Flavor-Changing Up-Type Quark Couplings

• Flavor-changing up-type quark couplings are non-diagonal interactions vital for inducing rare top decays (e.g., t → qZ, t → qH) and charm mixing.
• SMEFT dimension-6 operators and explicit new physics scenarios systematically parameterize these couplings, revealing key interference effects and parameter correlations.
• Collider studies at the LHC and HL-LHC, along with low-energy flavor observables, set stringent bounds that critically constrain the allowed new physics parameter space.

Flavor-changing couplings to up-type quarks refer to effective, non-diagonal interactions that connect distinct generations among the up-type quark sector. These couplings manifest in both Standard Model (SM) effective field theory extensions and explicit new-physics scenarios, inducing processes such as $t \to q Z$ or $t \to q H$ ($q=u,c$), $t \to qg$, as well as neutral-current phenomena in the charm sector (e.g., $D^0$–$\bar D^0$ mixing). These interactions are highly suppressed in the SM due to the Glashow–Iliopoulos–Maiani (GIM) mechanism, but numerous ultraviolet completions and effective operator analyses provide a fertile ground for experimental exploration and theoretical constraint.

1. Operator Basis and Effective Lagrangians for Up-Type FCNC

In the Standard Model Effective Field Theory (SMEFT), flavor-changing couplings to up-type quarks are generated primarily by dimension-6 operators invariant under $SU(3)_C \times SU(2)_L \times U(1)_Y$. For up-type neutral-current transitions such as $t \to q Z$ ($q=u,c$), the operator set includes (Hioki et al., 2019): $$\begin{aligned} &\mathcal{O}_{\phi q}^{(1)ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu \phi)(\bar q_i \gamma^\mu q_j),\ &\mathcal{O}_{\phi q}^{(3)ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu^I \phi)(\bar q_i \tau^I \gamma^\mu q_j),\ &\mathcal{O}_{\phi u}^{ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu \phi)(\bar u_i \gamma^\mu u_j),\ &\mathcal{O}_{uW}^{ij} = (\bar q_i \sigma^{\mu\nu} \tau^I u_j)\tilde\phi\, W^I_{\mu\nu},\ &\mathcal{O}_{uB}^{ij} = (\bar q_i \sigma^{\mu\nu} u_j) \tilde\phi\, B_{\mu\nu}, \end{aligned}$$ where $i\neq j$ are flavor indices, $\phi$ is the Higgs doublet, and $\tilde\phi$ its conjugate.

After electroweak symmetry breaking, the effective $tqZ$ Lagrangian can be reduced to: $$\mathcal{L}_{tqZ} = -\frac{g}{2\cos\theta_W} \bar{q}\gamma^\mu (f_1^L P_L + f_1^R P_R) t Z_\mu - \frac{g}{2\cos\theta_W} \bar{q} \frac{\sigma^{\mu\nu}}{M_Z}(f_2^L P_L + f_2^R P_R) t\,\partial_\mu Z_\nu + \text{h.c.}$$ with four independent complex coefficients per transition, $f_{1,2}^{L,R}(tqZ)$, parametrizing vector and dipole interactions (Hioki et al., 2019).

Gluonic FCNCs are governed by dimension-5 tensor operators,

$$\mathcal{L}_{\text{FCNC}}^{tgq} = \frac{\kappa_{tgq}}{\Lambda} g_s\,\bar{q}\sigma^{\mu\nu} T^a t\,G^a_{\mu\nu} + \text{h.c.}$$

where $\kappa_{tgq}$ is a dimensionless coupling and $\Lambda$ the NP scale (Collaboration et al., 2010).

Top-Higgs flavor-violating couplings are parametrized as: $$\mathcal{L}_{\text{FCNC}}^{tqH} = -\kappa_{tqH}\,\bar{t} H q + \text{h.c.},$$ with $\kappa_{tqH}$ real and dimensionless (Liu et al., 2015).

In multi-Higgs and extended gauge scenarios, analogous structures arise with flavor-off-diagonal entries in the mass-eigenstate basis, mediated by additional scalars or $Z'$ bosons, respectively (Duy et al., 2024, Gupta et al., 2010, Dinh et al., 2019).

2. Low-Energy Constraints and Phenomenological Implications

Up-type flavor-changing currents are stringently constrained by low-energy flavor observables, prominently $D^0$–$\bar D^0$ mixing, rare charm decays, and top rare decays. Explicitly, $D$-mixing probes new-physics scales to tens of TeV in the absence of suppression mechanisms.

For $Z'$ or new scalar mediators with tree-level $uc$ FCNC, the $D$-mixing bound demands

$$\frac{|(g'_L+g'_R)_{uc}|}{M_{Z'}} \lesssim 3\times 10^{-7}~\text{GeV}^{-1}$$

so for $M_{Z'}=1$ TeV, $|(g'_L+g'_R)_{uc}| \lesssim 3\times 10^{-4}$ (Duy et al., 2024, Gupta et al., 2010). Scalar-mediated $c\to u\ell^+\ell^-$ constrains $|Y^{h'}_{uc}| \lesssim 10^{-3}$ for $m_{h'}=1$ TeV via $\text{Br}(c \to ue^+e^-) < 8\times 10^{-6}$.

