Probing the Goldstone equivalence theorem in heavy weak doublet decays

This paper investigates the decays from heavy Higgsino-like weak doublets into $Z$, $h$ bosons and missing particles. When pair-produced at the LHC, the subsequent $Z$, $h\to \ell \ell$, $b\overline{b}$ decays in the doublet decay cascade can yield $4\ell$, $2\ell 2b$ and $4b+{\cancel{E}}_{\mathrm{T}}+j(\mathrm{s})$ final states. Mutual observation of any two of these channels would provide information on the associated doublets’ decay branching fractions into a $Z$ or $h$, thereby probing the Goldstone equivalence relation, shedding additional light on the Higgs sector of beyond the Standard Model theories and facilitating the discrimination of various contending models, in turn. We compare the $Z/h$ decay ratio expected in the minimal supersymmetric model, the next-to-minimal supersymmetric model (NMSSM)and a minimal singlet-doublet dark matter model. Additionally, we conduct a full Monte Carlo analysis of the prospects for detecting the targeted final states during 14 TeV running of the LHC in the context of a representative NMSSM benchmark model.

Figure 1

Near symmetric branching ratio of ${\chi }_{2,3}^0$ decays in the SDF dark matter model. $M_S=50\mathrm{GeV}$ and $M_D=200\mathrm{GeV}$ throughout.

Figure 2

The signal significance metric $S/\sqrt{1+B}$ is projected for each of the targeted final state topologies at a luminosity of $\mathrm{3,000}{\mathrm{fb}}^{-1}$ at the $\sqrt{s}=14\mathrm{TeV}$ LHC, using statistical errors on the simulated background estimation only. Collider modeling is based on NMSSM benchmark II, which features 270 GeV Higgsinos and a $Z/h$ ratio of ${\xi }^{Z/h}=2.1$. The horizontal axis represents numerical scaling of the production cross section relative to this benchmark. The optimized event selections employed are summarized in Table 5. Supplementary cuts on ${\cancel{E}}_{\mathrm{T}}$ are not considered here, although this could become a favorable strategy at very large luminosity or cross section for the middle $2\ell 2b$ scenario, as elaborated in Sec. 6. Notice that the scaling of the postcut $\sigma$ depends on both the Higgsino production cross section and the neutralino decay branching into the specific final state categories. Particularly at large luminosity, systematic errors in the background will likewise be important, summed in quadrature with the statistical fluctuation of the background.

Figure 3

Signal and background event shapes are compared for the final state topology with $4^{+}$ light leptons (category I). The $t\overline{t}$ background component delivers no appreciable contribution to this final state. Left: Over 90% of the signal features a reconstructed OS-LF dilepton in the $Z$-boson mass window $(92\pm 5)\mathrm{GeV}$. About half of the signal reconstructs precisely a single $Z$, whereas almost 85% of the unified vector backgrounds are actually observed to reconstruct two pair. Right: Neither the signal nor the dominant $VV+\text{jets}$ background are likely to be tagged for a $b$ jet at beyond the percent level, although likelihood for the signal is somewhat greater by comparison.

Figure 4

Signal and background event shapes are compared for the final state topology with $4^{+}$ light leptons (category I). The $t\overline{t}$ background component delivers no appreciable contribution to this final state. Left: The leading vectors plus jets background relies on jet mismeasurement in order to generate missing energy, and the ${\cancel{E}}_{\mathrm{T}}$ azimuthal direction is thereby here observed to be much more strongly correlated (smaller $\mathrm{\Delta }\varphi$) with the direction of a single hard jet than is the case for the signal’s legitimate missing energy. Right: Likewise, the quantity of missing transverse energy observed in signal is generally a much more substantial multiplier of the estimated uncertainty $\sqrt{H_{\mathrm{T}}}$ in the hard event scale.

Figure 5

Signal and background integrated event counts are compared for the final state topology with $4^{+}$ light leptons (category I) at a luminosity of 300 events per femtobarn as a function of the missing transverse energy ${\cancel{E}}_{\mathrm{T}}$ cut threshold. Left: The raw event categorization is intrinsically low background, although a weak signal may still struggle to compete at low missing transverse energy. Right: Enacting the secondary event selections (${\cancel{E}}_{\mathrm{T}}/\sqrt{H_{\mathrm{T}}}>6.0{\mathrm{GeV}}^{1/2}$, $0\tau$, 0 B’s) suggested by Figs. 3 and 4 preferentially suppresses the background, to a point approaching elimination. There is then no residual necessity for large missing energy, although neither is a modest cut in the vicinity of ${\cancel{E}}_{\mathrm{T}}>100\mathrm{GeV}$ strongly disfavored.

