Vector Bileptons in 331 Models

• Vector bileptons are spin-1 gauge bosons carrying two units of lepton number and, in doubly charged cases, two units of electric charge, arising in SU(3)_L × U(1)_X models.
• They exhibit distinct collider signatures, notably same-sign dilepton resonances, primarily produced via direct pair production and heavy-quark-mediated channels.
• Experimental searches constrain their mass in the TeV range, with future HL-LHC and FCC-hh studies expected to extend the discovery reach via precise invariant-mass reconstruction.

Vector bileptons are spin-1 bosons that carry two units of lepton number and, in the doubly charged case, two units of electric charge. In the contemporary phenomenology literature they arise most prominently in $SU(3)_C \times SU(3)_L \times U(1)_X$ extensions of the electroweak sector, where the enlarged gauge spectrum contains a neutral $Z'$, singly charged states denoted $Y^\pm$ or $V^\pm$, and doubly charged states denoted $Y^{\pm\pm}$, $U^{\pm\pm}$, or analogous notation. Their defining collider signature is the decay into like-sign lepton pairs, which makes multilepton final states—especially four-lepton states built from two same-sign pairs—the central discovery channel at hadron colliders (Coriano et al., 2018).

1. Definition, gauge origin, and nomenclature

In the 331 framework, vector bileptons are gauge bosons of the extended electroweak group $SU(3)_L \times U(1)_X$. The electric charge operator is written in the literature as

$Q = T_3 + \beta T_8 + X$

or, in the $\beta=\sqrt{3}$ convention used in several collider studies,

$Q = T_3 + \sqrt{3}\,T_8 + X.$

For the choices $Z'$0, the off-diagonal $Z'$1 generators generate singly and doubly charged gauge bosons, including the doubly charged vector bileptons. The literature represented here uses both $Z'$2 and $Z'$3 conventions, while agreeing on the existence of a doubly charged spin-1 state with $Z'$4 and $Z'$5 (Coriano et al., 2018, Barreto et al., 2011).

The fermion assignments that make these models distinctive are family non-universal. Two quark generations are placed in $Z'$6 triplets, one in an anti-triplet, and leptons are placed in anti-triplets such as $Z'$7 or equivalent conventions. This structure introduces exotic quarks $Z'$8 and $Z'$9 with charge $Y^\pm$0, and $Y^\pm$1 with charge $Y^\pm$2. A recurring result across the 331 literature is that anomaly cancellation requires the number of families to be a multiple of three, while QCD asymptotic freedom singles out three generations; this feature is one of the main theoretical motivations for bilepton models (Crivellin et al., 14 May 2026, Frampton, 2022).

Notation varies across papers. Doubly charged states are denoted $Y^\pm$3 in much of the 331 collider literature, $Y^\pm$4 in some phenomenological analyses, and singly charged companions appear as $Y^\pm$5 or $Y^\pm$6. This is a matter of convention rather than a change in the underlying spin-1 bilepton concept (Barela et al., 2019, Nepomuceno et al., 2019).

2. Interactions, chirality, and mass generation

The defining interaction is the bilepton coupling to two leptons of the same charge. In collider implementations this is often represented effectively as

$Y^\pm$7

with results quoted in terms of $Y^\pm$8 when the detailed chiral structure is not fixed beyond the model file. In explicit $Y^\pm$9 derivations, the current is purely chiral, originating from the left-handed gauge structure; one representative form is

$V^\pm$0

(Nepomuceno et al., 2016, Crivellin et al., 14 May 2026).

Vector bileptons also couple to exotic quarks. Representative interactions include

$V^\pm$1

and these couplings are essential both phenomenologically and for the high-energy behavior of $V^\pm$2 amplitudes (Crivellin et al., 14 May 2026, Meirose et al., 2011).

Non-Abelian gauge structure generates cubic vertices such as $V^\pm$3 and $V^\pm$4. In the minimal 331 model one explicit set of trilinear couplings is

$V^\pm$5

which underlies the Drell–Yan-like production channels used in collider studies (Barreto et al., 2011).

