5.1 Introduction

After the discovery of the Higgs boson (H) in 2012 with the LHC experiments [2], [3], [149], the detailed study of its properties has become one of the most important topics in fundamental physics. The experimental determinations of its couplings and production production rates by the CMS and ATLAS collaborations [27], [150], including the recent observations of the associated production of the Higgs boson with a \(\textrm{t}\bar{\textrm{t}}\) quark pair [151], [152], are found to be compatible with the Standard Model (SM) theoretical predictions. That said, several predicted properties remain unmeasured because of the difficulty of their experimental determination. Among them, the Higgs boson self-coupling being one of the most relevant parameters since it can be modified by physics beyond the standard model (BSM) [153]–[157].

A principled way to determine the Higgs self-coupling, and thus reconstruct the scalar potential of the Higgs field that is responsible for spontaneous symmetry breaking described in Section 1.1.4, is to measure the production of Higgs boson pairs (HH) [158]. The SM prediction for the inclusive HH production cross section for 13 TeV proton-proton collisions, assuming \(m_\textrm{H}=125.09\ \textrm{GeV}\) [27], [159], can be theoretically calculated [160]–[164] obtaining: \[ \sigma(pp \rightarrow HH + jets) = 33.49^{+4.3\%}_{-6.0\%} (\textrm{scale}) \pm 2.3\% (\alpha_S) \pm 2.1\% (\textrm{PDF})\ \textrm{fb} \qquad(5.1)\] where the listed sources of uncertainties correspond to factorisation \(\mu_\textrm{R}\) and renormalisation \(\mu_\textrm{F}\) scales, uncertainties in the strong coupling constant \(\alpha_S\), and the uncertainty associated with the parton distribution functions (PDF), respectively. The predicted cross section of the HH production process in the SM is very small, several orders or magnitude smaller than that of single Higgs production, and thus has not been directly observed the LHC data yet and will require targeted studies at the HL-LHC or other future colliders. New physics effects beyond the SM can enhance the HH production cross sections, e.g. as can be modelled by effective theories of anomalous couplings [165], in a way so HH production could be observed with the data already collected at the LHC.

The search of possible beyond the SM enhancements of HH production motivated early searches using \(\sqrt{s} = 8\ \textrm{TeV}\) LHC data [166], [167], as well as several analyses using data collected during 2015 and 2016 at the LHC experiments, including the one presented in this work. Several analyses looking for an enhancement of resonant HH production, leading to a peak in the reconstructed invariant mass of the Higgs pair due to decay of the hypothetical mediating particle, have also been performed, Such mechanism for the production of Higgs boson pairs is not considered in this analysis. Regarding non-resonant production of HH pairs at at \(\sqrt{s} = 13\ \textrm{TeV}\), both ATLAS and CMS collaborations have carried out searches for different decay channels including \(\textrm{b}\bar{\textrm{b}}\textrm{b}\bar{\textrm{b}}\) [168], \(\textrm{b}\bar{\textrm{b}}\textrm{l} \nu\textrm{l} \nu\) [169], \(\textrm{b}\bar{\textrm{b}} \tau \tau\) [170] and \(\textrm{b}\bar{\textrm{b}} \gamma \gamma\) [171]. In all the mentioned analyses, one of the Higgs bosons decays to a \(\textrm{b}\bar{\textrm{b}}\) quark pair, which its the most likely decay model (with a branching fraction of 57.7% for \(m_\textrm{H}=125\ \textrm{GeV}\)), in order to consider a large fraction of expected HH decays. The CMS Collaboration has also carried out an analysis complementary to the one presented here, where one of the \(\textrm{b}\bar{\textrm{b}}\) is highly boosted and thus reconstructed as a single large-area jet [172]. The most stringent expected upper limit on the SM HH production cross section to date, which corresponds to a \(95\%\) C.L. exclusion for rates about 19 times the SM prediction, was obtained by the CMS \(\textrm{b}\bar{\textrm{b}} \gamma \gamma\) channel search [170], which yielded an observed upper limit of 22 times the SM. The ATLAS \(\textrm{b}\bar{\textrm{b}}\textrm{b}\bar{\textrm{b}}\) channel search has a similar experimental reach [168], studying the same final state considered in this analysis, however with a different methodology regarding their summary statistic and background estimation.

A detailed description of the main characteristics and results of an analysis searching for HH production using CMS experiment data, with both Higgs bosons decaying into \(\textrm{b}\bar{\textrm{b}}\) quark pairs, is included in this chapter. The data considered was acquired by the CMS detector during the year 2016, corresponding to an integrated luminosity of \(35.9\ \textrm{fb}^{-1}\). In the final state considered here, each of the four \(\textrm{b}\) quark results in a distinct reconstructed jet. While it is the most likely decay mode for the Higgs pair, a much larger quantity of similar events with four or more jets are expected from hard quantum chromodynamics (QCD) interactions. The differences between signal and background are used to increase the sensitivity by using as a summary statistic the prediction of a multivariate probabilistic classifier. Because the expected contribution from the QCD multi-jet processes is so abundant, it could not be modelled with the required precision with the available simulations. To address this issues, a method for carrying out a fully data-driven background estimation was developed, that is described in Section 5.6.