In vector-like quark models, $t'$ admixtures induce FCNC $Z$-couplings to $t,c,u$, with limits $|V^L_{4u} V^L_{4c}| < 1.5 \times 10^{-4}$ (for $M_{t'} \sim 1$ TeV) from $D$-mixing, and $|V^L_{4t} V^L_{4c}| < 10^{-2}$ from $\text{Br}(t \to Z c)$ (Belfatto et al., 2021).

Scalar extensions with flavor non-universal PQ charges yield tree-level scalar and axion FCNCs; scalar-exchange operators for $c\to u$ transitions must satisfy $$|Y^{U\beta}_{uc}|/m_H \lesssim 10^{-7}\,\text{TeV}^{-1}$$ (Giraldo et al., 2020).

These constraints generically enforce $|f|\lesssim \mathcal{O}(10^{-3}\!-\!10^{-2})$ for $t\to uZ$ and $|f|\lesssim \mathcal{O}(10^{-2}\!-\!10^{-1})$ for $t\to cZ$ depending on the underlying model (Hioki et al., 2019, Duy et al., 2024, Belfatto et al., 2021, Gupta et al., 2010).

3. Collider Phenomenology: Top FCNC Decays and Production

Flavor-changing up-type couplings induce exotic top decays and non-standard top production channels:

• $t\to qZ$, $t\to qH$, $t\to qg$ decays, with partial widths determined by the corresponding effective couplings. For $t\to qZ$ (Hioki et al., 2019):

$$\Gamma(t \to qZ) = \frac{g^2 m_t}{64\pi\cos^2\theta_W}(1-x_Z^2)^2 \left\{ (1+2x_Z^2)(|f_1^L|^2+|f_1^R|^2) + \frac{m_t^2}{M_Z^2}(2+x_Z^2)(|f_2^L|^2+|f_2^R|^2) -6x_Z \operatorname{Re}[f_1^L f_2^{R*}+f_1^R f_2^{L*}] \right\}$$

with $x_Z = M_Z/m_t$. Similar expressions apply to $t\to qH$ and $t\to qg$, appropriately scaled (Hioki et al., 2019, Collaboration et al., 2010).

• Search limits: ATLAS sets $\mathrm{Br}(t\to uZ) < 1.7 \times 10^{-4}$, $\mathrm{Br}(t\to cZ) < 2.3 \times 10^{-4}$ at $95\%$ C.L. (Hioki et al., 2019). For $t\to qH$, HL-LHC/LHeC projections reach $\mathrm{Br}(t\to qH)\sim10^{-4}$ (Liu et al., 2015, Greljo et al., 2014). For $t\to gu$, best experimental bounds are $\mathrm{Br}(t\to gu)\!<\!2.0\times10^{-4}$, $\mathrm{Br}(t\to gc)\!<\!3.9\times10^{-3}$ (Collaboration et al., 2010).
• Single top plus $Z'$, $H$, or $h$ production via anomalous $tqZ'$, $tqH$, $tqh$: $pp\to tZ'$, $pp\to th$ can become prominent for $|g_{tq}| \gtrsim 10^{-2}$ and mediator mass in few hundred GeV to TeV scale (Gupta et al., 2010, Greljo et al., 2014).
• In $Z'$ scenarios, associated $tZ'$ production cross-section at $\sqrt{s}=14$ TeV is $\sigma(pp\to tZ') = C_{tq}(M_{Z'}) |g_{tq}|^2$, with $C_{tc}(1\,\text{TeV})=0.03$ pb, $C_{tu}(1\,\text{TeV})=0.7$ pb (Gupta et al., 2010).
• In models with new heavy scalars, $pp\to tH^0$ and $t\to H^0 q$ channels are controlled by Yukawa entries such as $g^{u}_{tq}$ in the mass basis (Duy et al., 2024, Lang et al., 2022, Buschmann et al., 2016).

