Maximizing the significance in Higgs boson pair analyses

We study Higgs pair production with a subsequent decay to a pair of photons and a pair of bottoms at the LHC. We use the log-likelihood ratio to identify the kinematic regions which either allow us to separate the di-Higgs signal from backgrounds or to determine the Higgs self-coupling. We find that both regions are separate enough to ensure that details of the background modeling will not affect the determination of the self-coupling. Assuming dominant statistical uncertainties we determine the best precision with which the Higgs self-coupling can be probed in this channel. We finally comment on the same questions at a future 100 TeV collider.

Figure 1

Feynman diagrams contributing to Higgs pair production at the LHC. Figure from Ref. [3].

Figure 2

First two panels: normalized invariant mass distributions of the dijet and diphoton systems as used in madmax and from CMS [31, 32]. Next four panels: di-Higgs invariant mass, transverse momentum spectra used in madmax, including NLO corrections [28], and including the fast detector simulation delphes [33].

Figure 3

Kinematic distributions after trigger cuts for the SM signal (red) vs the $bb\gamma \gamma$, $bbj\gamma$, $cc\gamma \gamma$, and $ZH$ backgrounds. The solid black line shows the differential distribution of the significance.

Figure 4

Kinematic distributions for the SM triangle diagram only (upper) and the SM box diagram only (lower). We require trigger cuts for the signal (red) vs the $bb\gamma \gamma$, $bbj\gamma$, $cc\gamma \gamma$, and $ZH$ backgrounds. The solid black line shows the differential distribution of the significance.

Figure 5

Differential distributions assuming a modified Higgs self-coupling of $\lambda /{\lambda }_{\mathrm{SM}}=0$ (upper panels) and $\lambda /{\lambda }_{\mathrm{SM}}=5$ (lower panels). We compare only the two Higgs pair signals and neglect backgrounds for illustration.

Figure 6

Signal cross section (red dashed line) and maximum significance (black solid line) for observing an anomalous Higgs self-coupling at the LHC with an integrated luminosity of $3{\mathrm{ab}}^{-1}$. We also show the significance from a cut-based rate measurement using the cuts suggested in Ref. [35] (black dashed line).

Figure 7

Differential distributions assuming a modified Higgs self-coupling of $\lambda /{\lambda }_{\mathrm{SM}}=0$, 2, 5 (left to right). Unlike for the illustration in Fig. 5 we compare the two proper hypotheses including signal and backgrounds.

Figure 8

Signal cross section (red) and maximum significance (black) for observing an anomalous Higgs self-coupling at a 100 TeV hadron collider with an integrated luminosity of $3{\mathrm{ab}}^{-1}$ and $20{\mathrm{ab}}^{-1}$. The setup corresponds to Fig. 6 for the high-luminosity LHC.

Figure 9

Differential distributions assuming a modified Higgs self-coupling of $\lambda /{\lambda }_{\mathrm{SM}}=0.8$, 1.2 in the presence of backgrounds. The setup corresponds to Fig. 7 for the high-luminosity LHC.