14.1 Introduction

We now present two searches for the simultaneous production of two highly energetic Higgs bosons using the CMS detector at the LHC and the AI developments described in the previous chapter. The first search targets nonresonant Higgs pair ($\mathrm{\text{H}}\mathrm{\text{H}}$) production as predicted by the standard model (SM) to measure critical SM parameters; while the second looks for resonant Higgs (H) and Higgs-like (Y) production resulting from new beyond-SM (BSM) particles (X) in the high energy Higgs sector, to explain mysteries such as the hierarchy problem and matter-antimatter asymmetry.

In the SM, $\mathrm{\text{H}}\mathrm{\text{H}}$ production is expected to be an extremely rare process: out of the 1,000,000,000,000,000 collisions observed by CMS in Run 2 of the LHC, only 6000 of them are expected to produce two Higgs bosons. On top of that, the each Higgs decays into a variety of different particles, or “final states”, splintering the signal further into myriad different experimental signatures, or “channels” (shown in Figure 4.24).

However, as detailed in Chapter 4.3, its measurement can uniquely probe the Higgs trilinear self- ($c_{\lambda }$) and quartic two-vector-boson- ($c_{2V}$) couplings, the former being critical to understanding the Higgs potential and the nature of electroweak symmetry breaking. Indeed, this is why it is considered one of the flagship measurements of the CMS and ATLAS experiments’ HL-LHC programs. Due to the rarity of $\mathrm{\text{H}}\mathrm{\text{H}}$ production, the current measurements of these couplings are some of our least precise, with $c_{\lambda }$ constrained to $[-1.39,7.02]$ and $c_{2V}$ to $[0.62,1.42]$ times their SM prediction at $95\%$ confidence level (CL) by CMS [32]. This calls for new, innovative techniques to cover the vast phase space of $\mathrm{\text{H}}\mathrm{\text{H}}$ decays.

This chapter presents one such idea, measuring for the first time the all-hadronic $\mathrm{\text{H}}\mathrm{\text{H}}\to \mathrm{\text{b}}\overline{\mathrm{\text{b}}}\mathrm{\text{V}}\mathrm{\text{V}}$ channel: where one Higgs decays into a pair of bottom quarks ($\mathrm{\text{b}}\overline{\mathrm{\text{b}}}$), and the other into a pair of vector bosons ($\mathrm{\text{V}}\mathrm{\text{V}}$), which then decay into four quarks ($4\mathrm{\text{q}}$) (Figure 14.1, left). While not a traditional “golden channel” (Chapter 4.3.3), due to its complicated and noisy experimental signature, by 1) targeting the extremely high energy $\mathrm{\text{H}}\mathrm{\text{H}}$ regime, where both Higgs bosons are produced highly Lorentz-boosted; and 2) exploiting and developing advanced ML techniques for identifying such boosted Higgs bosons (Chapter 13), we are able to achieve competitive sensitivity to boosted $\mathrm{\text{H}}\mathrm{\text{H}}$ production and the $c_{2V}$ coupling.

By measuring $\mathrm{\text{H}}\mathrm{\text{H}}$ production and couplings, especially in the boosted regime, the nonresonant search is also indirectly sensitive to new physics in the very high energy Higgs sector, which could manifest as deviations from SM predictions. To complement this, this chapter also presents a resonant search for direct evidence of such new physics, in the form of new particles in the Higgs sector: specifically, a heavy scalar X which can decay into a Higgs and Higgs-like boson Y, in the same final state (Figure 14.1, right). As described in Chapter 4.3.4, such additions to the Higgs sector are motivated by a variety of BSM models, such as composite Higgs models, supersymmetry, and extra dimensions, to solve the matter-antimatter asymmetry and hierarchy problems. The $\mathrm{\text{b}}\overline{\mathrm{\text{b}}}\mathrm{\text{V}}\mathrm{\text{V}}$ channel is particularly important for this search because for heavy Y boson masses, assuming SM Higgs-like couplings, the $\mathrm{\text{Y}}\to \mathrm{\text{V}}\mathrm{\text{V}}$ decay modes are completely dominant (Figure 4.18). Hence, the $\mathrm{\text{b}}\overline{\mathrm{\text{b}}}\mathrm{\text{V}}\mathrm{\text{V}}$ channel is expected to have the highest branching fraction. The resonant search exploits the same techniques and developments as the nonresonant, but searches more broadly for excesses, or “bumps”, in the resonant di-Higgs mass spectrum corresponding to the mass of the new particle X.

This chapter is organized as follows. Section 14.2 outlines the analysis strategy for both searches, based on the ML techniques described in Chapter 13 for identifying boosted Higgs jets, before detailing the online and offline event selection for both the nonresonant and resonant searches in Section 14.3. The background estimation strategy and systematic uncertainties are then described in Sections 14.4 and 14.5, respectively, followed by the Run 2 results of the nonresonant and expected results of the resonant searches in Section 14.6. Finally, we conclude in Section 14.7 with a summary and outlook for boosted $\mathrm{\text{H}}\mathrm{\text{H}}$ analyses in Run 3 and the HL-LHC.