Non-Universal Fermion Couplings in BSM Models

• Non-Universal Fermion Couplings are BSM extensions where gauge bosons and operators couple with different strengths to SM fermion flavors.
• Models employ extra U(1) symmetries, extra dimensions, and geometric mechanisms to generate unique flavor hierarchies and mass patterns.
• Distinct signatures such as controlled FCNCs and rare lepton decays provide actionable insights for both collider and low-energy experiments.

Non-Universal Fermion Couplings

Non-universal fermion couplings refer to extensions of the Standard Model (SM) in which gauge bosons, scalars, or effective operators couple to different SM fermion flavors with distinct strengths or chiral structures. These non-universal interactions are realized in a broad set of BSM frameworks motivated by flavor hierarchies, anomalies in low-energy data, or the structure of gauge and geometry-induced currents. The phenomenology and dynamical origin of such couplings exhibit significant model-dependent variety, ranging from additional Abelian gauge symmetries with generation-dependent charges to geometric origin via torsion, higher-dimensional constructions, and composite dynamics.

1. Model Building Frameworks and Charge Assignments

A range of minimal and non-minimal BSM constructions induce non-universal fermion couplings, typically by extending the SM gauge group with new gauge factors, altering matter representations, or invoking geometric or dynamical effects.

• Abelian U(1) Extensions: Non-universality is implemented by assigning family-dependent U(1) charges to left- and right-handed quarks and leptons. Anomaly cancellation highly constrains allowed charge patterns. Notable examples are:
  • Partial universality: Charges (1, 1, –2) for i=1,2,3 assign equal charge to the first two generations, separating the third (Mohanta et al., 7 Aug 2025).
  • General non-universal forms: Arbitrary chiral charge vectors parameterized by four independent parameters; anomaly cancellation can operate per family or between families (Benavides et al., 2016).
  • Two non-universal U(1)s: The sum reconstructs SM hypercharge; the mechanism enables cancellation via interplay among families, leading to a minimal set of free parameters to accommodate realistic fermion mass matrices (Benavides et al., 2024).
• Non-Abelian and Multi-site Models:
  • Three-site Pati-Salam: The gauge group is replicated per family; matter fields are localized by construction, yielding site/family-specific couplings after gauge symmetry breaking and decoupling link fields. Hierarchies in couplings follow from ratios of site-specific vacuum expectation values (VEVs) (Pagès, 2021).
  • 5D/Orbifold Constructions: Gauge fields and fermions propagate in extra dimensions, with flavor as an index induced by geometry. SO(3) breaking to U(1)' via orbifolding equips SM zero modes as neutral under U(1)', while non-universal Z′ couplings emerge from integrating out heavy Kaluza-Klein (KK) states after brane-localized symmetry breaking (Anda et al., 2020).
• Torsion and Geometric Origins: The interaction of fermion spin and spacetime torsion generates non-universal contact (four-fermion) interactions, with generically flavor- and chirality-dependent effective coupling constants arising at low energies. These couplings are independent parameters for each chirality and species (Chakraborty et al., 2024).
• String/Magnetized Brane Realizations: Chiral matter wavefunctions in compact space with background (non-commuting) fluxes yield non-universal overlap integrals, producing family-dependent Yukawa couplings (0904.0910).

2. Gauge Interactions and Coupling Structures

Non-universal couplings manifest in the gauge sector via the interaction Lagrangian: $$\mathcal{L}_{Z'} = g' \sum_{f,i,j} (Q_{f}^{L})_{ij}\,\overline{f_{Li}}\gamma^\mu f_{Lj}\,Z'_\mu + (L\to R)$$ where $(Q_{f}^{L})_{ij}$ is a non-diagonal, family-dependent charge matrix. For partial universality (e.g., $q=(1,1,-2)$), off-diagonal couplings are suppressed for the first two families, while couplings involving the third family remain (Mohanta et al., 7 Aug 2025).

Table: Example Chiral Couplings in Minimal Non-Universal U(1) Models (Benavides et al., 2024).

Fermion	$g_{Z'}\tilde\epsilon^L$ (families 1,2)	$g_{Z'}\tilde\epsilon^L$ (family 3)
$u, d$	$\frac{1}{3}z$	$\frac{1}{3}z$
$e, \nu$	$-z$	$-z$

Chirality and family separation persists because constraints from anomaly cancellation, Yukawa invariance, and charge normalization tightly link the allowed patterns (Benavides et al., 2016, Benavides et al., 2024).

3. Mechanisms for Fermion Mass and Mixing Hierarchies

Non-universal gauge couplings are intimately associated with explanations for fermion mass hierarchies.

• Radiative and Seesaw Mechanisms: Tree-level mass entries are forbidden or restricted by non-universal symmetries, enforced via charge selection rules. For instance:
  • Partial universality permits rank-1 tree-level mass matrices, yielding a massive third generation; lighter generations receive loop-suppressed contributions from gauge or scalar loops (Mohanta et al., 7 Aug 2025).
  • Flavour non-universal multiple U(1)s (e.g., $U(1)_x$, $U(1)_y$ with charges [0,1,–1] and [1,–1,0]) enable a two-step radiative mass hierarchy where the second and first generations receive masses from vector bosons with hierarchical gauge masses (Mohanta et al., 2022).
• Texture Zeros in Yukawa Matrices: Non-universal charges enforce forbidden elements in the Yukawa matrices, generating texture zeros essential to mass/mixing hierarchies, especially under multiple Higgs vevs (Díaz et al., 2017).
• Inverse Seesaw and Geometric Sequestration: In multi-site or extra-dimensional models, nearest-neighbor or exponentially localized VEVs/overlaps reproduce observed CKM/PMNS structures and generate acceptable neutrino masses (Pagès, 2021).

