By CMS Collaboration

Studying the production of two Higgs bosons is the most obvious way to understand the field responsible for the Higgs boson. A new result by the CMS collaboration gets closer than ever to measuring this field and its physics prediction.

The Higgs boson (H), discovered in 2012 by the ATLAS and CMS experiments, is the pinnacle of the scientific results obtained from the large hadron collider (LHC) at CERN. The properties of the Higgs boson are studied in minute detail by a large community of physicists using the data collected at the LHC. The experimental measurements are compared with predictions from the standard model, to vindicate it or to look for hints of physics beyond the standard model, the exact nature of that additional physics is yet unknown. This search for new physics includes the important aspect of studying the Higgs boson and its different interactions with other particles, the so-called couplings, comparing the observed behaviour to the prediction by the standard model. By now, reasonably precise measurements of the Higgs coupling to W and Z bosons, the top and bottom quarks, tau lepton and muon indicate that the mechanism of Electroweak Symmetry Breaking is likely to be very similar to the one proposed by Brout, Englert, and Higgs about 50 years ago. But since the story is far from complete, there is no reason for physicists to relax. What if the beyond standard model physics discretely affects the particles or properties that are not yet experimentally observed?

The fundamental particles that we know get their intrinsic masses via interactions with the Brout-Englert-Higgs field. Consequently, that also includes the Higgs boson itself! Naturally, that Higgs boson self-interaction is a direct consequence of the Brout-Englert-Higgs field behaviour, so of the exact physics parameters that describe the field. The Brout-Englert Higgs field has a considerable impact not only on our understanding of the properties of the very early universe but also influences its future. In the standard model it is possible that three or four Higgs bosons may interact via a single vertex, and with a strength of self-coupling that is called the Higgs self-coupling, λ. Obviously, measuring the Higgs boson self-coupling is one of the most important goals of the LHC physics program.

two feynman diagrams
Figure 2: These are some of the Feynman diagrams that describe how to produce a pair of Higgs bosons at the LHC.

The fundamental interactions of particles are represented with so-called Feynman diagrams. Figure 2 illustrates some of the possibilities of how the Higgs will interact with itself at the LHC. In these scenarios, two Higgs bosons would be produced at the same time. This would mean that the self-interaction can be estimated by measuring the rate of di-Higgs boson (HH) production. During the proton-proton collisions of the LHC, the HH production rate is about 1000 times smaller than the production rate of one Higgs boson.

In the data already collected by the CMS experiment, di-Higgs boson production is not yet expected to show up. But CMS physicists still look for di-Higgs bosons even now, because any deviation from the standard model, be it a stronger coupling, or the existence of additional particles, is likely to enhance the amount of di-Higgs boson production, meaning it could already be visible now. Any observed difference compared to the standard model prediction will be a hint of new physics at play. Using data collected by the CMS experiment from 2016 through 2018 and considering a particular class of signatures in the detector, the CMS collaboration has recently derived the most stringent constraint on the value of λ to date. The analysis also had a peek at other couplings and indicated all is well with the standard model, within large uncertainties of course!

The collisions examined for di-Higgs boson production consisted of at least a pair of photons and a pair of hadronic jets initiated by b quarks. One Higgs boson can create one of these signatures, so asking for both simultaneously is a good way to search for two independent decays of two Higgs bosons. One example of the improvements that were made to the search was to separate the different production modes of the Higgs boson pairs. This included a different and a specific production mode indicated by the presence of two extra light quark jets in the final state, a sign that the collision is one of those rare collisions where the LHC acts as a boson collider. This is a very striking signature, which can be clearly seen in Figure 1, which shows one of the candidate collisions collected in 2018. Accounting for this second type of HH production improved the overall sensitivity of the analysis and gives additional information in the coupling between two Higgs bosons and W (or Z) bosons. That coupling is constrained for the first time by the CMS experiment.

invariant mass distribution showing a possible (but not yet significant) peak of HH production
Figure 3: The diphoton invariant mass distribution in data (points) for ɣɣbb events consistent with di-Higgs production. The red line describes what the data would look like including the tiny HH signal contribution along with the expected backgrounds, while the blue line represents the situation without HH contribution. The dotted curve refers to the expected continuum background.

It is worthwhile to mention that cutting-edge results at the LHC require a lot of innovation. For this specific result, several innovative strategies were introduced compared to earlier studies, and substantial improvements were obtained by applying multiple machine learning algorithms to identify the photons, the b quark jets, and the selection of the signal that is used to remove the overwhelming background from other particles produced at the LHC, for example, backgrounds where only one Higgs boson was made. With all these improvements, this new analysis produced the best results to date. Figure 3 presents one of the distributions (the invariant mass of two photons) derived from data. The distribution is interpreted in terms of double Higgs and single Higgs production, peaking over a falling spectrum that is created when the two photons do not come from the same particle.  

The HH production process being extremely feeble, there is significant statistical uncertainty in the derived conclusion about the data. Still, it is possible to exclude the possibility that anomalous effects create a much higher rate of HH production: we now know that the HH rate is less than about 7.7 times the rate predicted by the standard model. This, in turn, translates into the self-coupling being like the standard model, albeit within uncertainties that still allow some possibility for deviations. The analysis also ruled out a large part of parameter space defined by signatures predicted by physics beyond the standard model.

These results are extremely encouraging to consolidate the nature of the Higgs boson, the nicest prize from the LHC so far. The CMS experiment is poised to hopefully see the production of Higgs boson pairs with better confidence in the near future when the LHC will start operating again from 2022. The observation and study of di-Higgs production and the Higgs field are part of the main topics to study at the High-Luminosity LHC, that will start in 2027 and will run until the mid-2030s.

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