Application of the Profile-Likelihood Method to the Combination of Cross Section Measurements

We use the method of maximum likelihood to obtain a combined value for the $Z \rightarrow \tau \tau$ cross section from measurements in three different final states. The profile likelihood method is applied to find confidence intervals on the stated result. We carefully justify the form of the employed likelihood function and discuss the frequentest foundations of the applied methods. The necessary algorithms are implemented with the RooFit framework and tested on simple examples. The Neyman construction and the unified approach are demonstrated in order to motivate the more sophisticated test statistic used in the combination.