Probing compressed triplet scalars with ISR jets and soft leptons at the LHC

Abstract: The Type-II seesaw model predicts doubly and singly charged scalars along with neutral Higgs states originating from an $SU(2)$ triplet. Current LHC searches by the ATLAS and CMS collaborations constrain these particles mainly under the assumption that the doubly charged scalar decays dominantly into same-sign dileptons or dibosons. However, when moderate mass splittings exist among the triplet scalars, cascade decays can dominate, suppressing these conventional search channels and leaving sizeable regions of parameter space weakly constrained. We study this compressed region characterized by $1~\text{GeV} \lesssim ΔM \lesssim 30~\text{GeV}$ and triplet vev $v_t \sim 10^{-7} - 10<sup>{-3}$ GeV. In this scenario, charged scalars predominantly undergo cascade decays, while neutral scalars decay invisibly into neutrinos, leading to final states with soft leptons and missing transverse energy. We propose a dedicated search strategy at the 14 TeV LHC exploiting a hard initial-state radiation jet to boost the scalar system. Using a cut-and-count analysis, we show that discovery-level sensitivity can be achieved in this previously unexplored region with an integrated luminosity of $3000~\mathrm{fb}<sup>{-1}$. Our results signify the importance of dedicated searches targeting cascade-dominated and compressed mass spectrum for beyond the standard model scenarios with an $SU(2)$ multiplet.

• The paper investigates the discovery potential for compressed triplet scalars at the LHC with a novel search strategy involving initial-state radiation (ISR) jets and soft leptons.
• Using a signature of soft leptons and jets along with modest missing transverse energy, the study targets scenarios where the neutral scalars decay invisibly to neutrinos.
• The proposed method extends the covered parameter space with {3000} f{b} ^[-1] at 3σ LHC sensitivity beyond the current boundaries set for doubly charged scalars by considering {κSigma} reactions.

Motivation and context

The Type-II seesaw model extends the Standard Model scalar sector with an $SU(2)_L$ triplet $\Delta$ of hypercharge $Y=2$, whose neutral component acquires a small vev $v_t$ and generates Majorana neutrino masses. The resulting spectrum contains a doubly charged scalar $H^{\pm\pm}$, a singly charged $H^{\pm}$, and two exotic neutral states $H^0$ and $A^0$. Existing LHC limits on these particles — for example, the ATLAS bound of roughly 1080 GeV on $m_{H^{\pm\pm}}$ in the same-sign dilepton channel (2603.15882) — rest on the assumption that the doubly charged scalar decays dominantly into same-sign dileptons or same-sign dibosons. The paper under discussion identifies a region where this assumption fails: for moderate mass splittings $$1~\text{GeV} \lesssim \Delta M \lesssim 30~\text{GeV}$$ (with $\Delta$0) and triplet vevs $\Delta$1 GeV, cascade decays dominate. The charged scalars decay through off-shell $\Delta$2 bosons ($\Delta$3, $\Delta$4), while the neutral scalars decay invisibly to neutrinos. The resulting signature — soft leptons, soft jets, and modest missing transverse energy — evades both standard triggers and standard analyses, leaving a sizeable portion of parameter space effectively unconstrained.

The authors also note that a prior analysis targeting this regime with a same-sign dilepton trigger relies on what they judge to be an unrealistic lepton-pair trigger combination, motivating their alternative strategy.

Scalar sector and theoretical constraints

The analysis is framed in the limit $\Delta$5, justified by the electroweak precision measurement $\Delta$6, which caps $\Delta$7 GeV at $\Delta$8. In this limit the triplet mixing angles are tiny, and the scalar phenomenology is controlled by three parameters: the bare mass $\Delta$9, the splitting $Y=2$0, and $Y=2$1. The mass-squared differences are set by $Y=2$2, so $Y=2$3 can take either sign; the authors focus on the positive hierarchy, where cascades open up. Perturbative unitarity and bounded-from-below conditions constrain the quartic couplings, while the observed Higgs signal strength restricts $Y=2$4 (in practice they take nearly vanishing CP-even mixing). Lepton-flavor-violating processes, chiefly $Y=2$5 and $Y=2$6, impose lower bounds on $Y=2$7 scaling as $Y=2$8 depending on the neutrino mass ordering. Electroweak precision data (the $Y=2$9 parameter) cap the splitting at $v_t$0 GeV, which guarantees that any cascade $v_t$1 boson is off-shell.

Branching-ratio maps in the $v_t$2–$v_t$3 plane show that for $v_t$4 GeV and $v_t$5 GeV, the cascade mode dominates both charged scalars, suppressing the conventional dilepton and diboson channels that underpin current exclusions. This establishes the target region: $v_t$6 GeV, $v_t$7 GeV, $v_t$8 GeV.

