Institute of research into the fundamental laws of the Universe

The Higgs boson in one word (or almost...)

Since the first observation of the Higgs boson by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) in 2012, the precise measurement of its properties has become one of the priorities of the LHC physics program. The Higgs boson decays instantaneously in the detector and is therefore studied thanks to its decay products. A golden decay channel for studying the properties of the Higgs boson is the two-photon channel. Indeed, despite its rarity (less than 0.3% of the Higgs boson decays), it allows to measure the mass of the Higgs boson with an excellent resolution thanks to the precise measurement (within about 1%) of the photon energy in the CMS electromagnetic calorimeter (ECAL). This decay channel, which was one of the two discovery channels in 2012, also allows access to all modes of Higgs boson production because the background noise is moderate. Finally, the background noise can be estimated directly from the data, which significantly reduces the sources of uncertainty compared to other channels. The IRFU CMS group played a central role in the construction of ECAL and continues to play a crucial role in its calibration. It has therefore naturally also played an important role in the discovery and measurement of the properties of the Higgs boson in its two-photon decay and in particular in recent years a leading role in the study of the production of the Higgs boson in association with a pair of top anti-top quarks (ttH).

The Higgs boson plays a central role in the theory that describes particles and their interactions, the Standard Model of Particle Physics (SM). This model, developed during the 20th century, acquired its present final form around the 1970s. It predicts the existence of a particle, the Higgs boson, as a consequence of the breaking of electroweak symmetry, a mechanism that allows elementary particles to acquire mass. The SM has been intensively tested and can account for almost all the phenomena observed in the laboratory to date, its latest success being the observation of the Higgs boson in 2012. However, the SM is only an incomplete description of our Universe. It does not explain many properties of elementary particles such as the number of their families or the differences between their mass scales. From a more general point of view, it also does not explain the origin of dark matter or dark energy necessary to describe astrophysical and cosmological observations. Physics beyond the Standard Model, or "New Physics" (NP) has been actively sought directly at the LHC, i.e. in the form of new particles not predicted by the SM. Unfortunately, this research has been unsuccessful and large ranges of mass and cross sections have been excluded by these searches. The lack of direct observation of new particles at the LHC has led to a paradigm shift: precision measurements are now of primary importance, in order to highlight inconsistencies in the model. Indeed, physics beyond the SM could interact and interfere with known particles and leave its imprint on the SM particle properties. Thus, accurate measurement of the properties of particles and the strength of their interactions could provide clues about the NP as soon as these measurements deviate from the predictions of the SM. Many properties of the Higgs boson have not yet been studied in detail. Does the Higgs boson interact with other particles as predicted by the SM? In the SM, the strength of the interaction between the Higgs boson and any other particle is directly related to the mass of the latter. Changes in these interactions are predicted by many new models, extensions of the SM. Thus, the precise study of the properties of the Higgs boson is a gateway to NP.  For example, the strength of the interaction could be different from that predicted by the SM.

In the past, measurements have been limited to the cross sections of the main production modes. The four main production modes of the Higgs boson at the LHC, whose diagrams are shown below, are:

(a)    gluon-gluon fusion (ggF),
(b)    vector bosons fusion (VBF),
(c)    production associated with a vector boson (VH),
(d)    production associated with a pair of top and anti-top quarks (ttH).

With the large data sample available at Run 2, 137 fb-1 of proton-proton collisions at an energy in the center of mass of 13 TeV, and experiments developing new methods of analysis, measurements that were previously impossible are emerging: rare production or decay modes become accessible, measurements with a finer granularity can also be made to test different corners of the phase space, some of which may be more sensitive to New Physics. The CMS collaboration presented its most successful current measurement of the properties of the Higgs boson in the diphoton channel at the ICHEP conference in August 2020.

Characterize the different production modes of the Higgs boson, an agreement between theorists and experimentalists!

Theorists and experimentalists have in recent years jointly defined a common framework for ATLAS and CMS that allows precision measurements in the Higgs boson sector in different predefined regions of the phase-space and increasingly finer over time. This common framework is called "Simplified template cross section" (STXS). In this framework, the main modes of production of the Higgs boson are themselves subdivided into different regions, defined by certain properties of the events, such as the transverse momentum of the Higgs boson or the number of additional jets. We propose to measure the production cross sections in each of these regions and to compare them with the SM predictions. These regions are chosen to maximize experimental sensitivity while decreasing as much as possible the dependence on the theory of results. This framework also allows an easy combination of results in the different decay channels and between experiments as well as an easier reinterpretation of the results by the theorists. The complete STXS measurement framework is presented below, with the different colors corresponding to the different modes of production of the Higgs boson.

The goal is to measure the production rates, or cross sections, for each of these boxes or "bin" in order to get a detailed picture of the properties of the Higgs boson. Some of these regions are more sensitive to physics beyond the SM, for example those with a Higgs boson produced with a very large transverse momentum.

Surgical tools

First, events with two well identified photons are selected. They are then classified according to their production mechanism (by requesting the presence of additional objects in the event that signs the production mode). For example, for the mechanism of Higgs boson production by vector boson fusion ("VBF"), one expects to find 2 jets in the forward regions of the detector. Thus, by labeling events with forward jets, one can construct event categories enriched in VBF production. In the same way, categories are constructed for the different production modes: production associated with a vector boson (VH), production associated with top quarks (ttH, tH) or production by gluon fusion (ggF).

