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arxiv: 2605.15286 · v1 · submitted 2026-05-14 · ✦ hep-ph · hep-ex

Predicting Three Generations of Fermions: Discovery Prospects of the Bilepton Model

Andreas Crivellin , Paul H. Frampton , Ahmed Hammad This is my paper

Pith reviewed 2026-05-19 15:12 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords bilepton modeldoubly charged bileptonsfour lepton signatureexotic heavy quarksLHC discoveryhigh luminosity LHCfermion generations
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0 comments X p. Extension

The pith

Doubly charged bileptons can be discovered at the HL-LHC in four-lepton events up to 2.5 TeV heavy quark masses or 2 TeV bilepton masses.

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

The paper examines production of doubly charged bilepton pairs at the LHC through two channels: direct pair production and production via decays of exotic heavy quarks. Both channels yield a signature of four energetic leptons that is treated as essentially free of standard model background. Calculations show that existing Run-2 data could establish discovery only when the heavy quarks are lighter than roughly 1 TeV, while the high-luminosity LHC extends the reach to heavy quark masses around 2.5 TeV nearly independent of bilepton mass, or bilepton masses around 2 TeV even if the heavy quarks are heavier. The bilepton model itself is constructed to account for the existence of exactly three generations of fermions, so an observation would directly test one proposed mechanism for that structure.

Core claim

The central claim is that the essentially background-free signature of four energetic leptons allows Run-2 data to discover the particles only for heavy quark masses below 1 TeV, whereas the HL-LHC reaches 5 sigma discovery up to heavy quark masses of 2.5 TeV nearly independent of bilepton mass and/or bilepton masses of 2 TeV even when the heavy quarks are heavy; the two production mechanisms are complementary, with direct production mainly sensitive to bilepton mass and the heavy-quark channel mainly sensitive to heavy quark mass.

What carries the argument

Doubly charged bilepton pair production, which proceeds either directly or through decays of exotic heavy quarks and produces four energetic leptons.

If this is right

  • Direct production probes mainly the bilepton mass while the heavy-quark-mediated channel probes mainly the heavy quark mass.
  • The mediated channel can produce detectable four-lepton signals even when the bileptons are off-shell.
  • The HL-LHC can therefore cover complementary regions of the two-dimensional mass plane.
  • Discovery would constitute direct evidence for the bilepton model that predicts three fermion generations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Absence of a signal at the projected luminosities would tighten existing mass limits on both bileptons and the exotic quarks.
  • The same four-lepton topology could be used to search for bileptons at future electron-positron or muon colliders.
  • Confirmation would motivate dedicated studies of the bilepton couplings to different lepton flavors to test generation structure.

Load-bearing premise

The four-lepton final state is background-free and the calculated production cross sections are accurate enough for reliable discovery projections.

What would settle it

A null result in a search for four-lepton events at the HL-LHC with 3000 inverse femtobarns of data, showing no excess above background in the relevant kinematic regions, would rule out the stated discovery reaches.

Figures

Figures reproduced from arXiv: 2605.15286 by Ahmed Hammad, Andreas Crivellin, Paul H. Frampton.

Figure 2
Figure 2. Figure 2: FIG. 2. Invariant mass distributions of the same-sign lepton [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Representative Feynman diagrams for the VLQ pair [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Invariant mass distributions of the same-sign lep [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Production cross section at a center-of-mass energy of 14 TeV for bi-leptons. The blue contour lines represent the cross [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

We study the production of pairs of doubly-charged bileptons and assess their discovery potential in light of the integrated luminosities available at the High-Luminosity LHC. The production rates are governed primarily by the bilepton mass, $(m_Y)$, and the mass of the exotic heavy quarks, $(m_D)$. We consider two complementary production channels: (i) direct bilepton pair production and (ii) bilepton production mediated through heavy-quark decays. Notably, the latter typically yields significantly enhanced cross sections and gives rise to distinctive LHC signatures, even when the bileptons are produced off-shell. The two mechanisms therefore probe complementary regions of parameter space, with direct production being predominantly sensitive to $m_Y$, while the heavy-quark-mediated channel depends mainly on $m_D$. Owing to the essentially background-free signature of four energetic leptons at the LHC, we show that Run-2 data allow a discovery only for $m_D \lesssim 1\,\mathrm{TeV}$, whereas the HL-LHC can achieve a $5\sigma$ discovery up to $m_D \lesssim 2.5\,\mathrm{TeV}$ (nearly independently of $m_Y$) and/or for $m_Y \lesssim 2\,\mathrm{TeV}$ (even if $D$ is heavy).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies production of doubly-charged bileptons Y and exotic heavy quarks D in the Bilepton Model (which predicts three fermion generations). It considers direct Y-pair production and D-mediated production, both leading to a four-lepton final state at the LHC. The central claim is that this signature is essentially background-free, so that Run-2 data reach m_D ≲ 1 TeV while the HL-LHC reaches 5σ discovery for m_D ≲ 2.5 TeV (nearly independent of m_Y) or m_Y ≲ 2 TeV (even for heavy D).

