A generalized lens equation for light deflection in weak gravitational fields

A generalized lens equation for weak gravitational fields in Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens equation is estimated to be smaller than or equal to 15 Pi/4 (m/d')^2, where m is the Schwarzschild radius of massive body and d' is Chandrasekhar's impact parameter. The main applications of this generalized lens equation are extreme astrometrical configurations, where 'Standard post-Newtonian approach' as well as 'Classical lens equation' cannot be applied. It is shown that in the appropriate limits the proposed lens equation yields the known post-Newtonian terms, 'enhanced' post-post-Newtonian terms and the Classical lens equation, thus provides a link between these both essential approaches for determining the light deflection.Comment: 11 pages, 3 figure

Probing the strange quark condensate by di-electrons from phi meson decays in heavy-ion collisions at SIS energies

QCD sum rules predict that the change of the strange quark condensate $<\bar s s>$ in hadron matter at finite baryon density causes a shift of the peak position of the di-electron spectra from $\phi$ meson decays. Due to the expansion of hadron matter in heavy-ion collisions, the $\phi$ peak suffers a smearing governed by the interval of density in the expanding fireball, which appears as effective broadening of the di-electron spectrum in the $\phi$ region. The emerging broadening is sensitive to the in-medium change of $<\bar s s>$. This allows to probe directly in-medium modifications of $$ via di-electron spectra in heavy-ion collisions at SIS energies with HADES

Evaluation of QCD sum rules for light vector mesons at finite density and temperature

QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons $\rho$, $\omega$ and $\phi$ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the $\rho$ and $\omega$ mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the $\rho$ meson and can lead to a change of the sign of the $\omega$ meson mass shift as a function of the density. In contrast, the in-medium mass of the $\phi$ meson is directly related to the chiral strange quark condensate which seems correspondingly accessible

Numerical versus analytical accuracy of the formulas for light propagation

Numerical integration of the differential equations of light propagation in the Schwarzschild metric shows that in some situations relevant for practical observations the well-known post-Newtonian solution for light propagation has an error up to 16 microarcsecond. The aim of this work is to demonstrate this fact, identify the reason for this error and to derive an analytical formula accurate at the level of 1 microarcsecond as needed for high-accuracy astrometric projects (e.g., Gaia). An analytical post-post-Newtonian solution for the light propagation for both Cauchy and boundary problems is given for the Schwarzschild metric augmented by the PPN and post-linear parameters $\beta$, $\gamma$ and $\epsilon$. Using analytical upper estimates of each term we investigate which post-post-Newtonian terms may play a role for an observer in the solar system at the level of 1 microarcsecond and conclude that only one post-post-Newtonian term remains important for this numerical accuracy. In this way, an analytical solution for the boundary problem for light propagation is derived. That solution contains terms of both post-Newtonian and post-post-Newtonian order, but is valid for the given numerical level of 1 microarcsecond. The derived analytical solution has been verified using the results of a high-accuracy numerical integration of differential equations of light propagation and found to be correct at the level well below 1 microarcsecond for arbitrary observer situated within the solar system. Furthermore, the origin of the post-post-Newtonian terms relevant for the microarcsecond accuracy is elucidated. We demonstrate that these terms result from an inadequate choice of the impact parameter in the standard post-Newtonian formulas

Freeze Out Process with In-Medium Nucleon Mass

We investigate the kinetic freeze out scenario of a nucleon gas through a finite layer. The in-medium mass modification of nucleons and it's impact on the freeze out process is studied. A considerable modification of the thermodynamical parameters temperature, flow-velocity, energy density and particle density has been found in comparison with evaluations which use a constant vacuum nucleon mass.Comment: 6 pages, 4 figures, Proceeding of the Conference "Quark Matter 2005", 4th - 9th August 2005, Budapest/Hungar

Pion Mass Shift and the Kinetic Freeze Out Process

The kinetic Freeze Out process of a pion gas through a finite layer with time-like normal is considered. The pion gas is described by a Boltzmann gas with elastic collisions among the pions. Within this model, the impact of the in-medium pion mass modification on the Freeze Out process is studied. A marginal change of the Freeze Out variables temperature and flow velocity and an insignificant modification of the frozen out particle distribution function has been found.Comment: European Physical Journal A (2009), in pres

Evidence for In-Medium Changes of Four-Quark Condensates

Utilizing the QCD sum rule approach to the behavior of the omega meson in nuclear matter we derive evidence for in-medium changes of particular four-quark condensates from the recent CB-TAPS experiment for the reaction gamma + A -> A' + omega (-> pi0 gamma) with A = Nb and LH2.Comment: Submitted to Phys. Rev. Lett., 4 page