The strength of the interaction between the Higgs field and a particle determines the mass it obtains from the Higgs and it is a mystery why the interaction strength is different for different particles. This puzzle is exacerbated as the leptons, quarks and neutrinos appear to be grouped into thee different generations with hierarchies of masses. It is therefore vital to measure the Higgs couplings to test if the Standard Model is indeed describing the properties of these particles.

Since the Higgs boson discovery, there has been an enormous effort to understand how the Higgs boson couplings with the other fundamental particles compare with the precise predictions of the standard model. The measurements performed so far have focused on the Higgs boson interactions with the most massive particles, such as the W and Z bosons, and only with particles from the most massive (third) generation, the top and bottom quark and the tau lepton. The interaction of the Higgs boson with the large span of lighter particles is so far experimentally untested. Measuring the full spread of Higgs boson interactions is a critical test necessary to understand whether the Higgs field can explain the full range of particle masses. Measuring the interaction of the Higgs boson with the muon, with a mass nearly two thousand times smaller than that of the top quark, is the next experimental frontier. Doing so will allow examining the Higgs field interactions with particles belonging to a different generation (the second) for the first time, and at a so-far untested mass scale.

The physics process of the Higgs boson decaying into muons is a rare phenomenon as only about one Higgs boson in 5000 decays into muons. These new results have pivotal importance for fundamental physics because they indicate for the first time that the Higgs boson interacts with second-generation elementary particles.

CMS found evidence of this decay with 3 sigma significance, which means that the chance of seeing the Higgs boson decaying into a muon pair from statistical fluctuation is less than one in 700. ATLAS’s two-sigma result means the chances are one in 40. The combination of both results would increase the significance well above 3 sigma and provides strong evidence for the Higgs boson decay to two muons.

“CMS is proud to have achieved this sensitivity to the decay of Higgs bosons to muons, and to show the first experimental evidence for this process. The Higgs boson seems to interact also with second-generation particles in agreement with the prediction of the Standard Model, a result that will be further refined with the data we expect to collect in the next run,” said Roberto Carlin, spokesperson for the CMS experiment.

Besides its world-class muon detectors, the CMS detector uses a tracking system to measure the trajectories of charged particles with high precision. The tracking system measures muons as they pass through the very strong 3.8T magnetic field. The CMS detector reconstructs a typical muon produced in an LHC collision within 1-2% of its true momentum and with very high efficiency. These extraordinary reconstruction capabilities have made it possible for the CMS Collaboration to report the first evidence for the Higgs field's meager interaction with muons.  The measurement sensitivity has been improved significantly compared to previous results. Four separate analyses were necessary to identify candidate signal events from the different modes by which Higgs bosons can be produced. The background prediction strategy includes sophisticated machine learning techniques like deep neural networks that help to differentiate the signal from the substantial background. The characteristic expected signature of the Higgs boson decay to muons is a small excess of events in the invariant mass of muon pairs near the Higgs boson mass of 125 GeV.

Figure 1: The Higgs boson candidate invariant mass distribution for the weighted sum of all event categories. In the lower panel, which subtracts the predicted background from the data, an excess of events is observed in data that is consistent with the Higgs boson decaying to a pair of muons, indicated by the red line.

The following figure (Fig.2) compares the latest CMS measurements of the Higgs boson interactions to the prediction by the standard model. With this new result, we can examine the Higgs field interaction with masses that are more than a factor 10 smaller than before. Though the muon measurement looks consistent with the blue line of the standard model predictions, there are still substantial uncertainties that need to be further reduced.

Figure 2: A summary of the CMS measurements of the Higgs boson couplings to the other fundamental particles, with the predictions by the standard model indicated by the dashed black line. In the lower panel, the ratio between the measured coupling and the standard model prediction is shown. This new CMS result presents the first measurement of the Higgs boson coupling to the muon, indicated by the left-most data point.

What makes these studies even more challenging is that, at the LHC, for every predicted Higgs boson decaying to two muons, there are thousands of muon pairs produced through other processes that mimic the expected experimental signature. The characteristic signature of the Higgs boson’s decay to muons is a small excess of events that cluster near a muon-pair mass of 125 GeV, which is the mass of the Higgs boson. Isolating the Higgs boson to muon-pair interactions is no easy feat. To do so, both experiments measure the energy, momentum and angles of muon candidates from the Higgs boson’s decay. To further increase the sensitivity of their analysis, ATLAS physicists divided their events into 20 mutually-exclusive “categories”. These categories focussed on the features of an event – such as the number and properties of its additional jets or leptons – to target specific production modes of the Higgs boson, including the scattering of two gluons or two weak bosons,  and the associated production with a weak W or Z boson or a top-quark pair. Inside these categories, events were further split using dedicated multivariate discriminants (Boosted Decision Trees). As a result of this complex division, ATLAS physicists could separate out the few Higgs-boson-like events from the more common, but less Higgs-boson-like, events.

In addition, ATLAS physicists developed a robust (and ambitious) background-modelling strategy using a variety of simulation techniques to create more than 10 billion simulated events. Detailed ATLAS detector simulations (totalling about five times the Run-2 dataset) were complemented by dedicated fast simulation samples (more than 100 times the dataset). The fast simulation samples were crucial to ensure that the overwhelming backgrounds could not mimic a false signal, while maximising the analysis sensitivity to a real signal.

Figure 3: The invariant-mass spectrum of the reconstructed muon-pairs in ATLAS data. Events are weighted according to the expected signal-to-background ratio of their category. In the top panel, the signal-plus-background fit is visible in blue, while in the lower panel the fitted signal (in red) is compared to the difference between the data and the background model. (Image: ATLAS Collaboration/CERN).

The new ATLAS result gives a first hint of the Higgs boson decaying to a muon pair; the significance of the observed signal amounts to 2.0 standard deviations and the ratio of the observed signal yield to the one expected in the Standard Model is 1.2 ± 0.6. The data, together with the signal-plus-background fit, are shown in Figure 3, where data events are weighted to reflect the signal-to-background ratio of their respective categories.

“This evidence of Higgs boson decays to second-generation matter particles complements a highly successful Run 2 Higgs physics programme. The measurements of the Higgs boson’s properties have reached a new stage in precision and rare decay modes can be addressed. These achievements rely on the large LHC dataset, the outstanding efficiency and performance of the ATLAS detector and the use of novel analysis techniques,” said Karl Jakobs, ATLAS spokesperson.

The results, which are so far consistent with the Standard Model predictions, used the full data set collected from the second run of the LHC. Because the Higgs boson decay to muons is so rare, the precision of this measurement is limited mainly by the amount of data collected so far. The quantity of accumulated data is expected to double from the upcoming Run-3 of the LHC, allowing for an improvement in the precision of this vital measurement in the next years. In the longer term, the unparalleled data quantities anticipated from the High-Luminosity LHC will enable the high-precision measurement of this interaction, one of the key milestones of the LHC physics program in the years to come.