Independent evaluation of the significance of the recent ATLAS and CMS data

This note describes an independent assessment of the statistical significance of the recently released ATLAS and CMS data, about 11 fb-1 per experiment acquired in 2011 and in the first part of 2012, for what concerns the Higgs search in the two high resolution decay channels especially suited for the low mass region, i.e. the diphoton and four-lepton decay channels. Scope of this note is not to reproduce the analysis of the Collaborations: this would be impossible given the enormous complexity of the complete profile likelihood procedure used to evaluate local and global the p-values, and the huge number of nuisance parameters which are used to incorporate the numerous systematic effects. Rather, its purpose is to show the significance that an outsider can infer only on the basis of the released data and plots, used as input of a simplified profile likelihood procedure in which the only contemplated nuisance parameter is the background normalization in the diphoton channel. In practice, this note tries to address the question of the independent judgment of the significance of new data that physicists are used to perform on their own when they are shown for the first time particularly relevant results with indication of new effects, and that in the complex LHC framework is not so easily doable as in other experimental contexts.

On the significance of the excesses in the ATLAS diphoton and four lepton decay channels

This note describes an assessment of the statistical significance of the recently released ATLAS data regarding the Higgs search in the decay channels especially suited for the low mass region, in particular the diphoton and four lepton decay channels. Besides providing the significance evaluation of the considered channels, alone or combined, in the low mass range from 110 to 146 GeV, some details of the profile likelihood procedure employed for the calculations are described, too. Special emphasis is given to the look elsewhere effect, which arises when the search of a new signal is carried out over a broad mass range, therefore specifying separately local and global significances. When combined together, the global p-value of the localized excesses detected in the two channels is found equal to either 0.033 or 0.013, corresponding, respectively, to a significance of 1.8 sigma and 2.2 sigma depending upon the assumption of mutual independence or dependence of the amplitudes of the expected signal in each channel. Among the other obtained results, the local and global significances of the two channels individually taken are computed in good agreement with those reported by the Collaboration, while only a minor discrepancy is found for their combined local significance. Finally, some considerations are illustrated related to the low statistics four lepton decay channel, showing that a search strategy different from the profile likelihood method, e.g. scan statistics, can result in a substantially different significance, enhanced to a 3.3 sigma global effect.

Binomial and ratio-of-Poisson-means frequentist confidence intervals applied to the error evaluation of cut efficiencies

The evaluation of the error to be attributed to cut efficiencies is a common question in the practice of experimental particle physics. Specifically, the need to evaluate the efficiency of the cuts for background removal, when they are tested in a signal-free-background-only energy window, originates a statistical problem which finds its natural framework in the ample family of solutions for two classical, and closely related, questions, i.e. the determination of confidence intervals for the parameter of a binomial proportion and for the ratio of Poisson means. In this paper the problem is first addressed from the traditional perspective, and afterwards naturally evolved towards the introduction of non standard confidence intervals both for the binomial and Poisson cases; in particular, special emphasis is given to the intervals obtained through the application of the likelihood ratio ordering to the traditional Neyman prescription for the confidence limits determination. Due to their attractiveness in term of reduced length and of coverage properties, the new intervals are well suited as interesting alternative to the standard Clopper-Pearson PDG intervals.