Three-pion reactions in dilepton production from hadron gas

Kinetic theory formulas are derived for the dilepton production rate from processes of the type $1+2+3\to l^{+}{l}^{-}$ and $1+2\to 3+\left(l^{+}{l}^{-}\right)$ in hadronic or partonic systems. The formalism is applied to three-pion reactions ${\pi }^{+}{\pi }^{-}{\pi }^0\to {\mu }^{+}{\mu }^{-}$, ${\pi }^{\pm }{\pi }^0\to {\pi }^{\pm }{\mu }^{+}{\mu }^{-}$, and ${\pi }^{+}{\pi }^{-}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ in a thermalized hadron gas. The dilepton mass spectra are compared to those from previously considered reactions at different temperatures. The three-pion processes amplify the $\omega \mathrm{}\left(783\right)\mathrm{}$ and $\phi \mathrm{}\left(1020\right)\mathrm{}$ peaks in the dilepton mass spectrum. The consequences for using resonance dileptons as a tool for measuring the mean lifetime and temperature of hadronic fireballs are discussed.