Figure 6

Signal and background event shapes are compared for the final state topology with 2–3 light leptons and $2^{+}$ $b$ jets (category II). Left: Around 70% of the signal features an OS-LF dilepton pair with an invariant mass of $92\pm 5\mathrm{GeV}$, whereas the same holds true for only approximately 3% of the $t\overline{t}$ background component. Right: The relative (dimensionful) significance of the missing transverse energy as a numerical ratio of ${\cancel{E}}_{\mathrm{T}}$ to the square-root of the event scale $M_{\mathrm{T}}$ (both in GeV) is substantially larger for the signal (as well as for $t\overline{t}$) than the vector background components.

Figure 7

Signal and background event shapes are compared for the final state topology with 2–3 light leptons and $2^{+}$ $b$ jets (category II). Left: About 80% of the signal features a reconstructed $b$-Jet pair in the $Z/H$-boson mass window ($92–20\mathrm{GeV}$ to $126+20\mathrm{GeV}$), whereas the same holds true for just 30%–40% of the unified background components. Right: The angular separation $\mathrm{\Delta }R$ of the pair of jets that come closest by invariant mass to reconstructing a Higgs is systematically smaller for the signal than the $t\overline{t}$ background component.

Figure 8

Signal and background integrated event counts are compared for the final state topology with 2–3 light leptons and $2^{+}$ $b$ jets (category II) at a luminosity of 300 events per femtobarn as a function of the missing transverse energy ${\cancel{E}}_{\mathrm{T}}$ cut threshold. Left: The raw event categorization reveals daunting background domination by $t\overline{t}+\text{jets}$, with no substantive improvement in the signal-to-background ratio at large values of the missing energy. Right: Enacting the secondary event selections ( 0 $\tau$, 1 leptonic $Z$, 0 single-track jets, 1 hadronic $Z/H$ with $\mathrm{\Delta }R<2.0$, and ${\cancel{E}}_{\mathrm{T}}/\sqrt{H_{\mathrm{T}}}>4.0$), the signal-to-background ratio is improved by 2 or 3 magnitude orders (more at larger ${\cancel{E}}_{\mathrm{T}}$ cuts), although it remains apparently intractable at the studied luminosity and signal cross section.

Figure 9

Signal and background event shapes are compared for the final state topology with 0–1 light leptons and $4^{+}$ $b\text{−}\text{jets}$ (category III). Left: The $t\overline{t}$ background is generally jettier than the signal, with a larger fraction of events at six or more jets. Right: The leading pair of signal jets is somewhat more likely to be $b$-tagged than the leading pair of jets in the $t\overline{t}$ background, one or more of which are likely to be initial state radiation.

Figure 10

Signal and background event shapes are compared for the final state topology with 0–1 light leptons and $4^{+}$ $b$ jets (category III). Left: The $t\overline{t}$ background is substantially more likely to retain a single lepton than the signal. Right: Around 65% of the signal features two reconstructed $b$-jet pairs in the $Z/H$-boson mass window ($92–20\mathrm{GeV}$ to $126+20\mathrm{GeV}$), whereas the same holds true for just around 40%–45% of the $t\overline{t}$ (vector) background components.

Figure 11

Signal and background integrated event counts are compared for the final state topology with 0–1 light leptons and $4^{+}$ $b$ jets (category II) at a luminosity of 300 events per femtobarn as a function of the missing transverse energy ${\cancel{E}}_{\mathrm{T}}$ cut threshold. Left: The raw event categorization reveals daunting background domination by $t\overline{t}+\text{jets}$, with no substantive improvement in the signal-to-background ratio at large values of the missing energy. Right: Enacting the secondary event selections (0 $e/\mu$, $0\tau$, 0–5 total jets, 2 leading $b$ jets, 0 single-track jets, 2 hadronic $Z/H$, and ${\cancel{E}}_{\mathrm{T}}/\sqrt{H_{\mathrm{T}}}>4.0$), the signal-to-background ratio is improved by around a magnitude order, although it remains apparently intractable at the studied luminosity and signal cross section.

Figure 12

The signal to background significance metric $S/\sqrt{1+B}$ is evaluated as a function of the missing transverse energy cut threshold for the category II (Left) and III (Right) final state topologies, applying the optimizations described in the right-hand panels of Figs. 8 and 11. Four contours are shown, corresponding to luminosities of 300 and $3,000{\mathrm{fb}}^{-1}$, for the baseline cross section of the benchmark model and also for a hypothetical spectrum that is sufficiently more light to engender a 1 magnitude order increase in the production cross section. Only by conspiracy of both factors may a significant excess be observed, and then only for category II. In this former case, a harder cut on ${\cancel{E}}_{\mathrm{T}}>400\mathrm{GeV}$ is suggested if luminosity and cross section are large enough to support it, in which case background is deeply contained and the signal is quite visible. By contrast, in the latter case similarities in the signal and background missing transverse energy shapes render a substantive ${\cancel{E}}_{\mathrm{T}}$ cut ineffective.