Searching for degenerate Higgs bosons using a profile likelihood ratio method

ATLAS and CMS collaborations at the Large Hadron Collider have observed a new resonance con- sistent with the standard model Higgs boson. However, it has been suggested that the observed signal could also be produced by multiple nearly mass-degenerate states that couple differently to the standard model particles. In this work, a method to discriminate between the hypothesis of a single Higgs boson and that of multiple mass-degenerate Higgs bosons was developed. Using the matrix of measured signal strengths in different production and decay modes, parametrizations for the two hypotheses were constructed as a general rank 1 matrix and the most general $5 \times 4$ matrix, respectively. The test statistic was defined as a ratio of profile likelihoods for the two hypotheses. The method was applied to the CMS measurements. The expected test statistic distribution was estimated twice by generating pseudo-experiments according to both the standard model hypothesis and the single Higgs boson hypothesis best fitting the data. The p-value for the single Higgs boson hypothesis was defined from both expected test statistic distributions, and it was $(8.0\pm0.3)\%$ and $(11.0\pm0.3)\%$, respectively. In addition to this, a p-value was also estimated in an alternative way using a $\chi^2$ distribution, fitted to the pseudo-experiments for the standard model Higgs boson hypothesis. The resulting p-value was $10.8\%$. Thus the three estimates yield similar p-values for the single Higgs boson hypothesis. These results suggest that the CMS data is compatible with the single Higgs boson hypothesis, as in the standard model. Furthermore, the result is insensitive to choice of the single Higgs boson hypothesis used to derive it, and it does not depend on the precise shape of the test statistic distribution. The developed method can be applied also to other arbitrarily-sized matrices, and it takes into account the uncertainties on the measurements, missing elements of data, and possible correlations. This thesis is an extensive description of the method that has also been published in EPJC (David, Heikkilä and Petrucciani), and the method has been used in the final Run 1 Higgs combination and properties article (CMS Collaboration, incl. Heikkilä).