Vector Leptoquarks (vLQs)

• Vector leptoquarks (vLQs) are spin-1 color-triplet bosons that mediate quark–lepton transitions and address flavor anomalies.
• They naturally arise in gauge extensions like SU(4) or ‘4321’ scenarios, featuring distinct chiral couplings and electric-charge patterns.
• Collider searches use QCD-driven pair production and interference effects in dilepton channels to set mass limits and explore coupling structures.

Vector leptoquarks (vLQs) are spin-1 color-triplet bosons that carry both baryon and lepton number and couple to quark–lepton currents. They occupy a distinctive place among extensions of the Standard Model because the same field can participate in collider signatures with leptons and jets, generate semileptonic four-fermion operators at low energy, and appear naturally in gauge-based constructions such as $SU(4)$ or “4321” scenarios. Contemporary collider literature also emphasizes a terminological caution: vLQs are not vector-like quarks (VLQs), even though the acronyms are often conflated; the former are spin-1 bosons mediating quark–lepton transitions, whereas the latter are spin-$\tfrac12$ colored fermions with SM-like gauge transformations for left- and right-handed components (Kuutmann, 30 Jan 2026).

1. Definition, nomenclature, and representation content

The modern literature uses several closely related naming conventions for vector leptoquarks. The singlet state with Standard Model quantum numbers $(3,1,2/3)$ is denoted $U_1$ in collider analyses and also appears as $V_1$ in flavor-oriented simplified models; both notations refer to the same gauge representation, not to different particles (Collaboration, 2022). Beyond this state, the most common representations in collider and EFT analyses include $U_3$, $V_2$, $\tilde V_2$, and $\tilde U_1$, each with distinct chiral couplings and electric-charge content (Das et al., 24 Jul 2025).

Label	SM representation	Typical role
$U_1$ or $\tfrac12$0	$\tfrac12$1	central benchmark for $\tfrac12$2-anomaly phenomenology
$\tfrac12$3	$\tfrac12$4	left-handed triplet with correlated charged and neutral currents
$\tfrac12$5	$\tfrac12$6	doublet with LR or RL structures
$\tfrac12$7	$\tfrac12$8	charge-shifted doublet
$\tfrac12$9	$(3,1,2/3)$0	singlet with larger electric charge

This classification is not merely taxonomic. The electroweak representation fixes the allowed fermion bilinears, the component electric charges, and the pattern of interference with Standard Model amplitudes. For example, $(3,1,2/3)$1 contains components with electric charges $(3,1,2/3)$2, $(3,1,2/3)$3, and $(3,1,2/3)$4, while the singlet $(3,1,2/3)$5 contains only the $(3,1,2/3)$6 state (Azizi et al., 2019). The broader representation lists used in collider and CLFV studies also track the fermion number $(3,1,2/3)$7, which is useful when organizing allowed operators and decay channels (Farooq et al., 2 Feb 2026).

A recurrent theme is that $(3,1,2/3)$8 dominates phenomenological discussions because it can address both neutral-current and charged-current flavor anomalies, while still admitting direct collider searches in $(3,1,2/3)$9, $U_1$0, $U_1$1, $U_1$2, and related channels (Bernigaud et al., 2021). By contrast, other vLQ species are often introduced to illustrate the model dependence of interference patterns, electric-charge enhancements, or CLFV matching (Das et al., 24 Jul 2025).

2. Interaction structure and effective descriptions

At the level of generic phenomenology, vLQs couple to quark–lepton currents through operators of the schematic form

$U_1$3

with generation-dependent couplings $U_1$4 and model-dependent chiral projectors (Kuutmann, 30 Jan 2026). In the $U_1$5 benchmark used in polarized-collider studies, the interaction is written more explicitly as

$U_1$6

which makes the left-handed and right-handed chiral structures manifest (Farooq et al., 2 Feb 2026).

The gauge and kinetic sector is equally important because vector production depends on the vLQ–gluon interaction. ATLAS-oriented summaries frequently employ

$U_1$7

with $U_1$8 identified as the Yang–Mills scenario and $U_1$9 as minimal coupling (Kuutmann, 30 Jan 2026). A recent LHC reinterpretation instead writes

$V_1$0

so the symbol $V_1$1 enters with a shifted convention, but the physical point is the same: pair production is highly sensitive to the anomalous vector–gluon coupling (Das et al., 24 Jul 2025).