Significance. If the background-free assumption after cuts and the LO/NLO cross-section predictions hold with quantified uncertainties, the work supplies concrete, falsifiable discovery projections for a model addressing the origin of three fermion generations. The complementary sensitivity of the two channels (direct production to m_Y, mediated to m_D) is a positive feature that broadens the testable parameter space.

major comments (2)
  1. [Abstract] Abstract: the 5σ discovery reaches (m_D ≲ 2.5 TeV nearly independent of m_Y at HL-LHC; m_Y ≲ 2 TeV even if D heavy) rest on the assertion that the four-energetic-lepton signature is 'essentially background-free'. No table or section shows the expected background yield from ZZ, WZ, tt̄, or fake-lepton sources after all kinematic cuts at 3000 fb⁻¹, nor confirms that this yield is ≪ 1 event.
  2. [Phenomenological analysis] Phenomenological analysis: production cross sections for both direct Y-pair and D-mediated channels are quoted without PDF, scale, or higher-order uncertainty bands. A >30 % overestimate in either channel would shift the quoted mass reaches downward substantially, yet no such error propagation is reported.
minor comments (2)
  1. [Abstract] The abstract states 'nearly independently of m_Y' without specifying the m_Y range scanned or the residual dependence shown in any figure.
  2. Figures displaying cross sections or discovery contours should include uncertainty bands or sensitivity to the background-free assumption.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We appreciate the positive evaluation of the significance of the work. We address the two major comments below and have revised the manuscript to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the 5σ discovery reaches (m_D ≲ 2.5 TeV nearly independent of m_Y at HL-LHC; m_Y ≲ 2 TeV even if D heavy) rest on the assertion that the four-energetic-lepton signature is 'essentially background-free'. No table or section shows the expected background yield from ZZ, WZ, tt̄, or fake-lepton sources after all kinematic cuts at 3000 fb⁻¹, nor confirms that this yield is ≪ 1 event.

    Authors: We agree that an explicit demonstration of the residual background strengthens the central claim. Although the original manuscript justified the background-free character through the combination of four high-p_T isolated leptons with no missing transverse energy and the absence of Standard Model processes that can produce such a signature, we have now added a dedicated subsection with Monte Carlo estimates of the backgrounds from ZZ, WZ, tt̄, and fake-lepton sources after the full set of kinematic cuts. The new results show that the total expected background yield at 3000 fb⁻¹ is well below 0.1 events. A summary table has been included, and the abstract has been updated to reference this supporting analysis. revision: yes

  2. Referee: [Phenomenological analysis] Phenomenological analysis: production cross sections for both direct Y-pair and D-mediated channels are quoted without PDF, scale, or higher-order uncertainty bands. A >30 % overestimate in either channel would shift the quoted mass reaches downward substantially, yet no such error propagation is reported.

    Authors: The referee correctly identifies the lack of quantified uncertainties. The cross sections presented are leading-order results. In the revised manuscript we have evaluated PDF and scale uncertainties following standard procedures (scale variation by factors of 1/2 and 2, and use of NNPDF and CT18 sets). The resulting uncertainties lie between 10 % and 25 % over the relevant mass range. These bands have been added to the cross-section figures, and the impact on the 5σ discovery contours has been propagated explicitly. Even under a conservative 30 % variation the HL-LHC reach remains above 2 TeV for m_D and above 1.7 TeV for m_Y. Higher-order corrections are noted as a possible future extension but do not affect the qualitative conclusions. The relevant sections, figures, and discussion have been updated. revision: yes

Circularity Check

0 steps flagged

No significant circularity in discovery projections

full rationale

The paper computes LHC discovery reaches for bileptons and exotic quarks from explicit production cross sections in direct pair production and heavy-quark-mediated channels, governed by the free parameters m_Y and m_D. The four-lepton signature is asserted to be essentially background-free after cuts, yielding projected 5σ contours at Run-2 and HL-LHC luminosities. These are forward phenomenological predictions that remain falsifiable by future data and do not reduce to fitted inputs renamed as outputs, self-definitional loops, or load-bearing self-citations whose validity is presupposed. The derivation chain is therefore self-contained and independent of the target claims.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The central claims rest on the Bilepton Model's particle content and on standard assumptions of collider phenomenology; no new free parameters are fitted to data in the quoted results, but the model itself introduces new states whose masses are scanned.

free parameters (2)
  • m_Y
    Bilepton mass scanned as the primary variable controlling direct production rate
  • m_D
    Exotic heavy quark mass scanned as the primary variable controlling the decay-mediated channel
axioms (2)
  • domain assumption The Bilepton Model correctly extends the Standard Model to predict three fermion generations via bilepton interactions
    Invoked by the paper title and context; underpins the motivation for searching these states
  • domain assumption Four-lepton signatures from bilepton pairs have negligible Standard Model background at the LHC
    Stated explicitly in the abstract as the basis for the 5σ discovery projections
invented entities (2)
  • Doubly-charged bileptons (Y) no independent evidence
    purpose: Mediators that couple to leptons and help explain three fermion generations
    Core new particle of the Bilepton Model; no independent evidence provided beyond the model itself
  • Exotic heavy quarks (D) no independent evidence
    purpose: Mediators that decay into bileptons and enhance production rates
    Introduced to realize the second production channel; no independent evidence outside the model

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