The influence of systematic errors on the calculation of the statistical significance of a $gamma$-ray signal with the frequently invoked Li and Ma method is investigated. A simple criterion is derived to decide whether the Li and Ma method can be ap
plied in the presence of systematic errors. An alternative method is discussed for cases where systematic errors are too large for the application of the original Li and Ma method. This alternative method reduces to the Li and Ma method when systematic errors are negligible. Finally, it is shown that the consideration of systematic errors will be important in many analyses of data from the planned Cherenkov Telescope Array.
An annihilation signal of dark matter is searched for from the central region of the Milky Way. Data acquired in dedicated ON/OFF observations of the Galactic center region with H.E.S.S. are analyzed for this purpose. No significant signal is found i
n a total of $sim 9$ h of ON/OFF observations. Upper limits on the velocity averaged cross section, $<sigma v >$, for the annihilation of dark matter particles with masses in the range of $sim 300$ GeV to $sim 10$ TeV are derived. In contrast to previous constraints derived from observations of the Galactic center region, the constraints that are derived here apply also under the assumption of a central core of constant dark matter density around the center of the Galaxy. Values of $<sigma v >$ that are larger than $3cdot 10^{-24}:mathrm{cm^3/s}$ are excluded for dark matter particles with masses between $sim 1$ and $sim 4$ TeV at 95% CL if the radius of the central dark matter density core does not exceed $500$ pc. This is the strongest constraint that is derived on $<sigma v>$ for annihilating TeV mass dark matter without the assumption of a centrally cusped dark matter density distribution in the search region.