4. Flavor-Changing Neutral Currents and Phenomenological Constraints

Non-universal couplings typically induce tree-level flavor-changing neutral currents (FCNCs) in the gauge interaction basis, rotated into the physical mass basis by the mismatch of diagonalizing matrices.

• Suppression Strategies:
  • Partial universality: FCNCs involving the first two generations are absent or highly suppressed if $q_1=q_2$, substantially relaxing typical constraints on new vector boson masses by several orders of magnitude (e.g., $M_{Z'} \gtrsim 200$ TeV, compared to $>10^4$ TeV in the fully non-universal case) (Mohanta et al., 7 Aug 2025).
  • CKM Alignment: If the flavor structure aligns with the CKM matrix, off-diagonal couplings are proportional to known mixing elements (e.g., $\Gamma^d_{sb}\propto V_{ts} V_{tb}^*$), leading to definite predictions for FCNC rates in $b \to s \ell^+ \ell^-$ and related channels (Fuentes-Martin, 2015).
• Lepton Flavor Violation: Non-universal couplings, especially when off-diagonal, mediate rare lepton decays such as $\mu\to 3e$, $\tau\to 3\mu$, with current experimental bounds implying $M_{Z'} > 2$–6 TeV for $g_{V,A}\sim 0.1$ and $g_{V,A}^{e\mu} \lesssim 10^{-4}$ for $M_{Z'}\sim 3$ TeV (Orduz-Ducuara, 2016).
• Collider and Precision Constraints: Dilepton resonance and precision electroweak data typically probe the parameter space wherever couplings to first- or second-generation fermions are significant. For third-generation-philic ("anogenophilic") couplings, LHC sensitivity is shifted to channels such as $t\bar{t}$ or $b\bar{b}$ final states, requiring alternate search strategies (Barbosa et al., 2022).

5. Scalar Sector, FCNC Cancellation, and Higgs Alignment

In non-universal setups with extended Higgs sectors (notably two-Higgs doublet models (2HDM)), flavor alignment is an acute issue:

• Yukawa Alignment: Assigning each right-handed fermion to couple only with a single Higgs doublet, enforced by charge assignments, results in tree-level Higgs-mediated FCNCs being identically zero in the mass basis. This mechanism is distinct from the usual natural flavor conservation criteria or generic type-II 2HDM approaches (Benavides et al., 2024).
• Radiative Yukawa Corrections: Loop corrections from non-universal gauge interactions induce calculable deviations in Higgs–fermion couplings (e.g., $\kappa_b$, $\kappa_\tau$ altered at the few-percent level), providing testable predictions in future precision Higgs measurements (Mohanta et al., 7 Aug 2025).

6. Ultraviolet Completions and Theoretical Realizations

Non-universal couplings have diverse origins, each with characteristic low-energy signatures and theoretical consistency requirements.

• 4D Gauge Extensions: Minimal models exploit anomaly-free chiral charge parameterizations, unifying scenarios such as $B\!-\!L$, lepton-philic, or top-philic Z′ by varying a small number of parameters (Benavides et al., 2016).
• Multi-site and 5D Constructions: Deconstructed gauge symmetries, 5D orbifolds with sites/defects, or warped extra dimensions realize non-universal couplings either via geometrical localization or link fields, explaining both gauge and Yukawa structures (Pagès, 2021, Anda et al., 2020).
• String Realizations: Magnetized brane models with general flux backgrounds yield zero-mode wavefunctions whose overlaps (Yukawa couplings) and gauge interactions are inherently family-dependent due to the geometry and flux quantum numbers, generating non-universal hierarchies matched to observed masses (0904.0910).
• Geometric Torsion: Gravitational torsion, once integrated out, generates flavor- and chirality-specific four-fermion contact interactions whose coefficients are largely unconstrained except by low-energy parity-violating observables (Chakraborty et al., 2024).

7. Experimental Signatures and Outlook

The phenomenological reach and future testability of non-universal fermion couplings depend on the size of non-universal parameters and the mass scale of new mediators:

• LHC/HL-LHC Probes: Suppressed universal (first/second generation) couplings hide Z′ from classic Drell-Yan searches; third-generation signatures ($t\bar{t}Z'$, $b\bar{b}$) with machine-learning event discrimination become central (Barbosa et al., 2022).
• Lepton-Flavor Violation and Parity-violation: Low-energy processes ($\mu \to 3 e$, PVDIS), atomic parity violation, and CKM unitarity remain critical, especially for off-diagonal and chirality-dependent couplings (Orduz-Ducuara, 2016, Chakraborty et al., 2024).
• Flavor Anomalies and Mixing: Models with non-universal fermion couplings and protected FCNC offer explanations for $b\to s\ell\ell$ (e.g., $R_K$) and predict specific pattern of deviations in semileptonic ratios and neutrino unitarity-violation observables (Fuentes-Martin, 2015, Pagès, 2021).

Non-universal fermion couplings thus represent a robust, theoretically and phenomenologically diverse framework. They connect flavor puzzles, mass hierarchies, and BSM searches, and remain a focal point for both indirect and direct experimental scrutiny across low- and high-energy domains.