Masses arise from the breaking

$V^\pm$6

typically through the triplets $V^\pm$7, $V^\pm$8, and $V^\pm$9, with a large $Y^{\pm\pm}$0 setting the TeV-scale 331 threshold and $Y^{\pm\pm}$1, $Y^{\pm\pm}$2 completing electroweak symmetry breaking. A representative tree-level relation is

$Y^{\pm\pm}$3

and, in the $Y^{\pm\pm}$4 setup,

$Y^{\pm\pm}$5

These relations place bileptons naturally in the TeV region when the 331 scale is itself near the TeV scale (Crivellin et al., 14 May 2026).

3. Production mechanisms and decay patterns

The dominant hadron-collider topology in the classic bilepton searches is pair production,

$Y^{\pm\pm}$6

followed by

$Y^{\pm\pm}$7

The partonic production amplitude includes $Y^{\pm\pm}$8-channel $Y^{\pm\pm}$9, $U^{\pm\pm}$0, and $U^{\pm\pm}$1 exchange, together with $U^{\pm\pm}$2-channel exotic-quark exchange. Multiple studies emphasize that the exotic-quark contribution is not optional: it is required to restore the correct high-energy behavior of the vector-bilepton amplitude (Barreto et al., 2011, Meirose et al., 2011).

Later analyses extended this picture in two directions. First, some studies include Higgs-mediated production, $U^{\pm\pm}$3 and $U^{\pm\pm}$4, through couplings of the form

$U^{\pm\pm}$5

Second, recent work emphasizes heavy-quark-mediated production, in which QCD-driven VLQ pair production is followed by decays $U^{\pm\pm}$6, giving

$U^{\pm\pm}$7

This channel can remain sensitive even when the bileptons are off shell, so direct $U^{\pm\pm}$8 production and VLQ-mediated production probe complementary regions of the $U^{\pm\pm}$9 plane (Crivellin et al., 14 May 2026, Calabrese et al., 2023).

Decay phenomenology is controlled by thresholds. If $SU(3)_L \times U(1)_X$0, the bilepton decays essentially only to leptons, and $SU(3)_L \times U(1)_X$1 can be close to the commonly assumed flavor-democratic value of $SU(3)_L \times U(1)_X$2 per lepton flavor. Once $SU(3)_L \times U(1)_X$3, hadronic channels such as $SU(3)_L \times U(1)_X$4 open, increasing the total width and suppressing the visible four-lepton rate (Nepomuceno et al., 2016, Meirose et al., 2011).

A concrete benchmark study of non-leptonic decays illustrates this effect sharply. For $SU(3)_L \times U(1)_X$5 GeV, MadWidth calculations gave per-flavor leptonic branching ratios

$SU(3)_L \times U(1)_X$6

with total widths

$SU(3)_L \times U(1)_X$7

The reduction in the leptonic rate is driven by the opening of $SU(3)_L \times U(1)_X$8, $SU(3)_L \times U(1)_X$9, and $Q = T_3 + \beta T_8 + X$0 in BM I, while BM II leaves only $Q = T_3 + \beta T_8 + X$1 kinematically open (Corcella et al., 2021).

4. Collider signatures and search strategies

The canonical signature is a narrow resonance in each same-sign dilepton pair. Different analyses target different flavor realizations of this general topology. The early “golden channel” study focused on

$Q = T_3 + \beta T_8 + X$2

treating the channel as effectively background free and exploiting the double invariant-mass peak at $Q = T_3 + \beta T_8 + X$3 (Meirose et al., 2011). Later work developed a dimuon-centered strategy for

$Q = T_3 + \beta T_8 + X$4

with Delphes simulation, same-sign pairing, and invariant-mass windows $Q = T_3 + \beta T_8 + X$5 around the signal peak (Nepomuceno et al., 2016). Other studies included extra jets explicitly and examined

$Q = T_3 + \beta T_8 + X$6

with showering, hadronization, and jet clustering, as well as multijet cascades from VLQ decays (Corcella et al., 2017, Calabrese et al., 2023).

Selection choices are correspondingly similar across papers: hard isolated leptons, central pseudorapidity, and same-sign invariant-mass reconstruction. Representative cuts include $Q = T_3 + \beta T_8 + X$7 GeV, $Q = T_3 + \beta T_8 + X$8, $Q = T_3 + \beta T_8 + X$9 GeV, $\beta=\sqrt{3}$0, $\beta=\sqrt{3}$1, $\beta=\sqrt{3}$2, and $\beta=\sqrt{3}$3. In the four-muon reinterpretation, the acceptance and selection efficiency was about $\beta=\sqrt{3}$4, with an external $\beta=\sqrt{3}$5 trigger factor, giving $\beta=\sqrt{3}$6; in the older golden-channel analysis, the overall event-level acceptance was about $\beta=\sqrt{3}$7 at $\beta=\sqrt{3}$8 GeV with a $\beta=\sqrt{3}$9 reconstruction efficiency (Nepomuceno et al., 2016, Meirose et al., 2011).

