---
title: Flavor-Changing Up-Type Quark Couplings
url: https://www.emergentmind.com/topics/flavor-changing-couplings-to-up-type-quarks
type: topic
---

# Flavor-Changing Up-Type Quark Couplings

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 [1909.06150]:
\[
\begin{aligned}
&\mathcal{O}_{\phi q}^{(1)ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu \phi)(\bar q_i \gamma^\mu q_j),\\
&\mathcal{O}_{\phi q}^{(3)ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu^I \phi)(\bar q_i \tau^I \gamma^\mu q_j),\\
&\mathcal{O}_{\phi u}^{ij} = (\phi^\dagger i \overleftrightarrow{D}_\mu \phi)(\bar u_i \gamma^\mu u_j),\\
&\mathcal{O}_{uW}^{ij} = (\bar q_i \sigma^{\mu\nu} \tau^I u_j)\tilde\phi\, W^I_{\mu\nu},\\
&\mathcal{O}_{uB}^{ij} = (\bar q_i \sigma^{\mu\nu} u_j) \tilde\phi\, B_{\mu\nu},
\end{aligned}
\]
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 [1909.06150].

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 [1006.3575].

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 [1507.03264].

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 [2410.15635][1005.4578][1901.07969].

## 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, $|(g'_L+g'_R)_{uc}| \lesssim 3\times 10^{-4}$ [2410.15635][1005.4578]. 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 $\text{Br}(t \to Z c)$ [2103.05549].

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 $|Y^{U\beta}_{uc}|/m_H \lesssim 10^{-7}\,\text{TeV}^{-1}$ [2007.05653].

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 [1909.06150][2410.15635][2103.05549][1005.4578].

## 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 $t\to qZ$ [1909.06150]:
  \[
  \Gamma(t \to qZ) = \frac{g^2 m_t}{64\pi\cos^2\theta_W}(1-x_Z^2)^2 \left\{ (1+2x_Z^2)(|f_1^L|^2+|f_1^R|^2) + \frac{m_t^2}{M_Z^2}(2+x_Z^2)(|f_2^L|^2+|f_2^R|^2) 
  -6x_Z \operatorname{Re}[f_1^L f_2^{R*}+f_1^R f_2^{L*}] \right\}
  \]
  with $x_Z = M_Z/m_t$. Similar expressions apply to $t\to qH$ and $t\to qg$, appropriately scaled [1909.06150][1006.3575].

- 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. [1909.06150]. For $t\to qH$, HL-LHC/LHeC projections reach $\mathrm{Br}(t\to qH)\sim10^{-4}$ [1507.03264][1404.1278]. For $t\to gu$, best experimental bounds are $\mathrm{Br}(t\to gu)\!<\!2.0\times10^{-4}$, $\mathrm{Br}(t\to gc)\!<\!3.9\times10^{-3}$ [1006.3575].

- 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 [1005.4578][1404.1278].

- 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 [1005.4578].

- 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 [2410.15635][2212.11086][1601.02616].

## 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 $5\times10^{-4}$) [1408.1371][1305.5537].
- Froggatt–Nielsen-type supersymmetric extensions: $\mathcal{O}(0.1-0.2)$ $tch$ couplings are possible if non-holomorphic textures are allowed [1408.1371].
- 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 [2212.11086].
- 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 [2410.15635][1901.07969].
- 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 [2007.05653].

## 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 [1909.06150]. 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) [2212.11086][2410.15635][2103.05549].

## 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 $\mathrm{Br}(t\to qH)\sim 10^{-4}$ [1909.06150][1507.03264].
- LHeC and muon colliders can directly observe or exclude anomalous $tqH$ couplings down to $\kappa_{tqH}\sim 0.016$, $\mathrm{Br}(t\to qH)\sim 1.3\times10^{-4}$ [1507.03264][2504.20045].
- 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 [1404.1278][1601.02616].

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 [2504.20045][2410.15635][1901.07969].

## 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 | [1909.06150][2410.15635] |
| $|g_{tc}|$ in $tZ'$                  | $5\times 10^{-2}$ (LHC)             | $D$-mixing, LHC associated production | [1005.4578]         |
| $|\kappa_{tqH}|$                     | $0.016$ (LHeC)                      | $\mathrm{Br}(t\to qH)$ (future)     | [1507.03264]        |
| $|Y_{ct}|$ (MFV)                     | $4\times10^{-2}$                    | CKM hierarchy                    | [1408.1371]         |
| $|g_{tc}(Z)|_\text{VLQ}$             | $10^{-2}$                            | $\mathrm{Br}(t\to Zq)$, $D$-mixing | [2103.05549]        |

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.

Source: https://www.emergentmind.com/topics/flavor-changing-couplings-to-up-type-quarks