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REVIEW 4 major objections 5 minor 28 references

Charged Higgs Signatures at Future Electron-Proton Colliders

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Future electron-proton colliders can discover the charged Higgs boson through its conventional decays, while the exotic W'Z cascade remains out of reach.

desk verdict Useful cut-and-count e-p study with one clean negative result, but the discovery reach plots are built on a 20% signal efficiency that contradicts the paper's own 3–12% cutflows, so the LHeC/FCC-eh discovery claims are not currently supported. read the letter →

arxiv 2508.04656 v1 pith:66VBEXQQ submitted 2025-08-06 hep-ph

Baradhwaj Coleppa , Gokul B. Krishna This is my paper · ORCID
classification hep-ph
keywords chargedHiggsbosonfutureelectron-protoncollidersLHeCFCC-ehextendedgaugemodelsW'colliderphenomenology5-sigmadiscoverysignificance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a charged Higgs boson from an extended gauge and scalar sector can be discovered at the proposed LHeC and FCC-eh electron-proton colliders through its conventional decays ($H^- \to \bar{t}b$ and $H^- \to W^-h$), while its exotic decay into a new $W'$ boson plus a $Z$ boson cannot be observed. The study generates signal and background events for the process $e^- p \to \nu_e H^- j$, applies optimized selection cuts for four final-state topologies, and computes the cross sections needed for 5σ discovery. Interpreting the results in a concrete extended gauge model, the authors find 5σ reach for three of the four signals at LHeC with 1000 fb$^{-1}$ and for all four at FCC-eh with 1000–2000 fb$^{-1}$, across a broad range of the parameter $\sin\beta$. If correct, this establishes future e-p colliders as a complementary discovery environment for charged Higgs sectors of non-minimal new-physics models.

What carries the argument

The central machinery is the single-production process $e^- p \to \nu_e H^- j$ followed by the charged-Higgs decay chain, simulated with MadGraph5_aMC@NLO, PYTHIA8 and Delphes3, and a cutflow that selects on $b$-jet and jet multiplicities plus kinematic variables (leading jet and $b$-jet $p_T$, invariant masses, $H_T$, angular separations) to suppress five Standard Model backgrounds. The significance estimates use the asymptotic discovery ($Z_D$) and exclusion ($Z_E$) formulae of Ref. [20] to convert surviving yields into required cross sections; the model interpretation uses branching ratios and production cross sections as functions of $\sin\beta$ and $x = m_W/m_{W'}$, with $\sin\$\alpha$ = -

What would settle it

Recalculate the 5-$\sigma$ required cross sections after adding a conservative 10–20% systematic uncertainty on each background yield and replacing the flat 20% signal efficiency with the benchmark-specific efficiencies from the cutflow tables; if the required cross sections then exceed the model's predicted $\sigma(e^-p\to\nu_e H^- j)\times BR(H^-\to \bar{t}b/W^-h)$ across the allowed $\sin\beta$ range at LHeC for signals 2, 3 and 4, the discovery claim is falsified.

Watch

Extended reading notes

Core claim

In the framework of a model with gauge group $SU(2)_0 \times SU(2)_1 \times U(1)_2$ (Ref. [6]), a charged Higgs boson $H^\pm$ can be produced via $e^- p \to \nu_e H^- j$ and decays either conventionally to $\bar{t}b$ or $W^-h$, or exotically to $W'^-Z$ with the cascade $W' \to WZ$. The paper demonstrates, through Monte Carlo simulation with MadGraph5/Pythia8/Delphes3 and a dedicated cutflow for each of the four conventional topologies, that these modes yield enough signal events for a 5σ discovery at FCC-eh (all four signals, 1000–2000 fb$^{-1}$) and at LHeC for the leptonic and $W^-h$ topologies (signals 2, 3 and 4, BP-dependent, at 1000 fb$^{-1}$). The exotic 4b+3j+MET channel from $H^- \t

Load-bearing premise

The whole reach rests on the assumption that only the specific Standard Model backgrounds simulated here contribute at the estimated rates, with no significant systematic uncertainty, and that a flat 20 percent signal efficiency is a fair proxy for the actual cutflow efficiencies; if other sources (mis-tagged b-jets, pile-up, W+jets) or sizeable systematic errors are added, the required signal rates rise and the claimed discovery regions could shrink or disappear.

