ATLAS searches for di-Higgs production at 13 TeV and prospects for HL-LHC

The latest results on production of Higgs boson pairs at 13 TeV by the ATLAS experiment at LHC are reported, including a combination of six different decay modes. Results include bb¯τ−τ+ , bb¯bb¯ , bb¯γγ , bb¯WW , WWWW and WWγγ final states, and they are interpreted both in terms of sensitivity to the SM and as limits on κ λ , a scaling of the triple-Higgs interaction strength. The most stringent constraint on di-Higgs production cross-section is set at 6.9 times SM cross-section and κ λ is constrained in the range −5–12 at 95% confidence level. A new search dedicated to the Vector-Boson-Fusion production was performed in the bb¯bb¯ final state. No significant excess, relative to the background-only Standard Model expectation, is observed and interpretation in terms of the coupling between a Higgs boson pair and two vector bosons is also provided: coupling values normalized to the Standard Model expectation of κ2V<−0.56 and 2.89<κ2V are excluded at the 95% confidence level. Future prospects of testing the Higgs self-couplings at the High Luminosity LHC are also reported.


Introduction
The Higgs boson (H) was discovered by the ATLAS and CMS collaborations in 2012 using proton-proton (pp) collisions at the Large Hadron Collider (LHC) [1,2]. Since then a lot of studies have been performed in order to investigate with increasing precision the properties of the Higgs boson. Even if up to now no significant discrepancy has been observed with respect to the Standard Model (SM) expectations, studies of Higgs Boson final states offer new opportunities in searching for new physics beyond the SM (BSM). In particular, many models predict enhanced cross-sections of Higgs pair production in pp collision. Spin-0 resonances that may decay into Higgs boson pairs, appear in scenarios beyond the SM [3,4]. Enhanced non-resonant Higgs boson pair production is predicted by many models, for example those featuring light coloured scalars [5] or new contact interactions, such as direct tt HH vertices [6,7].
In pp collisions at LHC, HH production is mainly due to two processes. The first one is the gluon-gluon Fusion (ggF) process whose diagrams are shown in figure 1. In the SM, the non-resonant processes of figures 1(a) and (b) appear, and the interference between the two diagrams is destructive. However, the amplitude of the diagram(a) is proportional to the Higgs self-coupling (HHH) and the cross-section can be enhanced significantly by new physics. The possible ggF resonant production of a hypothetical new heavy scalar state X is shown in figure 1(c). The second process is Vector Boson Fusion (VBF) whose diagrams are shown in figure 2. The VBF process (  pp HHjj) is characterized by the presence of two jets ( j) with a large rapidity gap resulting from quarks from which a vector boson (V ) is radiated. In the SM, three different types of couplings are involved in non-resonant HH production via VBF: HHH coupling, the Higgs-boson-di-vector-boson coupling (VVH) and the quartic (di-vector-boson-di-Higgs-boson, or VVHH) coupling, and the amplitudes of figures 2(b) and (c) are canceled out by negative interference. The amplitude of the diagram (c) is proportional to the VVHH coupling and the cross-section can be enhanced significantly due to possible new physics effects. The resonant production via VBF of a possible new BSM scalar state X is shown in figure 2(d). The resonant productions via ggF and VBF are complementary to each other for the specific parameters of the model due to the different couplings (tt X in ggF and VVX in VBF) involved in the production, as we can see in the diagrams.
In the ATLAS experiment, the search for the Higgs pair production via ggF and VBF are conducted using Run2 datasets of integrated luminosities in the range 27-139 fb −1 at = s 13 TeV. The significant analyses will be reported.

Searches for HH production via ggF using 2015-16 data
The searches for the HH production via ggF have been performed using datasets of integrated luminosities 27-36 fb −1 taken in 2015-2016 with = s 13 TeV at LHC. Table 1 shows the branching ratios in the different channels of the HH decay. The process  HH bbbb¯has the largest branching ratio but suffer from high backgrounds from QCD multi-jet. On the other hand, the other processes which contain leptons or photons in the final state, have lower statistics than  HH bbbb¯but much lower background. Therefore, we can search for the HH production in various final states. The analysis has been performed in the processes [12], and bbWW [13]. In order to search for the HH process, the analyses have to be well designed depending on the characteristic kinematics of the signal. For example, since the Higgs bosons are boosted in the hard scattering event, the analysis should be optimized for the HH invariant masses (m HH ) correlated with the energy of the parton scattering in the pp collision. Furthermore, the component of the backgrounds is different for each process. Therefore, the selection criteria should be well designed according to the kinematics of the signals and the backgrounds, specific to each process. In the following, the selected analyses and the combination results of all analyses are overviewed.

Search for HH-b bb b process via ggF
The feature of  HH bbbb¯process is high statistics due to the largest branching ratio of the HH decay. In this search, two approaches for the regions of low m HH and high m HH are pursued. The first one for the low m HH region, called 'resolved analysis', requires the presence of four b-jets. Resolved analysis has sensitivity in the region of < < m 260 GeV 1400 GeV

HH
. On the other hand, the angle between the two b-jets from boosted Higgs boson become small in high m HH region making it difficult to experimentally resolve the two b-jets. For this reason, in order to get a reasonable signal efficiency, the analysis in the high m HH region, called 'boosted analysis', requires two large radius jets with at least one b-tagged small radius jet matched to it. The boosted analysis has sensitivity in the region of < < m 800 GeV 3000 GeV HH . In both cases, the backgrounds are QCD multi-jet (about 95%) and tt (about 5%). The QCD multi-jet is modeled using data driven method with reduced b-tagging dataset and the tt is estimated using Monte Carlo (MC) sample. Figure 3 shows the distribution of m HH in the signal region of the Resolved analysis and the Boosted analysis. We observe no significant excess. The 95% confidence level (CL) upper limit on the non-resonant production is 147 fb, which corresponds to 12.9 times the SM expectation.

