Phi meson spectral moments and QCD condensates in nuclear matter

Abstract: A detailed analysis of the lowest two moments of the $\phi$ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kanonic degrees of freedom with the bare $\phi$ meson. In the vacuum, recent accurate measurements of the $e^+ e^- \to K^+ K^-$ cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by the interactions of the kaons from $\phi \rightarrow K\bar{K}$ with the surrounding nuclear medium. This leads primarily to a strong broadening and an asymmetric deformation of the $\phi$ meson peak structure. We confirm that, both in vacuum and nuclear matter, the zeroth and first moments of the corresponding spectral functions satisfy the requirements of the finite energy sum rules to a remarkable degree of accuracy. Limits on the strangeness sigma term of the nucleon are examined in this context. Applying our results to the second moment of the spectrum, we furthermore discuss constraints on four-quark condensates and the validity of the commonly used ground state saturation approximation.