Editorial extensions

If this is right

  • At FCC-eh with 1000–2000 fb$^{-1}$, all four conventional charged-Higgs signal channels reach 5σ in parts of the $\sin\beta$ plane, giving concrete benchmark regions for future searches.
  • At LHeC with 1000 fb$^{-1}$, discovery is viable for signals 2, 3 and 4 (BP-dependent), while signal 1 alone does not yield enough events, so the $\bar{t}b$ hadronic mode is not sufficient at $\sqrt{s}=1.3$ TeV.
  • The exotic NP→NP→SM cascade $H^-\to W'^-Z\to W^-ZZ$ cannot be discovered at either collider, meaning e-p facilities will not constrain that sector; LHC searches remain the primary route.
  • If the model is correct, a null result in these channels at LHeC or FCC-eh would exclude the corresponding parameter space, providing a model-specific exclusion reach beyond current LHC bounds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The reach plots impose a flat 20% signal efficiency whereas the detailed cutflows show efficiencies that vary with benchmark point and topology; a reader should treat the precise $\sin\beta$ boundaries of the discovery regions as approximate until the cutflow-derived efficiencies are used consistently.
  • Because the $H^-\to W'Z$ coupling depends only on $\sin\beta$ (not $x^2$), the failure of the exotic channel at e-p colliders reflects the small production cross section and the demanding 4b final state, not a small branching ratio; the same channel could still be more promising at the LHC, so this conclusion does not transfer to hadron colliders.
  • A natural extension would be to add realistic systematic uncertainties (e.g., 10–20% on background normalisation) and fake b-tag rates, then re-evaluate the required cross sections; the claimed discovery regions at LHeC are the most sensitive to such additions.
  • The charge-conjugate process with a positron beam would have different backgrounds; the model's symmetry suggests comparable reach, but that case is not tested here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies charged-Higgs production in future electron-proton collisions at the LHeC (1.3 TeV) and FCC-eh (3.5 TeV) within an extended gauge model containing W′, Z′, and extra scalars. Four conventional signal topologies are analyzed: H−→tb and H−→Wh, each with hadronic (Signals 1 and 2) and leptonic (Signals 3 and 4) W decays, all produced via e−p→νH−j. Signal and background events are generated with MadGraph5/PYTHIA8/Delphes, cutflows are given for two mass benchmarks, and required cross sections for 1.96σ exclusion, 3σ, and 5σ discovery are computed with Cowan–Cranmer–Gross asymptotic formulas. The model-dependent reach is then shown as σ(ep→νHj)×BR(H→X) versus sinβ. The paper concludes that LHeC can discover Signals 2, 3, and 4 at 1000 fb−1, that FCC-eh can discover all four channels, and that the exotic H−→W′Z→WZZ cascade has no discovery potential.

Significance. If the quantitative conclusions survive scrutiny, the paper would provide useful first estimates of charged-Higgs sensitivity at future e−p colliders in a non-minimal model, and the negative result for the NP→NP→SM cascade is a useful caution. The study is based on independent MC simulations with explicit cutflows, and the required-cross-section tables are a reproducible starting point for the model interpretation. However, the reach plots rely on a flat signal efficiency of εs=0.20 that is directly contradicted by the paper's own cutflows, which give efficiencies of roughly 3–12%. Because those plots are the sole basis for the discovery claims, this is a load-bearing inconsistency rather than a presentation issue. The statistical treatment also neglects systematic uncertainties. The paper is therefore not acceptable in its present form, but the central framework is sound enough that a careful revision could make the claims reliable.

