In-medium omega-meson broadening and S-wave pion annihilation into e^+e^- pairs

An $\omega$-meson in motion with respect to a nuclear medium can couple to a $\sigma$-meson through a particle-hole excitation. This coupling is large. We investigate its consequences for the width of $\omega$-mesons in matter and for the s-wave annihilation of pions into lepton pairs which can take place in relativistic heavy ion collisions. We find that the two pion decay of $\omega$-mesons, resulting from the $\omega-\sigma$ transition and the subsequent $2\pi$ decay of the $\sigma$-meson, leads to a substantial broadening of $\omega$-mesons in matter and possibly to an observable effect in experiments measuring the $e^+e^-$ decay of vector mesons produced in nuclei and in relativistic heavy-ion collisions. The inverse process, the s-wave annihilation of pions into $\omega$-mesons decaying into $e^+e^-$ pairs, has in general a much smaller cross section than the corresponding p-wave annihilation through $\rho$-mesons and is expected to contribute rather little to the total $e^+e^-$ pair production in relativistic heavy ion collisions.