Search strategy

The key experimental difficulty is that pair-produced compressed triplets carry little transverse momentum, so the invisible neutral scalars yield negligible missing energy on their own. The proposed remedy is to require a hard initial-state radiation (ISR) jet, selecting the associated production modes

$v_t$9

where the ISR jet boosts the scalar pair and converts its collective recoil into sizable $H^{\pm\pm}$0. Only leptonic decays of the off-shell $H^{\pm\pm}$1s are retained, since hadronic daughters fall below the 40 GeV jet reconstruction threshold. Signal and backgrounds are generated with MadGraph5_aMC@NLO (NNPDF23 LO, MLM matching, parton-level jet requirement $H^{\pm\pm}$2 GeV), showered with Pythia 8, and passed through Delphes with the CMS Phase-II card configured for low-$H^{\pm\pm}$3 leptons down to 5 GeV.

The cut flow proceeds through a $H^{\pm\pm}$4-jet veto and a hadronic-tau veto (removing roughly one-third of top-associated and 40% of tau-pair background events respectively), a single-jet requirement, hard leading-jet and missing-energy thresholds ($H^{\pm\pm}$5 GeV, $H^{\pm\pm}$6 GeV, $H^{\pm\pm}$7), exactly two soft leptons, and finally upper bounds exploiting the softness of the cascade leptons: $H^{\pm\pm}$8 GeV and $H^{\pm\pm}$9 GeV. A distinctive element is the asymmetric cut on the collinear-approximation di-tau invariant mass $H^{\pm}$0, reconstructed from the ISR jet momentum and the two leptons: requiring $H^{\pm}$1 GeV or $H^{\pm}$2 GeV removes events clustered near the $H^{\pm}$3 pole (the dominant $H^{\pm}$4jets background) and the bulk of $H^{\pm}$5jets. The two-lepton requirement is costly — only about 10% of signal survives it because of the low tagging efficiency below 10 GeV — but the authors argue it is essential for background suppression.

Results

For $H^{\pm}$6 GeV, the final signal cross sections after all cuts are 0.204 fb ($H^{\pm}$7 GeV) and 0.130 fb ($H^{\pm}$8 GeV), against a combined residual background of about 6.9 fb dominated by $H^{\pm}$9jets, $H^0$0jets, $H^0$1jets, and $H^0$2. With the significance estimator $H^0$3 and $H^0$4, the projected reach in the $H^0$5–$H^0$6 plane extends to $H^0$7–230 GeV at the $H^0$8 exclusion level, with a robust $H^0$9 discovery for $A^0$0 GeV over $A^0$1–25 GeV. These are discovery-level sensitivities in a region the authors identify as previously unexplored by direct searches.

Sensitivity degrades at both ends of the splitting range: for very small $A^0$2 the leptons fall below reconstruction thresholds, while for larger $A^0$3 the leptons harden and the signal mimics SM backgrounds more closely; large $A^0$4 suffers from the falling production cross section. All results are obtained at tree level with a cut-and-count approach, and the significance estimate assumes perfect control of the residual backgrounds.

Limitations and open questions

Several caveats bear directly on the quoted reach. The analysis fixes $A^0$5 GeV; sensitivity across the full cascade-dominated window $A^0$6 GeV is not established. The Delphes-based treatment of sub-10 GeV lepton tagging, while using official Phase-II parameterizations, is a simulation-level assumption whose validation would require a full detector study, particularly given that the entire strategy hinges on triggering via $A^0$7 plus soft objects — a trigger menu whose feasibility at the HL-LHC is asserted rather than demonstrated. The statistical treatment uses a simple cut-and-count formula without systematic uncertainties on backgrounds or luminosity. Finally, only leptonic off-shell $A^0$8 decays are included; the interplay with hadronic modes and multivariate discrimination against the residual $A^0$9 and $m_{H^{\pm\pm}}$0 backgrounds remains open.

Conclusion

This work demonstrates that a dedicated ISR-assisted search — one hard jet, large $m_{H^{\pm\pm}}$1, two soft leptons, and an asymmetric di-tau mass veto — can deliver $m_{H^{\pm\pm}}$2 discovery sensitivity for compressed triplet scalars with $m_{H^{\pm\pm}}$3 GeV and $m_{H^{\pm\pm}}$4 exclusion up to $m_{H^{\pm\pm}}$5–230 GeV at the 14 TeV LHC with 3000 fb$m_{H^{\pm\pm}}$6. The broader lesson is methodological: collider limits on extended scalar sectors are contingent on decay-mode assumptions, and cascade-dominated, compressed spectra demand search strategies orthogonal to the high-$m_{H^{\pm\pm}}$7 channels that currently define the exclusions.