TeV-Scale Vectorlike Leptons in BSM

• TeV-scale vectorlike leptons are hypothetical fermions with identical left- and right-handed gauge interactions, allowing Dirac mass terms independent of the Higgs mechanism.
• They impact electroweak precision data and lepton flavor observables, offering insights into neutrino mass generation, extended Higgs sectors, and grand unification.
• Collider searches and indirect measurements constrain their masses to the TeV regime, encouraging targeted strategies in BSM model building and experimental investigations.

TeV-scale vectorlike leptons are hypothetical fermions beyond the Standard Model that possess left- and right-handed components transforming identically under the gauge group, allowing for vectorlike mass terms. Unlike the chiral leptons of the Standard Model, these states can obtain masses independent of electroweak symmetry breaking. The TeV mass regime is motivated by a broad set of phenomenological, theoretical, and cosmological considerations, and TeV-scale vectorlike leptons play prominent roles in models addressing neutrino masses, the Higgs sector, lepton flavor, precision observables, and collider phenomenology. This article surveys the theoretical structure, experimental signatures, and phenomenological implications of TeV-scale vectorlike leptons, with emphasis on constraints from precision measurements, their roles in model building, and prospects for detection.

1. Theoretical Structure and Realizations

Vectorlike leptons are characterized by the property that their left- and right-chiral components transform identically under the SM gauge group, so gauge-invariant Dirac mass terms $M \bar{\Psi}_L \Psi_R$ can be written independently of the Higgs mechanism. Generic representations studied in the literature include $SU(2)_L$ singlets and doublets with hypercharges matching those of standard leptons or neutrinos. These states can arise in various UV completions such as grand unified theories (e.g., $E_6$ or $SO(10)$ multiplets (Hebbar et al., 2016)), string-inspired constructions, extra-dimensional models (Megias et al., 2017), or extended gauge sectors (e.g., left-right symmetric or Pati–Salam models (Dev et al., 2015, Iguro et al., 2021)).

In many frameworks, the vectorlike nature is enforced either by symmetry-breaking patterns (e.g., via a singlet VEV in $E_6$ models) or by embedding in complete representations (to preserve gauge coupling unification (Joglekar et al., 2013)). Masses are often at or above the electroweak scale, with phenomenological lower bounds of hundreds of GeV up to several TeV depending on the representation and collider searches.

2. Constraints from Electroweak Precision and Lepton Flavor Observables

Vectorlike leptons modify SM observables through mixing with ordinary leptons and extra loop contributions. Their dominant indirect effects fall into two categories:

• Electroweak Precision Data (EWPD): Integrating out heavy vectorlike leptons generates dimension-6 operators in the effective Lagrangian, resulting in modified Z and W couplings to leptons, and corrections to the invisible Z width and various asymmetries. Global electroweak fits constrain the mixing angles to be small (order 0.01–0.08 at 90% confidence) and show that the SM plus vectorlike leptons provides a fit comparable in quality to the SM alone. Importantly, the presence of a neutral singlet vectorlike lepton (mixing with the electron or muon) can relax the upper bound on the Higgs mass set by EWPD fits, permitting values of $M_H$ up to $\sim 260$ GeV, alleviating tension with LEP limits (0803.4008).
• Lepton Flavor Violation (LFV): If the new leptons mix with more than one SM flavor, they mediate flavor-changing decays such as $\mu \to e\gamma$ or $\mu \to 3e$ and contribute to the electron EDM. These processes are extremely suppressed in the SM but receive unsuppressed chirality-flipping contributions from vectorlike leptons (of the form $$C_{ij} \sim \lambda_L^i \lambda_E^j h_E^{\prime\prime}/M_E M_L$$) (Ishiwata et al., 2013). Empirically, this limits sizeable off-diagonal mixing and can probe vectorlike lepton masses up to $\sim 100$ TeV for natural-size couplings. The combined constraints enforce nearly flavor-diagonal mixing patterns.

