The Higgs Boson is the only missing piece in the Standard Model of particle physics and its search is undoubtedly one of the most important searches in the history of physics. The Higgs boson is the generator of all elementary particle masses in nature. The mass of the Higgs boson itself is unknown, and before the LHC it was searched for in previous experiments but not found.
LHC experiments have produced excellent results since the start of the data taking. In ATLAS and CMS a discussion was initiated about a year ago to combine the Higgs search results from both experiments. The framework and the procedure to combine results had to be defined and agreed upon before the combined analysis could proceed.
The LHC Higgs working groups of ATLAS and CMS are made of a few hundreds people and the challenge of combining Higgs boson results from different experiments was not just a technical challenge but also a sociological one. Each experiment sent its experts and representatives to discuss with the other experiment experts. From the beginning of 2011, statistical experts and representatives from both experiments started meeting regularly to discuss and converge on the combination procedure. This was the first example of this kind of scientific collaboration at the LHC. I was involved in these discussions as the ATLAS contact person for the combined analyses. Many different issues needed to be addressed for a successful combination.
The ATLAS and CMS analyses need to use consistent Higgs boson production cross-sections and decay branching ratios. The cross-sections and the branching ratios are related to the production rate of the Higgs boson and its decay probability. The Higgs has a very low lifetime and it is searched for in its decay patterns. The branching ratios are related to the relative weight of various decay patterns.
The LHC Higgs cross-section group, formed much earlier, includes members of ATLAS, CMS and the theory community. A lot of efforts have been made in the LHC Higgs cross-section group to provide common tools to compute Higgs cross-sections and decay branching ratios, and their uncertainties. Common tools to estimate the background (noise) cross-sections were also discussed and used. The background is a process which has looks similar to the Higgs boson signal and therefore sophisticated analysis tools are used to separate, as much as possible, the Higgs boson signal from the background noise. Most backgrounds were obtained from data control region measurements (meaning that the data itself was used to estimate the background), only a handful of the background estimations relied upon theoretical predictions.
The combined analyses necessitate a unified framework for common statistical tools and data exchange. After some validation efforts, the RooStat (a statistical analysis framework developed at CERN) was adopted for the combination. RooStat is built upon a common platform for exchanging information, known as the WorkSpace. The WorkSpace contains all the needed information for statistical analyses and simplifies the logistics of data exchange between the collaborations.
There were many discussions to identify the systematics uncertainties that should be correlated between the experiments and the degrees of the correlation. Uncertainties affect our theoretical computations or experimental measurements, often due to our limited understanding, the complexity of the computations and/or the precisions of our measurements. When the uncertainties are of the same sources in both experiments or in different analyses, we say that they are correlated. Theoretical uncertainties from PDF (Parton Density Functions), αs (strong coupling constant), and QCD (Quantum Chromo Dynamics) renormalization and factorization scales - uncertainties resulting from the precision of the theoretical computations of the cross-sections --- were correlated between the experiments and between processes. Uncertainties include:
- The modeling of the underlying event (the proton is made of many constituents, namely quarks and gluons. When two protons collide besides the main interaction there are other additional interactions, that take place making the underlying events)
- Parton shower (the process by which the way the basic constituents of matter such as quarks and gluons manifest themselves in nature) as well as experimental uncertainties on luminosity measurements were also correlated between the experiments (the luminosity is related to the total intensity of the collisions).
QCD scale uncertainties on jet counting (jets are the result of parton showers) in Higgs boson production are also treated as well as QCD uncertainties in data-driven background (noise) estimations where extrapolation factors from data control regions to signal regions were taken from theory.
If particular uncertainties (within one or both experiments) were taken to be 100% correlated they were given the same name. Different names imply no correlation. Any two sources of uncertainties that were believed to be only partially correlated were either broken further down to the independent sub-contributions or declared to be correlated/uncorrelated, whichever was believed to be more appropriate or more conservative. To avoid accidental correlations in the combination, uncertainties specific to each experiment had a prefix ATLAS or CMS. Uncertainties without such prefixes were assumed to be 100% correlated between the two experiments.
The only observable that interests us is the Higgs boson production rate; all other related parameters are called nuisance parameters. In the statistical analyses of the combination, systematic uncertainties on observables were handled by introducing nuisance parameters associated to probability density functions (pdf), with the best estimate of the uncertainties (mean, median, peak) and additional parameters characterizing the shape of the pdf. Many different