Search for HH-b
bτ À τ + process via ggF The t t  -+ HH bb process has fairly high statistics and quite clean final states in case of leptonic decay of the τ-lepton. In this analysis, the t t lep had and t t had had channels are considered, where the subscripts (lep = electron or muon, had = hadrons) indicate the decay mode of the τ-lepton. To distinguish the signal and the backgrounds of tt, single-top-quark, QCD multi-jet, and W or Z bosons associated with jets in the entire range of m HH , a Boosted Decision Tree (BDT) is used. Several variables have been used as input to the BDT, among them the invariant masses of HH, bb, and tt, the angles of the bb and tt (for more details see [9]). The uncertainty is dominated by the data statistics and the observation was consistent with no enhanced di-Higgs production. The 95% CL upper limit on the non-resonant production is 12.7 times the SM expectation [9].

Combination of different channels
The combination of the analyses of  HH bbbb¯, t t -+ bb , gg bb , WWWW, gg WW , and bbWW has been performed [14]. Figure 4 shows the 95% CL upper limit on the cross-section of the ggF non-resonant SM HH production as a function of κ λ , the strength of the Higgs self-coupling, normalized to the SM value. The combination results in an observed (expected) upper limit of about 6.9 (10) times the SM cross-section. The coupling κ λ is constrained in the range −5-12 at 95% CL. Figure 5 shows the 95% CL upper limit on the cross-section of the ggF resonant HH production as a function of the mass of a heavy scalar decaying to HH. The limits on the heavy scalar resonance have been interpreted as constraints on the EWKsinglet model

Search for HH-b blνlν process via ggF
For precise measurement of the Higgs coupling, it is important to exploit different channels and combine their results. ATLAS focused on the 2-leptons final states to study the processes  HH bbWW , bbZZ , and t t -+ bb [15]. In order to distinguish the signal from the main backgrounds of top and Z/γ processes, a discriminant has been constructed exploiting a deep neural network (DNN). The input variables for the DNN include the transverse momentum of leptons and b-jets and the angle between the leptons (for more details see [15]). Observation is consistent with SM hypothesis. An observed (expected) upper limit at 95% CL of about 40 (29) times the SM cross-section has been obtained, which means a factor 10 improvement on previous bbWW result [13].

Search for HH-b bb b process via VBF
This analysis focuses on the HH production via VBF and has been performed adding the VBF jet selections to the di-Higgs selection from ggF resolved analysis [16]. Furthermore, the b-jet energy correction based on BDT is implemented to account for energy loss due to semi-leptonic decays and soft particles result in out-of-cone leakage. As a result, the resolution of the mass of the reconstructed Higgs boson is improved by 25%. The background is dominated by the QCD multi-jet and it is estimated by data-driven method with reduced b-tagging as well as in ggF  HH bbbb¯analysis. Figure 6 shows the invariant mass of the 4b-jets, m 4b . No significant deviation was observed. Figure 7(a) shows the 95% CL upper limit on the crosssection of the production of a spin-0 resonance decaying into two Higgs bosons via VBF. This result is complementary with the ggF analysis. Figure 7(b) shows the 95% CL upper limit on the cross-section of the non-resonant signal with VVHH coupling modifier k V 2 . The excluded region at 95% CL for the VVHH coupling normalized to the SM expectation is k < -0.56

HL-LHC prospects
High luminosity LHC (HL-LHC) will deliver more than 3000fb −1 at = s 14 TeV by late 2030ʼs. The latest studies for the Higgs physics at HL-LHC are presented in [17], thanks to a joint ATLAS+CMS+Theory effort. Regarding the di-Higgs production, the analyses of Run2 datasets, using integrated luminosities of 27-36fb −1 , has been combined with extrapolated statistics and expected systematics. The signal significance on the SM is expected to be 4σand κ λ constraint is expected to be 0.1<κ λ <2.3 at 95% CL with combined ATLAS and CMS results. Note that the new analysis with full Run2 dataset are not included in this  predictions. The limit on k V 2 is also expected to be improved not only for the much larger statistics but also for the inclusion of more channels and the improved detector performances.

Conclusion
The HH studies can access the SM Higgs couplings and new physics beyond the SM. A combination of all 2015-16 ATLAS analyses and two new analyses performed on the full LHC-Run2 dataset are summarized. No observation for enhanced HH production has been found up to now. The most stringent constraint on HH production cross-section is set as 6.9 times the SM cross-section and the κ λ is constrained in the range −5-12 at 95% CL by ggF analyses. The first constraint on VVHH coupling modifier has been set to be k < -0.56 V 2 and k < 2.89 V 2 by the VBF analysis of  HH bbbb¯process. The HL-LHC prospects with a total integrated luminosity of the order of 3000fb −1 at 14TeV will allow a discovery significance of 4σfor the SM di-Higgs production process and κ λ constraints of 0.1<κ λ <2.3 at 95% CL with combined ATLAS and CMS results. Inclusion of new channels, new ideas for physics analysis, and improved detector performances can further improve the measurement.