These categories are subdivided into sub-categories, enriched with events of different "STXS bins". In doing so, it becomes possible to measure the cross-sections in each "bin" in order to construct the desired fine description of the Higgs boson.  Machine learning algorithms are used extensively to increase the purity of the categories and to reject background, with the ultimate goal of minimizing measurement uncertainties. This part of the work requires fine optimization. Each algorithm has a specific goal, for example the identification of photons, or the rejection of a dominant background for a particular process, or the rejection of another production mode of the Higgs boson that would pollute the category. The purer the categories are in events corresponding to the targeted STXS bin, the greater the accuracy because the uncertainty on the contaminations decreases. Likewise as the background is lower, the uncertainty on the background, and therefore the uncertainty of the final measurement, decreases. These algorithms are trained using simulated data and sometimes also real data when possible or desirable. These algorithms use many input variables to discriminate background or other production modes. Each type of category uses for its selection one or more of these algorithms dedicated and optimized for that particular type of category.

For example, for the first time, a "Deep Neural Network" is used to separate events where the Higgs boson is produced with a single quark top (tH) from those where it is produced with a pair of top quarks (ttH). Separating these events that have very close topologies in the detector is difficult and the production with a single quark top is a very rare process, never yet observed at the LHC. The image below shows a possible tH event, recorded by the CMS detector in August 2018.

The measured quantities are used to assign a "bin STXS" to each event. For some "bins", this choice is made through a self-learning algorithm called "boosted decision tree". In the case of ttH production, the measured transverse momentum is used to classify the events, in order to make for the very first time measurements based on the Higgs boson transverse pulse.

Thanks to the excellent performance of the CMS electromagnetic calorimeter, it is possible to measure the photon energy very precisely and thus to determine the mass of the Higgs boson with a good resolution. Thanks to this high accuracy, photon pairs originating from the Higgs boson appear as a narrow peak corresponding to the mass of the Higgs boson (125 GeV) in the diphoton invariant mass distribution, whereas the background, dominated by photon pairs not originating from a Higgs boson, has a continuous and slowly decreasing invariant mass spectrum, as shown in the figure below. In order to extract the cross sections, a model describing the shapes of the mass distributions of events with a Higgs boson ("signal") and of the background are determined through simulation, after various corrections have been applied to the simulation to make it faithful to the real data. These corrections and calibrations are determined on the real data using known processes, such as the two-electron Z-boson decay used to calibrate the properties of the photons resulting from the decay of the Higgs boson into two photons, the two signatures being very similar in the detector. These models are then fitted to the data in the different categories to determine the cross sections for each STXS bin. The figure below shows the model (in red) and data (in black) for all categories (88 categories) of the analysis combined.

Precision above everything

Many measurements can be made thanks to the defined categories, depending on the parameters that one decides to leave free in the fit and which are therefore determined by it. First of all, the total production rate of the Higgs boson as well as the production rates for the different main production modes are measured by determining the "signal strength", µ. The "signal strength" is defined as the ratio between the measured production rate and the theoretically predicted production rate, where 1 means that the production rate is exactly as predicted by the SM. The measured values and their uncertainties are shown opposite, where the colored dots are the measurements by production mode and the black dot represents the measurement of the total production. Here, the tH production is measured together with the ttH production, via the µtop parameter. Although fluctuations are observed with respect to unity, the results are compatible with the SM within the uncertainties. Note that the uncertainty on the total production rate is about ten percent, this measurement being dominated by the main gluon fusion production mode, while it is about thirty percent for the VBF, VH and ttH modes.

Higgs Boson dissection

Then, to go further, the cross-sections in the different STXS "bins" are measured. The figure below shows the measured values as well as their uncertainties for 24 "bins", simultaneously determined when fitting the model to the data. Here, some "bins" have been grouped together to avoid too large measurement uncertainties. The color scheme corresponds to the one used in the previous figures: the gluon fusion is in blue, the vector boson fusion and the production associated with a vector boson decaying into quarks are in orange, the production associated with a vector boson decaying into leptons is in green, and finally the ttH and tH productions are in pink and yellow respectively. The SM predictions for each point, with their theoretical uncertainties, are represented by the grey dotted boxes.

This result provides the very first dedicated study of tH production, a rare mode of production that was previously inaccessible. It is also the first measurements of ttH production in different regions of the Higgs boson transverse momentum. The measured cross sections are in very good agreement with the predictions of the Standard Model, which is still triumphant and leaves an increasingly narrow margin to New Physics. However, statistical uncertainties are still the dominant uncertainties in these measurements, meaning that new data would increase their accuracy. At the next run of the LHC, which should start in 2022, then at the High-Luminosity LHC, starting around 2027, the available data will increase very significantly (up to 20 times more data). In addition, the combinations of these measurements in different Higgs boson decay channels and in the different experiments will also increase the accuracy, in order to test the Standard Model in these smallest corners.

Contact: Julie Malclès

For further information:

http://cms-results.web.cern.ch/cms-results/public-results/preliminary-results/HIG-19-015/index.html