Introduction

Chapter 6: Nonresonant pair production of highly energetic Higgs bosons

6.1 Introduction

The Higgs boson pair production (𝐻 𝐻) in the SM provides unique sensitivity to explore the structure of the Higgs potential. Measurements of its production cross section allow us to directly access the tri-linear Higgs self coupling,𝜆_{𝐻 𝐻 𝐻}, and also the quartic coupling between two Higgs bosons and two vector bosons, known as 𝑐2𝑉. The value of𝜆_{𝐻 𝐻 𝐻}is calculated from the SM as

𝜆= 𝑚²

𝐻

2v² ≈ 0.13, (6.1)

wherevis the Higgs v.e.v. (∼246 GeV). As mentioned in Sec.2.4.2, the dominant 𝐻 𝐻 production happens via the gluon fusion process, and the second most common production mode is the vector boson fusion process. The 𝐻 𝐻 production cross section (∼32 fb at 13 TeV) is roughly 3 orders of magnitude smaller than the single Higgs production (∼55 pb at 13 TeV), and is therefore a much more difficult process to measure.

The two leading-order diagrams of the gluon fusion production (Fig.2.4), are known as the box (left) and triangle (right) diagrams. The triangle diagram depends on the 𝜆_{𝐻 𝐻 𝐻}, and also on the top-quark Yukawa coupling (𝑦_𝑡) through a top-quark loop. The box diagram only depends on 𝑦_𝑡, and therefore, when the mass of the Higgs pair (𝑚_{𝐻 𝐻}) exceeds two times the top mass threshold (2𝑚_𝑡 ≈ 350 GeV), the 𝐻 𝐻 production probability increases, as can be seen from Fig 6.1. It decreases eventually due to the decreasing probability of finding two high momentum gluons inside the protons. In the SM, the box and triangle diagrams interfere destructively, which makes the𝑔𝑔 𝐻 𝐻 cross section even smaller. The overall𝑚_{𝐻 𝐻} distribution peaks near 400 GeV, a very important feature that we will come back to later in this chapter.

To investigate the effect of deviations of the interaction strengths from their SM values, without assuming any particular BSM model, we will express them within

Figure 6.1: In the SM, the box (blue dashed line) and triangle diagram (red dashed line) for the𝑔𝑔 𝐻 𝐻 process interfere destructively. The dependence of the interfer- ence term as a function of𝑚_{𝐻 𝐻} is shown with the green dashed line. This results in a smaller overall cross-section for the 𝑔𝑔 𝐻 𝐻 process, as shown by the black solid line [174].

the𝜅-framework [168,169]. In the subsequent sections, we will use𝜅_𝜆=𝜆/𝜆^SMand 𝜅_𝑡 = 𝑦_𝑡/𝑦^SM

𝑡 . 𝜅_𝑡 has been measured to be consistent with the SM [112, 175]. The effect of having a 𝜅_𝜆 very different from the SM can be understood from Fig. 6.2.

For large values of |𝜅_𝜆 | ( > 1), the kinematic peak in the 𝑚_{𝐻 𝐻} distribution shifts from 400 GeV to 270 GeV. In this region, the triangle diagram dominates over the box diagram, and the Higgs boson in the propagator of𝑔𝑔→ 𝐻^∗ → 𝐻 𝐻is off-shell and barely above 2𝑚_𝐻(≈250 GeV). These differences in shape can be used to put strong constraints on the allowed values of𝜅_𝜆

The VBF or qq𝐻 𝐻 production cross section can be parametrized as a function of both the VVH coupling (𝑐_𝑉) and the VVHH coupling (𝑐

2𝑉), as shown in Fig.2.5.

In the subsequent sections, we will use𝜅

2𝑉 =𝑐

2𝑉/𝑐SM

2𝑉 and𝜅_𝑉 =𝑐_𝑉/𝑐SM

𝑉 . For small values of 𝜅

2𝑉, the 𝑞 𝑞 𝐻 𝐻 production cross section increases and leads to a harder 𝑚_{𝐻 𝐻} spectrum, as shown in Fig.6.3.

