Optimally combined confidence limits

An analytical and optimal procedure to combine statistically independent sets of confidence levels on a quantity is presented. This procedure does not impose any constraint on the methods followed by each analysis to derive its own limit. It incorporates the a priori statistical power of each of the analyses to be combined, in order to optimize the overall sensitivity. It can, in particular, be used to combine the mass limits obtained by several analyses searching for the Higgs boson in different decay channels, with different selection efficiencies, mass resolution and expected background. It can also be used to combine the mass limits obtained by several experiments (e.g. ALEPH, DELPHI, L3 and OPAL, at LEP 2) independently of the method followed by each of these experiments to derive their own limit. A method to derive the limit set by one analysis is also presented, along with an unbiased prescription to optimize the expected mass limit in the no-signal-hypothesis.