major comments (4)
  1. [§IV, Fig. 7–8; Tables III–XI] The reach plots impose a flat signal cut efficiency εs=0.20, but the paper's own cutflows give much smaller efficiencies. For example, Signal 1 BP2 LHeC ends at 5822.4/100000=5.8% and FCC-eh at 5341.8/100000=5.3%; Signal 3 BP2 FCC-eh ends at 2932.8/100000=2.9%; Signal 4 BP2 FCC-eh ends at 2761.3/100000=2.8%. Even the most efficient channel is below 20%. Since Tables XII/XIII list the post-cut signal cross section S/L required for a given significance, dividing those numbers by 0.20 instead of the actual cutflow efficiency overestimates the production cross-section reach by factors of ~1.7–7, and by more if daughter branching ratios must also be unfolded. The LHeC discovery claims for Signals 2–4 and the marginal FCC-eh BP2 claims are therefore not supported by the paper's own data. Please recompute the reach curves using the actual cutflow efficiencies (and state explicitly whether εs is
  2. [§III, Eqs. (1)–(2); Tables II, VII] The significance estimates are purely statistical. Equations (1) and (2) contain only S and B, with no systematic-uncertainty terms. Given that the claimed reach regions correspond to small numbers of signal events above backgrounds of order tens to hundreds of fb, a 5σ claim is sensitive to background normalization uncertainties, fast-simulation b-tag misidentification rates, pile-up, and missing backgrounds such as W+jets with fake b-tags. All cross sections are leading order with no k-factors. Please quantify these effects, e.g. by profiling over a nuisance parameter, or at least show how the required cross sections change under a conservative background uncertainty.
  3. [§VI, Table XV] The appendix's conclusion that H−→W′Z has no discovery potential is not backed by a complete calculation. Table XV lists the exotic-signal backgrounds but omits their cross sections entirely, unlike Tables II and VII. Tables XVI and XVII show only normalized cutflow counts, so the absolute background yield B that enters Eqs. (1)–(2) cannot be reconstructed. Without the background cross sections (in pb/fb) and the initial normalization used for the cutflow, the statement that the event yield remains below 5 events is not verifiable. Please add the missing cross-section columns and, if possible, the corresponding LHeC and FCC-eh values.
  4. [§IV, Fig. 5–8] The conversion from the required post-cut cross sections in Tables XII/XIII to the plotted σ(ep→νHj)×BR(H→X) is not fully documented. The text says 'we have also imposed a signal cut efficiency of εs=0.20' only in the paragraph after the figures, and it is not defined which stages of the selection (object reconstruction, b-tagging, kinematic cuts) it is supposed to represent. Please state the exact relation, including whether the daughter branching ratios (W→jj, h→bb, W→ℓν) are already contained in the generated signal samples or are divided out separately. A worked numerical example for one benchmark point would remove the ambiguity.
minor comments (5)
  1. [§V] The conclusion sentence 'we find viable discovery prospects in signal 2,3 and signal 4, corresponding to the final state 2b+j+ℓ−+MET' is incorrect for Signal 2, which has the hadronic final state 2b+3j+MET. Please correct.
  2. [Tables XII–XIII] The luminosity column header appears as 'f b−1' in the text; it should read 'fb−1'. Also, the table headers call the second column 'Background (fb)', but the entry is a post-cut background cross section rather than an event yield; please label it explicitly.
  3. [Figure 7 caption] The caption text lists 'BP1: MH±=500 GeV' for a Signal-2 panel, while BP1 is defined as MH±=300 GeV throughout Section III. The figure-caption/label combination should be checked.
  4. [Figures 2–4] Each figure combines several kinematic distributions, but the captions mention only the first observable. Please add panel labels or a legend so the reader can identify which distribution each panel shows.
  5. [§IV] The production cross sections in Fig. 5 are shown only as curves, not tabulated. Since the reach plots depend on these numbers, providing a small table of σ(e−p→νH−j) for the benchmark masses and representative sinβ values would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the reach claims come from independent MC simulations, not from fitted or self-defined inputs. Minor self-citation to the authors' prior model is present, and an internal flat-20% efficiency assumption conflicts with the paper's own cutflows, but that is a correctness risk, not circular reasoning.

full rationale

The central discovery claims are derived from MadGraph5 + PYTHIA8 + Delphes3 simulations of the four signal topologies and their SM backgrounds. The required post-cut signal cross sections in Tables XII/XIII come from the Cowan-Cranmer-Gross-Vitells significance formulas applied to simulated background yields; these are not fitted to the claimed discovery and are internally defined. The transition from those post-cut cross sections to the σ×BR axis of the reach plots uses an explicit assumption: 'For this analysis, we have also imposed a signal cut efficiency of ϵs = 0.20' (Section IV, Fig. 7/8 paragraph). This is not a circular step, because the reach is not defined in terms of the efficiency and the efficiency is not fitted to the target result; however, it is inconsistent with the paper's own cutflows, which give final efficiencies of only 5.8% (Signal 1 BP2 LHeC, 5822.4/1e5 in Table III), 2.9% (Signal 3 BP2 FCC-eh, 2932.8/1e5 in Table IX), and 2.8% (Signal 4 BP2 FCC-eh, 2761.3/1e5 in Table XI). That inconsistency makes the reach plots optimistic and weakens the LHeC discovery claims for Signals 2-4 and the marginal FCC-eh channels, but it is an internal-error/correctness issue rather than a circular derivation. The model couplings and branching ratios are taken from the authors' prior papers [6] and [7] (self-citation), but those are external model inputs with their own stated constraints; the present paper's MC reach is not constructed to return those inputs. No parameter is fitted to the claimed 5σ regions, and no uniqueness theorem or ansatz is imported to forbid alternatives. Therefore the paper is not circular in the sense of reducing to its inputs by construction; the minor self-citation and the efficiency mismatch are weighed as a score of 2.