Background treatment depends on the final state. Some same-sign multilepton channels were treated as background free, while others retained irreducible backgrounds such as $Q = T_3 + \sqrt{3}\,T_8 + X.$0, $Q = T_3 + \sqrt{3}\,T_8 + X.$1, $Q = T_3 + \sqrt{3}\,T_8 + X.$2, and $Q = T_3 + \sqrt{3}\,T_8 + X.$3. Tight mass windows and hard kinematic cuts suppress these backgrounds very strongly. In one 13 TeV study of $Q = T_3 + \sqrt{3}\,T_8 + X.$4, the signal cross section after baseline cuts was $Q = T_3 + \sqrt{3}\,T_8 + X.$5 fb, compared with $Q = T_3 + \sqrt{3}\,T_8 + X.$6 fb for $Q = T_3 + \sqrt{3}\,T_8 + X.$7 and $Q = T_3 + \sqrt{3}\,T_8 + X.$8 fb for $Q = T_3 + \sqrt{3}\,T_8 + X.$9, but the same-sign mass peak at $Z'$00 GeV rendered the signal region highly discriminating (Corcella et al., 2017). In the HL-LHC direct-production study of doubly charged bileptons, requiring $Z'$01 GeV removed all events from a sample of $Z'$02 simulated $Z'$03 events, and for the VLQ-mediated channel the stronger cut $Z'$04 GeV likewise left no background events in simulation (Crivellin et al., 14 May 2026).

A distinct extension of the bilepton program is lepton-flavor violation. The process

$Z'$05

was proposed as a vector-bilepton signal with no Standard Model irreducible contribution, controlled by a PMNS-like matrix in the bilepton charged current. Under the assumptions of that study, 13 TeV data with $Z'$06 could exclude masses up to approximately $Z'$07 TeV for favorable flavor mixing (Barela et al., 2019).

5. Experimental limits and discovery prospects

The collider bounds have evolved from sub-TeV exclusions based on reinterpretations of doubly charged Higgs searches to direct multilepton recasts extending into the TeV regime. A concise chronology is shown below.

Study	Dataset or setup	Representative result
“Searching for doubly-charged vector bileptons in the Golden Channel at the LHC” (Meirose et al., 2011)	7 TeV projections	95% C.L. exclusions up to $Z'$08 GeV at $Z'$09; sLHC discovery reach $Z'$10–$Z'$11 GeV
“First results on Bilepton production based on LHC collision data and predictions for Run II” (Nepomuceno et al., 2016)	ATLAS 7 TeV, $Z'$12	$Z'$13–$Z'$14 GeV excluded at 95% C.L., strongest bound $Z'$15 GeV for $Z'$16 GeV
“Limits on 331 vector bosons from LHC proton collision data” (Nepomuceno et al., 2019)	13 TeV, $Z'$17	$Z'$18: approximately $Z'$19 excluded; $Z'$20: approximately $Z'$21 excluded
“331 Models and Bilepton Searches at LHC” (Calabrese et al., 2023)	ATLAS 13 TeV multilepton recast, $Z'$22	$Z'$23 GeV at 90% C.L.
“Predicting Three Generations of Fermions: Discovery Prospects of the Bilepton Model” (Crivellin et al., 14 May 2026)	HL-LHC projections	$Z'$24 discovery up to $Z'$25 TeV nearly independently of $Z'$26, and/or for $Z'$27 TeV

Several caveats accompany these bounds. The 2016 reinterpretation explicitly avoided the restrictive flavor assumptions behind some older low-energy limits and treated the dimuon branching ratio as model dependent (Nepomuceno et al., 2016). The 2019 analysis set the first direct LHC limits on singly charged vector bileptons and reported that the new doubly charged bound improved an over-20-year-old limit by about $Z'$28 (Nepomuceno et al., 2019). The 2023 ATLAS recast showed that once VLQ-associated production and VLQ pair production feeding $Z'$29 are included, the inclusive bilepton signal is strengthened, even though the $Z'$30-jet veto suppresses much of the $Z'$31 contribution (Calabrese et al., 2023).