Branching-fraction notation is standardized across much of the collider literature. One defines

$V_1$2

with generation assignments usually grouped into first $V_1$3, second $V_1$4, and third $V_1$5 families (Kuutmann, 30 Jan 2026). In the ATLAS pair-production search for $V_1$6, nominal samples were generated with purely left-handed couplings and $V_1$7, then reweighted to scan $V_1$8 charged lepton$V_1$9 (Collaboration, 2022).

For indirect observables, integrating out vLQs generates SMEFT operators such as $U_3$0, $U_3$1, $U_3$2, $U_3$3, $U_3$4, $U_3$5, and $U_3$6. In the vector case, the CLFV analysis of tau processes gives explicit matching relations, for example

$U_3$7

for the $U_3$8 singlet, and analogous relations for $U_3$9, $V_2$0, $V_2$1, and $V_2$2 (Husek et al., 2021).

3. Production mechanisms and characteristic kinematics

At hadron colliders, vLQ pair production is dominantly QCD-driven through $V_2$3 and $V_2$4 initial states. For the ATLAS $V_2$5 search, this production was treated as largely insensitive to the leptoquark–lepton couplings and controlled instead by the vector–gluon interaction, with separate Yang–Mills and minimal-coupling scenarios giving enhanced or reduced cross sections, respectively (Collaboration, 2022). Standard ATLAS interpretations also note that $V_2$6 is larger than for scalar leptoquarks at the same mass and depends strongly on the anomalous gluon coupling (Kuutmann, 30 Jan 2026).

Single production probes a different part of parameter space because it scales with the fermionic couplings. Standard resonant topologies include $V_2$7 or $V_2$8, and the salient observable is a lepton–jet resonance $V_2$9 (Kuutmann, 30 Jan 2026). In flavorful $\tilde V_2$0 models with dominant $\tilde V_2$1 couplings, the decay pattern is fixed by $\tilde V_2$2: approximately,

$\tilde V_2$3

with the ratio of second- to third-generation final states determined by $\tilde V_2$4 (Bernigaud et al., 2021).

A more recent development is the systematic inclusion of nonresonant channels in dilepton tails. The LHC reinterpretation in “Fresh look at the LHC limits on vector leptoquarks” organizes the full signal into pair production, single production, indirect production from t/u-channel vLQ exchange, and indirect interference with Standard Model Drell–Yan. The interference term can be constructive or destructive depending on the vLQ species and chirality; notably, it is destructive for $\tilde V_2$5 with LL or RR couplings, negative for $\tilde V_2$6 with LR couplings, positive for $\tilde V_2$7 with RL couplings, and sign-dependent across $\tilde V_2$8 components (Das et al., 24 Jul 2025). This substantially alters the high-$\tilde V_2$9 dilepton spectrum.

Future lepton colliders access a different production regime. In the polarized $\tilde U_1$0 study centered on $\tilde U_1$1, pair production proceeds primarily through $\tilde U_1$2-channel $\tilde U_1$3 exchange, and helicity conservation favors RL and LR initial states. The polarized cross section is written as

$\tilde U_1$4

which makes beam polarization a direct handle on both signal enhancement and chirality diagnostics (Farooq et al., 2 Feb 2026).

4. Collider searches and exclusion limits

The first dedicated ATLAS search for pair-produced scalar and vector leptoquarks decaying to third-generation quarks and first- or second-generation leptons used the full Run 2 dataset of $\tilde U_1$5 at $\tilde U_1$6 TeV and selected events with exactly one signal electron or muon, $\tilde U_1$7 GeV, at least four small-$\tilde U_1$8 jets, at least one $\tilde U_1$9-tagged jet at the $U_1$0 working point, and a hadronic top candidate reconstructed by iterative reclustering. Separate NeuroBayes networks were trained for vector hypotheses at $U_1$1, and no significant deviation from the Standard Model expectation was observed (Collaboration, 2022).