Assumptions & free parameters 5 free parameters · 5 assumptions · 3 invented entities

The paper rests on the extended gauge model from the authors' prior work plus the assumption that a handful of leading-order backgrounds dominates. The benchmark masses, mixing angle, and the 20 percent cut efficiency are hand-set inputs that shape the reach plots. No entities are newly invented in this paper; they are inherited from the model.

free parameters (5)
  • Charged Higgs mass benchmarks = 300, 500 GeV (main text); 450, 550 GeV (appendix)
    Chosen by hand to span the mass range allowed by LHC exclusions; all reach results are conditional on these choices.
  • Heavy W' mass = 350 GeV
    Chosen ad hoc for the appendix exotic W'Z analysis; the non-discovery conclusion depends on this benchmark.
  • CP-even Higgs mixing angle sin alpha = -1/sqrt(2)
    Fixed by hand, stated to be compatible with Higgs data for sin beta > 0.4; this sets the H- to W h coupling strength.
  • Signal cut efficiency epsilon_s = 0.20
    Imposed in the reach plots, differing from the detailed cutflow efficiencies; the reach curves are therefore approximate.
  • sin beta = scanned 0.1 to 1.0; region below about 0.4 excluded by b to s gamma
    Model input parameter that controls production cross section and branching ratios; the reach plots quantify discovery as a function of it.
assumptions (5)
  • domain assumption Existence of a charged Higgs H+/- and additional heavy gauge bosons W' and Z' beyond the SM, with W' and Z' assumed fermiophobic.
    Section II.A; the entire study presupposes this spectrum and the fermiophobia to evade direct LHC limits.
  • domain assumption The extended gauge model of Ref. [6] (SU(2)_0 x SU(2)_1 x U(1)_2 with two doublets and a nonlinear sigma field) correctly describes the couplings and mass spectrum used in the simulations.
    Section IV; all branching ratios and production cross sections are evaluated with this model, taken from prior work.
  • standard math The effective H+/- W-/+ Z coupling formula from Ref. [21] (Eq. 8) is correct.
    Appendix VI, Eq. 8; used to argue that H- to WZ is suppressed while H- to W'Z is unsuppressed.
  • domain assumption MadGraph5_aMC@NLO, PYTHIA8, and Delphes3 with an e-p specific detector card give a faithful enough description of signal and background rates.
    Section III; the analysis is based entirely on fast simulation with no validation against full detector simulation.
  • domain assumption The listed SM background processes are the only relevant ones for each final state.
    Tables II, VII, XV; no fake-rate, pile-up, or additional multi-jet backgrounds are included.
invented entities (3)
  • W' heavy charged gauge boson
    purpose: Allows exotic decay H- to W'Z and the NP to NP to SM cascade.
    Taken from the model of Ref. [6]; no direct experimental evidence, assumed fermiophobic to evade limits.
  • Z' heavy neutral gauge boson
    purpose: Partner of W' in the extended gauge sector; appears in H- to W Z'.
    Same model of Ref. [6]; no direct experimental evidence.
  • Heavy neutral scalars H and A
    purpose: Complete the extended scalar sector; assumed heavier than H+/- to forbid H+/- to VH or VA decays.
    Section IV; states are assumed heavier, with no direct evidence.

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Cite this review

Pith. "Pith review of Charged Higgs Signatures at Future Electron-Proton Colliders." pith.science (2026). https://pith.science/paper/66VBEXQQ

@misc{pith2026250804656,
  author       = {Pith},
  title        = {Pith review of: Charged Higgs Signatures at Future Electron-Proton Colliders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/66VBEXQQ}},
  note         = {Machine review of arXiv:2508.04656}
}
abstract

In this work, we present a detailed collider phenomenology study of the charged Higgs boson within a Beyond the Standard Model (BSM) framework featuring an extended gauge and scalar sector. The charged Higgs can decay via conventional modes, such as $H^- \to \bar{t}b$ and $H^- \to W^-h$, as well as through exotic channels like $H^- \to W'Z$ (or $WZ'$). These decays lead to distinct final-state topologies determined by the nature of the intermediate particles. We perform a comprehensive phenomenological analysis at future electron-proton colliders, namely the LHeC and FCC-eh, considering the luminosity projections provided in their design reports. Our results indicate that the conventional decay modes of the charged Higgs boson can achieve observable sensitivity and even discovery prospects at sufficiently high luminosities. In contrast, the exotic decay channel $H^- \to W'Z$ does not exhibit any viable discovery potential. These findings highlight the complementarity of future electron-proton colliders in probing extended Higgs sectors, particularly through conventional charged Higgs signatures.

Figures

Figures reproduced from arXiv: 2508.04656 by the authors.

Figure 1
Figure 1. FIG. 1: Representative Feynman diagrams for the production process [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Distributions of kinematic observables for Signal 1 at benchmark point BP–1 ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Distributions of kinematic observables for Signal 1 at benchmark point BP–2 ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Distributions of kinematic observables for Signal 3 at benchmark point BP–1 ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Charged Higgs production cross section for the process [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Branching ratios of the charged Higgs boson into various decay modes for two representative values of sin [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Reach plots for the FCC-eh setup showing the parameter space accessible for all four signal scenarios considered [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Reach plots illustrating the accessible parameter space at the LHeC for signal 3 and signal 4 for both [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Estimated signal reach for the NP [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.