Prospects remain strong beyond the present limit curve. The 2016 Run II study estimated that with about $Z'$32 at 13 TeV, bileptons with $Z'$33 up to about $Z'$34 GeV were within reach, while $Z'$35 could discover masses in the $Z'$36–$Z'$37 GeV range depending on $Z'$38 (Nepomuceno et al., 2016). More recent HL-LHC studies shift the emphasis toward complementarity: direct pair production primarily probes $Z'$39, while the heavy-quark-mediated channel probes $Z'$40 and remains effective even for off-shell bileptons (Crivellin et al., 14 May 2026).

At future hadron colliders, non-leptonic cascades become visible rather than merely dilutive. For $Z'$41 GeV at FCC-hh, one study found

$Z'$42

and, after cuts and tagging in the benchmark $Z'$43 final state, a signal cross section of $Z'$44 fb corresponding to about $Z'$45 events at $Z'$46, against dominant backgrounds of about $Z'$47 and $Z'$48 events from $Z'$49 and $Z'$50, respectively (Corcella et al., 2021).

6. Conceptual issues, common caveats, and broader phenomenology

Three caveats recur throughout the literature. The first concerns flavor assumptions. Historical low-energy bounds such as $Z'$51 GeV from LEP-era analyses and $Z'$52 GeV from muonium–antimuonium conversion were often derived under flavor-diagonal or diagonal-mixing assumptions. Several collider reinterpretations stress that these assumptions need not hold in the hadron-collider analyses and that the effective sensitivity scales directly with $Z'$53 or the relevant flavor combination (Nepomuceno et al., 2016, Meirose et al., 2011).

The second concerns the relation between vector and scalar doubly charged states. Scalar $Z'$54 searches are experimentally useful templates, but they are not dynamically equivalent to vector bilepton searches. Vector bileptons are spin-1 gauge bosons with $Z'$55-channel $Z'$56 production, $Z'$57-channel VLQ exchange, different angular distributions, and gauge-fixed couplings. This is why scalar limits can be recast only with care. Quantitatively, the minimal 331 calculation found the vector-pair cross section to be about three orders of magnitude larger than scalar-pair production at both 7 and 14 TeV, and a later full-simulation study at 13 TeV obtained $Z'$58 fb versus $Z'$59 fb for a quasi-degenerate benchmark (Barreto et al., 2011, Corcella et al., 2018).

The third concerns ultraviolet consistency. In $Z'$60 models, the coupling relation

$Z'$61

implies a low-energy Landau pole as $Z'$62. One recent study quoted $Z'$63–$Z'$64 TeV from Standard Model running, while a dedicated one-loop analysis of the minimal model found $Z'$65 GeV in the 2HDM-like case below $Z'$66, with $Z'$67 and the pole appearing near $Z'$68 GeV if $Z'$69 GeV. The same work showed that extra $Z'$70-like triplets, a scalar sextet, or a sequential fourth family can raise the pole to about $Z'$71–$Z'$72 TeV, corresponding to bilepton masses of about $Z'$73–$Z'$74 TeV (Crivellin et al., 14 May 2026, Morisi et al., 21 May 2025).

Beyond direct production, vector bileptons enter other observables. In the RM331 model, singly and doubly charged vector bileptons contribute at one loop to $Z'$75 and $Z'$76, enhancing the former and reducing the latter in an anti-correlated pattern under the parameter choices studied there (Yue et al., 2013). In a broader model-independent classification of charged-lepton-flavor-violating vectors, the doubly charged state can also be embedded as the $Z'$77 component of an $Z'$78 doublet with $Z'$79, and future lepton colliders were found to probe parameter space complementary to low-energy experiments (Li et al., 2019).

Taken together, these results define vector bileptons as one of the most sharply constrained and experimentally distinctive gauge-sector extensions of the Standard Model. Their theoretical motivation is tied to anomaly cancellation and family structure in 331 models; their collider phenomenology is governed by narrow same-sign dilepton resonances, exotic-quark thresholds, and, increasingly, VLQ-mediated production; and their present direct limit has reached the $Z'$80 GeV level in multilepton recasts, with HL-LHC and future collider studies extending the program further into the multi-TeV regime (Calabrese et al., 2023).