3. Roles in BSM Model Building: Higgs Physics, Neutrino Mass, and Unification

Vectorlike leptons enable new mechanisms within extended Higgs sectors and neutrino mass models:

• Vacuum Stability and Higgs Diphoton Rate: Large Yukawa couplings of vectorlike leptons to the Higgs can destabilize the Higgs potential, driving the quartic towards negative values at relatively low scales. Supersymmetric extensions resolve this by superpartner loops stabilizing the potential and aligning quartic couplings with gauge couplings. Embedding the extra matter in a complete $SO(10)$ $16+\overline{16}$ multiplet preserves gauge unification. The combined contributions of heavy leptons and sleptons can enhance the $h \to \gamma\gamma$ rate by up to $\sim 50\%$ (for $M_{L,E}, \mu \gtrsim 100$ GeV and perturbative Yukawas) while maintaining stability (Joglekar et al., 2013).
• Neutrino Mass and Leptogenesis: In left-right (L-R) symmetric and seesaw models at the TeV scale, vectorlike leptons naturally arise and impact the structure of Dirac and Majorana mass matrices. The enhanced mixing parameters required for heavy-light neutrino mixing can give rise to observable vectorlike leptons, and their interactions are constrained by the dynamics of resonant leptogenesis. Constraints on $m_{W_R}$ from successful baryogenesis (typically $m_{W_R} \geq 10$ TeV) also correlate to the allowed parameter space for heavy leptons (Dev et al., 2015).
• Grand Unification: In the context of $E_6$ or $SO(10)$ SUSY GUTs, third-generation vectorlike leptons share Yukawa couplings with the standard $t$, $b$, and $\tau$, being embedded in the $27_3 \times 27_3 \times 27_H$ invariant. TeV-scale VEVs of singlet components set the masses, leading to experimental lower bounds of $M_L \gtrsim 2.9$ TeV, set by $Z'_\psi$ searches (Hebbar et al., 2016).

4. Collider Signatures and Search Strategies

TeV-scale vectorlike leptons can yield distinctive signatures at hadron and lepton colliders, although their observability depends strongly on their gauge quantum numbers and flavor couplings:

• Direct Production: For $SU(2)$ doublets, production cross-sections are larger due to additional gauge couplings and lead to final states with multiple leptons (particularly $\tau$ or multi-lepton events), whereas singlet leptons have smaller rates and decay dominantly to $W\nu$ (with weaker signatures). At the LHC, doublet VLLs can be probed up to $275$ GeV (8 TeV data) and potentially $440$ GeV (13 TeV, 100 fb$^{-1}$, doublet case). For future colliders, a 100 TeV FCC-hh could exclude doublets to nearly $6$ TeV, but singlet leptons only to $2.85$ TeV (for exotic decay scenarios) (Kumar et al., 2015, Bhattiprolu et al., 2019).
• Cascade Decays via Extended Higgs Sectors: In two Higgs doublet models or Higgs-rich frameworks, heavy Higgs bosons above the $t\bar{t}$ threshold may decay into vectorlike leptons and a SM lepton, with subsequent cascade decays into $Z$, $h$, or $W$ plus leptons or missing energy. Multi-lepton final states with suppressed invariant mass near $Z/W/h$ provide key observables. The HL-LHC can probe heavy Higgs masses up to $2.7$ TeV and vectorlike lepton masses up to $2$ TeV via such channels (Dermisek et al., 2022, Dermisek et al., 2022).
• Specialized Observables and EFT Approaches: For scenarios where production or decay is via higher-dimensional operators, effective field theory (EFT) techniques constrain contact interactions to $0.05$ TeV$^{-2}$, and observables such as invariant mass reconstruction in multi-jet plus lepton events enhance sensitivity (Chala et al., 2020).
• Indirect Signatures: In addition to direct searches, precision measurements such as the muon or electron $g-2$, and rare decays (e.g., $\mu \to e\gamma$) provide indirect sensitivity to much heavier states due to chiral enhancement in loops.

