ρ-ω mixing effects in relativistic heavy-ion collisions

We show that even moderate excess of neutrons over protons in nuclear matter, such as in Pb, can lead to large ρ-ω mixing at densities of the order of twice the nuclear saturation density and higher. The typical mixing angle is of the order of 10. The mixing may result in noticeable shifts of the positions and widths of resonances. We also analyze temperature effects and find that temperatures up to 50 MeV have practically no effect on the mixing. Over the past few years considerable theoretical efforts have been made to understand in-medium properties of mesons [1,2]. Moreover, the measurement of dilepton spectra in CERES [3] and HELIOS [4] experiments at CERN provides a possibility of verifying various theoretical predictions concerning light vector mesons [5,6]. A number of medium effects is expected to occur in the ρ and ω channels: shift of position of resonances, broadening of their widths, reduction of strength, emergence of collective branches, or mixing of states which have different quantum numbers in the vacuum. The mechanism of mixing induced by the medium has a different origin than the mixing due to explicit symmetry-breaking terms in the Hamiltonian. It results from the breaking of the symmetry by the medium. A well-known example is the mixing of the scalar-isoscalar σ meson with the longitudinal component of the vector ω meson [7]. It is allowed, since the matter state breaks the Lorentz invariance. Recently Dutt-Mazumder, Dutta-Roy and Kundu [8] analyzed the effects of isospin asymmetry in matter on ρ-ω mixing. Their analysis, carried out in the Walecka model [9], implies that at asymmetries such as in Pb and at nuclear saturation density the ρ and ω mix with an angle of about 2. In this Letter we show that the matter-induced ρ-ω mixing effects may in fact be much larger. Denote the correlator for vanishing 3-momentum q in the coupled neutral ρ and ⋆ Research supported by the Polish State Committee for Scientific Research 2P03B-080-12 Preprint submitted to Elsevier Preprint 9 February 2008 ρ G ω G ω G ρ G crossed ρ ω