Scenario at $U_1$2 charged lepton$U_1$3	Decay mode	Observed 95% CL lower limit
Yang–Mills	$U_1$4	$U_1$5 GeV
Yang–Mills	$U_1$6	$U_1$7 GeV
Minimal coupling	$U_1$8	$U_1$9 GeV
Minimal coupling	$\tfrac12$00	$\tfrac12$01 GeV

These limits are particularly relevant for $\tfrac12$02-anomaly-motivated $\tfrac12$03 scenarios with $\tfrac12$04, where decays to charged and neutral second-generation leptons are comparable (Collaboration, 2022). The same analysis also provided exclusion contours versus branching fraction, with sensitivity degrading as $\tfrac12$05 charged lepton$\tfrac12$06 because the observed lepton increasingly originates from top decay and becomes more background-like.

A separate source of confusion is the 2026 ATLAS proceedings summary, which discusses leptoquark searches but does not present direct vLQ mass limits. The only vector-leptoquark appearance there is as an intermediate $\tfrac12$07 state in a “4321” search for pair-produced vector-like leptons $\tfrac12$08 and $\tfrac12$09, where the excluded mass range is $\tfrac12$10 to $\tfrac12$11 GeV for the VLL cross section predicted by the model; no direct $\tfrac12$12 mass, $\tfrac12$13, or $\tfrac12$14 constraint is extracted (Kuutmann, 30 Jan 2026). This is a common misreading of the proceedings.

Beyond dedicated resonance searches, the 2025 reinterpretation of LHC data shows that including QCD–QED mixed pair-production channels and Drell–Yan interference materially shifts exclusions. At $\tfrac12$15 TeV with $\tfrac12$16, model-independent mass bounds in the $\tfrac12$17 mode extend, after including QCD+QED channels, from $\tfrac12$18 TeV for $\tfrac12$19 at $\tfrac12$20 to $\tfrac12$21 TeV for $\tfrac12$22 at $\tfrac12$23, with typical upward shifts of $\tfrac12$24–$\tfrac12$25 GeV relative to QCD-only limits (Das et al., 24 Jul 2025). The same study emphasizes that destructive interference in dimuon tails can make coupling bounds stronger than direct pair- or single-production recasts for some species, especially $\tfrac12$26.

For $\tfrac12$27-flavoured $\tfrac12$28 states, collider sensitivity depends strongly on branching structure. In the simplified $\tfrac12$29 model, direct third-generation searches constrain the mass up to $\tfrac12$30–$\tfrac12$31 GeV when the branching fraction is entirely to third-generation quarks, while jets-plus-missing-energy searches constrain it up to $\tfrac12$32–$\tfrac12$33 GeV and are largely insensitive to the third-generation branching fraction (Bernigaud et al., 2021).

5. Flavor anomalies, SMEFT matching, and indirect constraints

The theoretical prominence of vLQs derives from their ability to generate the two semileptonic operator patterns most often invoked in flavor anomalies. In the left-handed $\tfrac12$34 simplified model, tree-level exchange yields

$\tfrac12$35

so $\tfrac12$36 is generated in $\tfrac12$37, while charged-current $\tfrac12$38 transitions receive

$\tfrac12$39

Global fits with $\tfrac12$40, $\tfrac12$41, and $\tfrac12$42 TeV gave Standard-Model pulls of approximately $\tfrac12$43, $\tfrac12$44, and $\tfrac12$45, respectively, while future discovery or exclusion power was identified in $\tfrac12$46, $\tfrac12$47, LFV $\tfrac12$48 decays, and $\tfrac12$49–$\tfrac12$50 conversion (Hati et al., 2020).

Earlier $\tfrac12$51 and $\tfrac12$52 analyses expressed the same mechanism in the Wilson coefficients of the weak effective Hamiltonian. For $\tfrac12$53,

$\tfrac12$54

while $\tfrac12$55 receives $\tfrac12$56 and, for $\tfrac12$57, potentially $\tfrac12$58 (Sahoo et al., 2016). This explains why the singlet and triplet states remain the canonical flavor benchmarks.