5. Impact on Precision Observables and Low-Energy Phenomenology

Vectorlike leptons have non-decoupling effects in certain observables, with technical highlights including:

• Lepton Anomalous Magnetic Moments: Mixing-induced chiral flips with TeV-scale vectorlike leptons, combined with mechanisms such as extended Higgs sectors (where contributions are amplified by $\tan^2\beta$), can explain the observed $(g-2)_\mu$ anomaly even for lepton and Higgs masses in the several- or even tens of TeV regime, for order-one Yukawas—see estimates such as

$$\Delta a_\mu^{H, A, H^\pm} \propto \frac{\tan^2\beta}{16\pi^2} \frac{m_\mu m_\mu^{LE}}{v^2}$$

with $m_\mu^{LE}$ encoding the chiral enhancement from heavy lepton mixing (Dermisek et al., 2020).

• Electric Dipole Moments and $\mu \to 3e$: The chirality flip from vectorlike lepton mixing is unsuppressed by SM lepton masses, so even very massive ($\sim 10$–100 TeV) extra generations can yield order-current EDM and LFV rates if natural-size couplings exist (Ishiwata et al., 2013).
• Higgs Coupling Deviations: Large mixing can alter $h\mu\mu$ and $h ee$ couplings, with implications for precision Higgs physics at future lepton colliders (Dermisek et al., 2020).

6. Phenomenological and Model-Building Implications

TeV-scale vectorlike leptons are theoretically well-motivated in scenarios involving:

• Grand Unification, family replication, and the flavor puzzle: Incorporation in $E_6$ or Pati–Salam models provides successful unification and links VLL masses and couplings to GUT scales, also explaining the flavor structure via mechanisms like flavor democracy (Hebbar et al., 2016, Acar et al., 2021).
• Neutrino mass generation at the TeV scale: Vectorlike leptons participate in low- or linear-seesaw constructions, establishing correlations among lepton mixing, collider signatures, and baryogenesis (resonant leptogenesis) (Dev et al., 2015).
• Solutions to precision anomalies and Higgs sector extensions: Their presence offers dynamically viable means of addressing the measured value of $g-2$ and provides new channels influencing Higgs decays, especially where extended Higgs sectors are invoked (Dermisek et al., 2020, Dermisek et al., 2022).
• Relaxing EWPD tension/allowing for a heavier Higgs: The effects of weak-scale VLLs on EWPD global fits can relax the upper bounds on the Higgs mass compatible with data, reconciling mild tension with LEP bounds (0803.4008).

Model constraints frequently require precise control of flavor structures—typically invoking nearly flavor-diagonal mixing—and, in cases with more elaborate flavor structure (e.g., involving additional scalars mediating flavor), novel multi-lepton collider signatures provide clean signals (Bißmann et al., 2020).

7. Future Prospects and Open Questions

Future LHC runs and next-generation colliders will significantly expand the direct and indirect reach for TeV-scale vectorlike leptons. Promising avenues include:

• Enhanced multi-lepton and cascade searches at the HL-LHC and future hadron colliders, pushing mass sensitivity to several TeV, especially in doublet scenarios or those with extended Higgs sectors (Bhattiprolu et al., 2019, Dermisek et al., 2022).
• Precision flavor, EDM, and lepton universality measurements that continue to probe very high mass scales via virtual effects, possibly pushing sensitivity for vectorlike lepton masses to the $10$–100 TeV range for reasonable couplings.
• The interplay between their discovery and extended sectors such as axion-like particles (ALPs), Pati–Salam leptoquarks, or additional heavy gauge or Higgs bosons, with correlated signals in flavor anomalies and rare decay processes.
• For scenarios with TeV-scale PQ symmetry breaking and vectorlike leptons, novel signatures and ALP phenomenology are anticipated due to suppressed but non-negligible couplings, enabling both collider and low-energy probes (Giorgi et al., 27 Nov 2024).

Ongoing theoretical work seeks to further clarify the viable parameter spaces, the naturalness of the required mass and mixing patterns, and the optimal search strategies in both direct and indirect settings.