4. Flavored Model Realizations and Spurion Analysis

Beyond model-independent effective operators, flavored UV completions provide distinctive patterns of up-type FCNC couplings:

• Minimal Flavor Violation (MFV): Up-sector FCNC couplings are controlled by CKM and quark-mass insertions. E.g., $Y_{ct}\sim V_{cb}$, $Y_{tc}\sim(m_c/m_t)V_{cb}$, resulting in $|Y_{ct}|\sim 4\times10^{-2}$, $|Y_{tc}|\sim 10^{-4}$ for MFV (thus $t\to h c$ at $5\times10^{-4}$) (Dery et al., 2014, Bai et al., 2013).
• Froggatt–Nielsen-type supersymmetric extensions: $\mathcal{O}(0.1-0.2)$ $tch$ couplings are possible if non-holomorphic textures are allowed (Dery et al., 2014).
• Two-Higgs-Doublet Models, spurion-based: Flavor-changing neutral Higgs couplings with magnitudes $|g_{ct}| \lesssim 0.1-0.2$ for heavy Higgs and large $\tan\beta$, tight correlations with rare $B$-decays due to mixing effects and scalar loops (Lang et al., 2022).
• Non-universal $U(1)$ and trinification: FCNCs arise from flavor-dependent charges or representations. After diagonalization, the flavor-changing $Z'$ interactions in the up-basis can be written as $$g'_{L,R}\left(V_{uL,R}^\dag \text{diag}(-x,-x,+x)V_{uL,R}\right)_{ij}$$, $i\ne j$, with typical upper bounds $|g'_{uc}| \lesssim 3\times10^{-4}$ for $M_{Z'}=1$ TeV (Duy et al., 2024, Dinh et al., 2019).
• PQ/axion and GUT-motivated four Higgs doublets: Tree-level scalar and axion up-type FCNCs present, suppressed by mass misalignment and small mixing, $|Y_{uc}| \lesssim 10^{-3}$ for multi-TeV scalar masses (Giraldo et al., 2020).

5. Correlations and Parameter Space Structure

A recurring feature is the non-trivial correlation among multiple effective couplings. For generalized $tqZ$ interactions, interference between vector and dipole operators produces negative correlations, such that

$$\mathrm{Re}\,f_1^L \simeq -C\,\mathrm{Re}\,f_2^R,\quad 0.65\lesssim C\lesssim0.73~\text{at the bounds}$$

and analogous relations for other chirality pairs (Hioki et al., 2019). This arises from destructive interference terms in the decay width, enlarging the physically allowed parameter region in multi-coupling scans versus one-at-a-time limits.

In extended Higgs models or $U(1)'$ with mixing, the allowed regions in the space of off-diagonal couplings are tightly constrained by $D$-mixing and rare decay bounds, but can admit sizably larger individual couplings when cancellations are present (e.g., in the alignment or in the presence of complex phases) (Lang et al., 2022, Duy et al., 2024, Belfatto et al., 2021).

6. Experimental Outlook and Future Probes

Next-generation colliders and increased luminosity can further probe up-type FCNCs:

• HL-LHC is projected to tighten $|f|$ bounds on $tqZ$ couplings by $\sim30\%$ and access $\mathrm{Br}(t\to qH)\sim 10^{-4}$ (Hioki et al., 2019, Liu et al., 2015).
• LHeC and muon colliders can directly observe or exclude anomalous $tqH$ couplings down to $\kappa_{tqH}\sim 0.016$, $\mathrm{Br}(t\to qH)\sim 1.3\times10^{-4}$ (Liu et al., 2015, Bhattacharya et al., 28 Apr 2025).
• Exotic signatures such as $pp\to thh$ and $pp\to tZ'$, as well as jet-substructure-enhanced detection strategies, provide complementary and potentially more sensitive channels for up-type FCNCs (Greljo et al., 2014, Buschmann et al., 2016).

A notable synergy is seen in explicit models that relate up-type FCNCs to dark matter stability or neutrino mass generation, testing multiple sectors with a unified parameter space (Bhattacharya et al., 28 Apr 2025, Duy et al., 2024, Dinh et al., 2019).

7. Summary Table: Representative Up-Type FCNC Coupling Limits

Coupling Type	Upper Limit	Dominant Constraint	Reference
$|f_{1,2}^{L,R}(tuZ)|$	$5\times10^{-3}$–$4\times10^{-2}$	$\mathrm{Br}(t\to uZ)$, $D$-mixing	(Hioki et al., 2019, Duy et al., 2024)
$|g_{tc}|$ in $tZ'$	$5\times 10^{-2}$ (LHC)	$D$-mixing, LHC associated production	(Gupta et al., 2010)
$|\kappa_{tqH}|$	$0.016$ (LHeC)	$\mathrm{Br}(t\to qH)$ (future)	(Liu et al., 2015)
$|Y_{ct}|$ (MFV)	$4\times10^{-2}$	CKM hierarchy	(Dery et al., 2014)
$|g_{tc}(Z)|_\text{VLQ}$	$10^{-2}$	$\mathrm{Br}(t\to Zq)$, $D$-mixing	(Belfatto et al., 2021)

The table summarizes the experimentally allowed sizes and theoretical constraints on various classes of up-sector FCNC couplings.

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These flavor-changing up-type couplings are powerful probes of new physics across energy scales, interfacing collider searches, low-energy flavor measurements, and indirect constraints in a quantitatively robust framework, and their further exploration is a central objective of present and future high-precision experiments.