Strange mesons in nuclear matter at finite temperature

Abstract

We study the properties of $K$ and $\bar{K}$ mesons in nuclear matter at finite temperature from a chiral unitary approach in coupled channels which incorporates the $s$- and p-waves of the kaon-nucleon interaction. The in-medium solution accounts for Pauli blocking effects, mean-field binding on all the baryons involved, and $\pi$ and kaon self-energies. We calculate $K$ and $\bar{K}$ (off-shell) spectral functions and single particle properties. The $\bar{K}$ effective mass gets lowered by about -50 MeV in cold nuclear matter at saturation density and by half this reduction at T=100 MeV. The p-wave contribution to the $\bar{K}$ optical potential, due to $\Lambda$, $\Sigma$ and ${\Sigma }^{\ast }$ excitations, becomes significant for momenta larger than 200 MeV/c and reduces the attraction felt by the $\bar{K}$ in the nuclear medium.The $\bar{K}$ spectral function spreads over a wide range of energies, reflecting the melting of the $\Lambda (1405)$ resonance and the contribution of $Y{N}^{-1}$ components at finite temperature. In the $KN$ sector, we find that the low-density theorem is a good approximation for the $K$ self-energy close to saturation density due to the absence of resonance-hole excitations. The $K$ potential shows a moderate repulsive behavior, whereas the quasi-particle peak is considerably broadened with increasing density and temperature. We discuss the implications for the decay of the $\varphi$ meson at SIS/GSI energies as well as in the future FAIR/GSI project.

35 pages, 10 figures, 1 table

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