi$ mesons are exceptionally narrow in vacua being about 8 and 4 MeV. At finite temperature they will scatter with other hadrons in their approach to equilibrium and thereafter. These dynamics induce broadening to the already unstable vector mesons which is calculated in the framework of relativistic kinetic theory. A rather complete set of low-lying mesons provide reaction partners whose interactions are modeled using effective Lagrangians. Collision rates for $\rho$ and $\omega$ are found to be $\sim$ 100 MeV at $T$=200 MeV while the rate for $\phi$ is $\sim$ 25 MeV. Corresponding mean free paths are about 1 and 4 fm! Possible observable consequences are discussed.