The public data from the EGRET space telescope on diffuse Galactic gamma rays in the energy range from 0.1 to 10 GeV are reanalyzed with the purpose of searching for signals of Dark Matter annihilation (DMA). The analysis confirms the previously observed excess for energies above 1 GeV in comparison with the expectations from conventional Galactic models. In addition, the excess was found to show all the key features of a signal from Dark Matter Annihilation (DMA): a) the excess is observable in all sky directions and has the same shape everywhere, thus pointing to a common source; b) the shape corresponds to the expected spectrum of the annihilation of non-relativistic massive particles into -among others -neutral π 0 mesons, which decay into photons. From the energy spectrum of the excess we deduce a WIMP mass between 50 and 100 GeV, while from the intensity of the excess in all sky directions the shape of the halo could be reconstructed. The DM halo is consistent with an almost spherical isothermal profile with substructure in the Galactic plane in the form of toroidal rings at 4 and 14 kpc from the center. These rings lead to a peculiar shape of the rotation curve, in agreement with the data, which proves that the EGRET excess traces the Dark Matter.

Recently it was shown that the excess of diffuse Galactic gamma rays above 1 GeV traces the Dark Matter halo, as proven by reconstructing the peculiar shape of the rotation curve of our Galaxy from the gamma ray excess. This can be interpreted as a Dark Matter annihilation signal. In this paper we investigate if this interpretation is consistent with Supersymmetry. It is found that the EGRET excess combined with all electroweak constraints is fully consistent with the minimal mSUGRA model for scalars in the TeV range and gauginos below 500 GeV.

New NLO b → X s γ calculations have become available using resummed radiative corrections. Using these calculations we perform a global fit of the supergravity inspired constrained minimal supersymmetric model. We find that the resummed calculations show similar constraints as the LO calculations, namely that only with a relatively heavy supersymmetric mass spectrum of O(1 TeV) the b−τ Yukawa unification and the b → X s γ rate can coexist in the large tan β scenario. The resummed b → X s γ calculations are found to reduce the renormalization scale uncertainty considerably. The low tan β scenario is excluded by the present Higgs limits from LEP II. The constraint from the Higgs limit in the m 0 , m 1/2 plane is severe, if the trilinear coupling A 0 at the GUT scale is fixed to zero, but is considerably reduced for A 0 ≤ −2m 0 . The relatively heavy SUSY spectrum required by b → X s γ corresponds to a Higgs mass of m h = 119 ± 1 (stop masses) ± 2 (theory) ± 3 (top mass) GeV in the CMSSM.