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The $πρ$ Cloud Contribution to the $ω$ Width in Nuclear Matter

The width of the $ω$ meson in cold nuclear matter is computed in a hadronic many-body approach, focusing on a detailed treatment of the medium modifications of intermediate $πρ$ states. The $π$ and $ρ$ propagators are dressed by their selfenergies in nuclear matter taken from previously constrained many-body calculations. The pion selfenergy includes $Nh$ and $Δh$ excitations with short-range correlations, while the $ρ$ selfenergy incorporates the same dressing of its $2π$ cloud with a full 3-momentum dependence and vertex corrections, as well as direct resonance-hole excitations; both contributions were quantitatively fit to total photo-absorption spectra and $πN\toρN$ scattering. Our calculations account for in-medium decays of type $ωN\to πN^{(*)}, ππN(Δ)$, and 2-body absorptions $ωNN\to NN^{(*)},πNN$. This causes deviations of the in-medium $ω$ width from a linear behavior in density, with important contributions from spacelike $ρ$ propagators. The $ω$ width from the $ρπ$ cloud may reach up to 200 MeV at normal nuclear matter density, with a moderate 3-momentum dependence. This largely resolves the discrepancy of linear $T$-$\varrho$ approximations with the values deduced from nuclear photoproduction measurements.