Reconstructing $\rho^0$ and $\omega$ mesons from non-leptonic decays in C+C at 2AGeV

We predict transverse and longitudinal momentum spectra and yields of $\rho^0$ and $\omega$ mesons reconstructed from hadron correlations in C+C reactions at 2~AGeV. The rapidity and $p_T$ distributions for reconstructable $\rho^0$ mesons differs strongly from the primary distribution, while the $\omega$'s distributions are only weakly modified. We discuss the temporal and spatial distributions of the particles emitted in the hadron channel. Finally, we report on the mass shift of the $\rho^0$ due to its coupling to the $N^*(1520)$, which is observable in both the di-lepton and $\pi\pi$ channel. Our calculations can be tested with the Hades experiment at GSI, Darmstadt.