---
title: Vector-Like Singlet Top Quarks (T)
url: https://www.emergentmind.com/topics/vector-like-singlet-top-quarks-t
type: topic
---

# Vector-Like Singlet Top Quarks (T)

A vector-like singlet top quark, usually denoted as $T$, is a hypothetical color-triplet, weak-isospin singlet fermion with electric charge $+\tfrac{2}{3}$. Its left- and right-handed components transform identically under $SU(2)_L \times U(1)_Y$, allowing a gauge-invariant Dirac mass term distinct from the Standard Model (SM) chiral structure. Such particles are introduced in many theories addressing the gauge hierarchy problem, notably composite Higgs, Little Higgs, extra-dimensional, and extended scalar sector models. The $T$ quark mixes dominantly with the SM top via dimension-four Yukawa terms, altering its phenomenology compared to chiral quarks.

## 1. Theoretical Framework and Couplings

Vector-like singlet top partners have quantum numbers $T \sim (3,1,2/3)$. The leading interactions governing phenomenology are encapsulated by an effective Lagrangian after electroweak symmetry breaking:
\[
\mathcal{L}_{\rm eff} \supset 
\frac{g\,g^*}{2\sqrt2}\left[
  \bar T_L \gamma^\mu W^+_\mu b_L
  + \frac{1}{c_W} \bar T_L \gamma^\mu Z_\mu t_L
  - \frac{m_T}{m_W} \bar T_R h t_L
  - \frac{m_t}{m_W} \bar T_L h t_R
\right] + \mathrm{h.c.}
\]
Here, $g$ is the $SU(2)_L$ gauge coupling, $c_W = \cos\theta_W$ is the weak mixing cosine, $h$ is the physical Higgs field, and $g^*$ parametrizes the electroweak strength of the $T$ couplings; it is related to the left-handed mixing angle $\theta_L$ by $g^* = \sqrt{2} \sin\theta_L$ [2206.06562, 1404.3374].

The mass matrix for $t$--$T$ mixing is
\[
\mathcal{L}_{\rm mass} =
- \begin{pmatrix} \bar t_L & \bar T_L \end{pmatrix}
\begin{pmatrix}
m_t^{(0)} & \delta \\
0 & M_T
\end{pmatrix}
\begin{pmatrix}
t_R \\ T_R
\end{pmatrix}
+ \mathrm{h.c.},
\]
with $m_t^{(0)}$ the SM top mass before mixing, $M_T$ the bare vector-like mass, and $\delta$ a Yukawa-induced mixing term [1404.3374, 2409.16054]. Diagonalization leads to physical mass eigenstates and modified gauge currents, inducing $T$--$t$--$Z$ flavor-changing neutral currents (FCNCs) and $T$--$b$--$W$ interactions.

## 2. Decay Channels and Branching Ratios

The $T$ quark exhibits three principal two-body decays:
\[
T \to W^+b, \quad T\to Z t, \quad T\to h t,
\]
with tree-level widths (neglecting subleading mass effects)
\[
\Gamma(T\to Wb) \propto (g^*)^2 \frac{m_T^3}{m_W^2}, \quad
\Gamma(T\to Z t) \propto (g^*)^2 \frac{m_T^3}{m_Z^2}, \quad
\Gamma(T\to h t) \propto (g^*)^2 m_T\,.
\]
In the heavy mass limit $m_T \gg m_W, m_Z, m_h, m_t$, the Goldstone equivalence theorem yields the approximate proportion [2206.06562, 1404.3374, 1811.11496]:
\[
\Gamma(T\to Wb) : \Gamma(T\to Z t) : \Gamma(T\to h t) \simeq 2:1:1
\]
so that
\[
\mathrm{BR}(T\to Wb) \simeq 50\%,\quad \mathrm{BR}(T\to Zt)\simeq 25\%,\quad \mathrm{BR}(T\to ht)\simeq 25\%.
\]
These ratios are robust for $m_T \gtrsim 1$ TeV, and only weakly sensitive to the precise value of $g^*$ as long as the total width remains small compared to $m_T$ [2206.06562, 1811.11496]. For "non-minimal" scenarios (e.g. with exotic singlet scalar/pseudoscalar or extended Higgs sectors), new decay topologies such as $T\to t\Phi$ can dominate, distorting standard BR patterns [1907.05929, 2204.09005, 1911.10202].

## 3. Collider Production and Phenomenology

**Pair production** is primarily via QCD and is independent of electroweak mixing:
\[
gg,\,q\bar q \to T \bar T,
\]
with cross sections set by $m_T$ and known up to NNLO+NNLL. For $m_T=1$ TeV at $\sqrt{s}=13$ TeV, $\sigma \sim 1$ fb [1404.3374, 1811.11496]. 

**Single production** becomes dominant for higher $m_T$, especially for moderate $g^*$. At hadron colliders, $T$ is produced via $t$-channel exchange:
\[
q b \to T q' \ \textrm{via} \ W\textrm{-fusion},
\]
with $\sigma(pp\to Tj) \sim (g^*)^2 \sigma_0(m_T)$ [1811.11496, 1709.06427]. At $e^+ e^-$ colliders, the leading process is $e^+e^- \to T t$ via $s$-channel $Z$ exchange, giving direct sensitivity to the $T$--$t$--$Z$ coupling [2206.06562].

In $pp$ collisions at $\sqrt{s}=13$ TeV, current analysis strategies include:
- **$T \to Wb$**: isolated lepton + $b$-jet + forward jet + missing $E_T$; backgrounds: $W$+jets, $t\bar t$, single top [1811.11496, 2506.15515].
- **$T \to Zt$**: dilepton or trilepton (from $Z$), top-tagged jet, $b$-jet, forward jet; backgrounds: $t\bar tZ$, $WZ$+jets, $Z$+jets [1811.11496, 2302.14642, 1708.03124].
- **$T \to h t$**: highly boosted jets ($H\to b\bar

Source: https://www.emergentmind.com/topics/vector-like-singlet-top-quarks-t