Challenges in Moving the LEP Higgs Statistics to the LHC

Higgs searches at LEP were based on marginal signal expectations and small background uncertainties. In contrast, Higgs searches at the LHC are based on strong signal expectations and relatively large background uncertainties. Based on our experience with the LEP Higgs search, our group tried to move the tools we had developed at LEP to the LHC environment. In particular, our calculation of confidence levels was based on an analytic computation with the Fast Fourier Transform and the log-likelihood ratio as a test statistic (and systematic errors based on the Cousins-Highland approach). We encountered three types of problems when calculating ATLAS’ combined sensitivity to the Standard Model Higgs Boson: problems associated with large numbers of expected events, problems arising from very high significance levels, and problems related to the incorporation of systematic errors. Previously, it was shown that the migration of the statistical techniques that were used in the LEP Higgs Working Group to the LHC environment is not as straightforward as one might näively expect [1]. After a brief overview in Section 2, those difficulties and their ultimate solution are discussed in Section 3. Our group has developed two independent software solutions (both in C++; both with FORTRAN bindings; one ROOT based and the other standalone) which can be found at: http://wisconsin.cern.ch/software In Section 4 we discuss the incorporation of systematic errors and compare a few different strategies. In Section 5 we present and discuss the discovery luminosity (the luminosity expected to be required for discovery). Lastly, in Section 6 we discuss the statistical notion of power (which is related to the probability of Type II error (the probability we do reject the “signal-plus-background hypothesis” when it is true).