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.

💡 Research Summary

The paper provides a careful statistical re‑evaluation of the excesses reported by the ATLAS Collaboration in the low‑mass Higgs search, focusing on the diphoton (γγ) and four‑lepton (4ℓ) decay channels. Using a profile‑likelihood framework, the authors construct a test statistic q = −2 ln λ(μ), where λ is the ratio of the likelihood under the signal‑plus‑background hypothesis to that under the background‑only hypothesis, and μ denotes the signal strength. They treat the test statistic as asymptotically χ²(1) distributed, employing Asimov data sets and large numbers of background‑only pseudo‑experiments to obtain both local and global p‑values.

A central theme is the “look‑elsewhere effect” (LEE). Because the search is performed over a wide mass interval (110–146 GeV), the probability of observing a fluctuation as large as the one seen at any point in that interval must be accounted for. By scanning the full mass range in each pseudo‑experiment and recording the maximum q, the authors derive a global p‑value that is substantially larger than the local p‑value at the most significant mass point. For the diphoton channel the local significance is about 2.8 σ, reduced to roughly 1.5 σ globally; for the four‑lepton channel the local significance is about 2.1 σ, dropping to ≈0.9 σ globally.

When the two channels are combined, the treatment of the signal strengths in each channel becomes crucial. The authors consider two limiting scenarios: (a) the signal strengths μ₁ (γγ) and μ₂ (4ℓ) are statistically independent, and (b) they are perfectly correlated because both arise from the same Higgs production cross‑section. Under the independence assumption the combined global p‑value is 0.033, corresponding to a 1.8 σ effect. If the amplitudes are forced to be equal (the correlated case), the global p‑value improves to 0.013, i.e., a 2.2 σ effect. In both cases the combined local significance is close to the 3 σ value reported by ATLAS, but the global significance is reduced once the LEE is taken into account.

A particularly interesting contribution of the paper is the discussion of alternative statistical techniques for the four‑lepton channel, which suffers from very low event counts (typically three or four events in the signal window). The authors argue that the standard profile‑likelihood approach can be overly conservative in such a regime. They therefore apply scan statistics, a method that directly evaluates the probability of observing a cluster of events within a given mass interval. Using this technique, the global p‑value for the four‑lepton excess drops to about 0.001, corresponding to a 3.3 σ effect—substantially higher than the ≈0.9 σ obtained with the likelihood method.

The paper concludes that (i) the ATLAS local excesses are compatible with the Collaboration’s published numbers, (ii) the global significance is strongly dependent on how the LEE and inter‑channel correlations are modeled, and (iii) for channels with sparse data, non‑standard methods such as scan statistics can provide a more sensitive assessment. While the current data do not yet reach the conventional 5 σ discovery threshold, the authors emphasize that a diversified statistical toolbox will be essential as more data are accumulated, potentially turning these modest excesses into a robust Higgs signal or revealing new physics beyond the Standard Model.