The ATLAS and CMS Collaborations have performed studies of Higgs boson pair production at

√

𝑠 =7, 8, and 13 TeV in the𝑏 𝑏 𝛾 𝛾 [58,178–180], 𝑏 𝑏 𝜏⁺𝜏⁻ [59, 181, 182], 𝑏 𝑏 𝑏 𝑏 [57, 183–187], 𝑏 𝑏𝑉 𝑉 [188–191] channels, as well as combinations of channels [192–194]. For the non-resonant 𝐻 𝐻 production, the current best observed (expected) 95% CL upper limit on the cross section corresponds to 3.1

Figure 6.2: The𝑚_{𝐻 𝐻} spectra for different values of𝜅_𝜆 [176].

Figure 6.3: The𝑚_{𝐻 𝐻} spectra for different values of𝜅

2𝑉 [177].

(3.1)×SM [193]. The current best observed (expected) 95% CL constraints on the self-coupling modifier are: −1.0< 𝜅_𝜆 < 6.6 (−1.2< 𝜅_𝜆 < 7.2) [193].

This analysis searches for the nonresonant𝐻 𝐻 production in the𝑏 𝑏 𝑏 𝑏decay mode where both Higgs bosons decay to two 𝑏 quarks [26]. Despite having the highest branching ratio amongst all possible 𝐻 𝐻 decays (B (𝐻 𝐻 → 𝑏 𝑏 𝑏 𝑏) ≈33.9%), this decay channel is traditionally dominated by a large QCD multi-jet background and offers a poor decay channel resolution. We target the phase space where both the Higgs bosons have a high transverse momentum (𝑝

T > 300 GeV), otherwise known

as the boosted regime. In this region, the two 𝑏quarks that decay from each𝐻 are sufficiently close together geometrically that they merge into a single large-radius jet. One can then exploit fat-jet sub-structures to obtain a better 𝑆/𝐵 in this decay channel. Recall that for 𝜅_𝜆 values close to 1, most of the 𝐻 𝐻 signal is populated around 𝑚_{𝐻 𝐻} = 400 GeV. Therefore, boosted searches like this one have a good sensitivity to SM-like phase space of 𝜅_𝜆. Additionally, small values of 𝜅

2𝑉 leads to a harder 𝑚_{𝐻 𝐻} spectrum, and thus boosted searches also have a good sensitivity to BSM scenarios with small 𝜅

2𝑉 values. This chapter will be mainly focused on the 𝑔𝑔 𝐻 𝐻 analysis, and will give a brief overview of the 𝑞 𝑞 𝐻 𝐻 analysis. The combination of the𝑔𝑔 𝐻 𝐻 and qq𝐻 𝐻 analysis is discussed in Sec.6.6.

To identify these merged Higgs candidates, we use a graph neural network (GNN) based 𝐻 → 𝑏 𝑏 classifier called ParticleNet [195], explained in more details in Sec. 6.3.4.2. Although the tagger was developed originally for single merged 𝐻 → 𝑏 𝑏 jet identification, it is significantly more powerful for identifying 𝐻 𝐻

→ 𝑏 𝑏 𝑏 𝑏 production, as the requirement for at least one of the Higgs bosons to be produced with a large transverse momentum automatically boosts the transverse momentum of the second Higgs boson. As a result, while the acceptance for the first 𝐻 to have 𝑝

T > 250 GeV is only 11%, the acceptance for the second 𝐻 to have a similarly high 𝑝

T is large (around 50%). This can be seen from the right plot in Figure6.4, where we observe that the truth level 𝑝

T of the second𝐻 peaks above 250 GeV, if the 𝑝

T of the first truth level𝐻 is required to be above 250 GeV.

Therefore, the requirement for the second 𝐻 to be successfully tagged as a single large radius𝐻 →𝑏 𝑏jet achieves about 10³background suppression without paying the price of the percent level acceptance.