Indirect constraints are often far stronger on coupling products than direct collider searches are on masses. In the CLFV analysis based on $\tfrac12$59-LFV hadronic decays and $\tfrac12$60–$\tfrac12$61 conversion, Belle II projections imply $\tfrac12$62–$\tfrac12$63 TeV for several LL, LR, RL, and RR coupling products with $\tfrac12$64, and up to $\tfrac12$65 TeV for the $\tfrac12$66 combination entering $\tfrac12$67; by contrast, current $\tfrac12$68–$\tfrac12$69 conversion bounds are much weaker (Husek et al., 2021). These are EFT bounds on coupling products, not direct resonance exclusions, but they strongly constrain off-diagonal flavor structure.

Loop effects can also be numerically important in gauge-based vLQ models. In an $\tfrac12$70-based framework with $\tfrac12$71, one-loop corrections at fixed on-shell couplings enhance the left-handed SMEFT coefficient $\tfrac12$72 by approximately $\tfrac12$73 and the right-handed scalar coefficient $\tfrac12$74 by approximately $\tfrac12$75 for $\tfrac12$76, while radiatively generating $\tfrac12$77 at roughly $\tfrac12$78 of the LO $\tfrac12$79 normalization (Fuentes-Martin et al., 2019). This directly modifies the mapping between low-energy fits and collider constraints.

The same left-handed vector structure propagates into baryonic semileptonic decays. For $\tfrac12$80 in $\tfrac12$81, the model induces only

$\tfrac12$82

so normalized angular quantities remain largely SM-like while normalization-sensitive observables shift. In the reported fits, $\tfrac12$83 moved from the SM range $\tfrac12$84–$\tfrac12$85 to $\tfrac12$86–$\tfrac12$87 in one solution and $\tfrac12$88–$\tfrac12$89 in another (Azizi et al., 2019).

6. Future directions and unresolved issues

The next stage of vLQ phenomenology is shaped by both luminosity and methodology. ATLAS already frames the near-term collider outlook in terms of growing Run 3 luminosity and the HL-LHC, with improved sensitivity expected in pair-production channels because spin-1 cross sections are larger, and in single-production channels because they directly probe the flavor couplings $\tfrac12$90 (Kuutmann, 30 Jan 2026). In $\tfrac12$91-flavoured $\tfrac12$92 models, conservative HL-LHC extrapolations based on MET searches reach about $\tfrac12$93 TeV for minimal couplings and $\tfrac12$94 TeV for Yang–Mills-like couplings (Bernigaud et al., 2021).

A parallel frontier is polarized lepton collisions. For $\tfrac12$95 at $\tfrac12$96 TeV with $\tfrac12$97 TeV, the beam configuration $\tfrac12$98, $\tfrac12$99 maximizes the cross section at approximately $(3,1,2/3)$00 fb, compared with an unpolarized baseline of approximately $(3,1,2/3)$01 fb. The same study finds $(3,1,2/3)$02 up to $(3,1,2/3)$03 under full polarization and $(3,1,2/3)$04 up to approximately $(3,1,2/3)$05–$(3,1,2/3)$06, while $(3,1,2/3)$07 annihilation remains about $(3,1,2/3)$08 times larger than $(3,1,2/3)$09 fusion for the same $(3,1,2/3)$10 (Farooq et al., 2 Feb 2026). This makes polarization a genuine characterization tool, not merely a luminosity enhancement.

Several open issues remain model-dependent. First, direct reinterpretation of scalar-LQ limits as vector-LQ limits is not justified, because pair and single production have different kinematics and systematic structures, and the anomalous vector–gluon coupling plays a central role for vLQs (Kuutmann, 30 Jan 2026). Second, the fresh LHC recast shows that EFT descriptions reproduce the full theory reliably only once $(3,1,2/3)$11 TeV for first-generation couplings, with higher thresholds for heavier flavors (Das et al., 24 Jul 2025). Third, widths are not always negligible: the ATLAS $(3,1,2/3)$12 search used $(3,1,2/3)$13, corresponding to a modeled width of approximately $(3,1,2/3)$14, and treated decays with MadSpin rather than a strict narrow-width approximation (Collaboration, 2022).

Taken together, these developments place vLQs in an unusual theoretical position. They are simultaneously direct-search targets, low-energy EFT mediators, and benchmarks for correlated flavor anomalies. This suggests that future progress will depend less on any single exclusion number than on consistent global treatments combining resonance production, nonresonant interference, chirality-sensitive observables, and flavor data across collider and non-collider experiments (Das et al., 24 Jul 2025).