⚛️ phenomenology

Minimal cascade decay of the top quark through a new scalar

This paper proposes a minimal model where the top quark undergoes a nonstandard cascade decay into a new scalar and a charm quark via a dimension-5 operator mediated by a heavy vectorlike quark, leading to distinctive collider signatures such as $t\bar{t} \to c\bar{c}b\bar{b}W^+W^-$ and vectorlike quark production events at the LHC.

Original authors: Bogdan A. Dobrescu, Max H. Fieg, Alessandro Russo

Published 2026-10-07

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CC BY 4.0

Original authors: Bogdan A. Dobrescu, Max H. Fieg, Alessandro Russo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, the top quark has held a unique place in the universe of particle physics. Discovered in 1995, it is the heaviest known elementary particle, a fleeting speck of matter that weighs nearly as much as a gold atom but exists for only a fraction of a billionth of a second before vanishing. Because it is so heavy, it decays almost instantly into other, lighter particles. In the standard model of physics, which serves as the rulebook for how the universe works, the top quark has only one known way to break apart: it splits into a W boson and a bottom quark. This single, predictable path has been confirmed countless times in massive particle colliders, yet it remains peculiar. Every other heavy particle discovered in nature has multiple ways to decay, like a person with many different exits from a room. The top quark, by contrast, seems to have only one door.

This singular behavior has led physicists to wonder if there is a second, hidden door that has simply been too small to notice. If the top quark could occasionally take a different path, it would signal the existence of new physics beyond our current understanding. Such a discovery would be a gateway to a deeper layer of reality, potentially revealing new forces or particles that have remained invisible until now. The question is not just whether this alternative path exists, but how often it might happen and what it would look like if we could finally see it.

A recent study by researchers at Fermilab, SLAC, and Stanford University explores exactly this possibility. They propose a specific scenario where the top quark decays into a charm quark and a new, short-lived particle called a scalar. This new particle, which they name phi-t, is a type of matter that has no electric charge and does not interact with the strong nuclear force, but it decays almost immediately into visible particles. The researchers suggest that this decay is not a random accident but is driven by a heavy, unseen partner particle known as a vector-like quark. This heavy partner acts as a bridge, allowing the top quark to transform into the new scalar and a charm quark. While the top quark usually follows its standard path, this new route might occur in about one out of every hundred decays. Though this sounds rare, given that billions of top quarks have been created in recent experiments, this small percentage translates to millions of events that could be hiding in plain sight within the data.

The story does not end with the creation of this new scalar particle. The researchers calculated that this particle is unstable and must decay almost immediately into other particles. Because it is lighter than a top quark but heavier than a W boson, it cannot simply split into two pieces. Instead, it undergoes a cascade, a chain reaction where it briefly turns into a virtual, off-shell top quark before breaking down further. This virtual top quark then decays into a bottom quark and a W boson. The result is a complex final state: a single top quark that started the process ends up producing a charm quark, a bottom quark, a W boson, and another charm quark. When two top quarks collide and both undergo this unusual decay, the detector sees a spray of particles including two W bosons, two bottom quarks, and two charm quarks plus two anti-charm quarks. This specific signature is the "smoking gun" the researchers are looking for.

The team used powerful computer simulations to map out exactly how these events would appear in the detectors at the Large Hadron Collider. They found that the particles produced in this new decay have distinct energy patterns that differ from the background noise of standard collisions. For instance, the charm quarks produced in this process tend to be softer, carrying less energy than those produced by standard radiation. Similarly, the W bosons and the resulting leptons are less energetic. These subtle differences are crucial because they allow scientists to separate the rare signal from the overwhelming sea of ordinary events. The simulations show that with the data already collected, and with even more data expected in the coming years, the Large Hadron Collider has the sensitivity to detect this process if it occurs at the predicted rate.

However, finding this signal is not a matter of simply counting particles. The researchers emphasize that the current searches for similar events were designed to look for charm quarks produced by standard quantum chromodynamics radiation, which creates a different pattern of energy and spacing. The new decay path produces particles that are closer together and have different energy distributions. The study suggests that if experimental teams adjust their search strategies to look for these specific, softer patterns, they could uncover the existence of this new scalar particle and the heavy vector-like quark that enables it. The researchers also note that the heavy vector-like quark itself could be produced directly in collisions, leading to a different but related signal involving three charm quarks and other debris. This creates a complementary way to search for the new physics: looking for the heavy particle directly, or looking for its subtle influence on the top quark's decay.

The paper concludes that while the branching fraction for this new decay is small, it is large enough to have already produced millions of events in the detectors of the ATLAS and CMS experiments. The fact that this signal has not been seen yet does not mean it is absent; it may simply be that the search criteria have not been tuned to catch it. The researchers argue that a dedicated search, one that focuses on the unique kinematic fingerprints of this cascade decay, could reveal the existence of this new scalar and the heavy quark that mediates it. If successful, this would open a window into physics at the multi-TeV scale, a realm of energy that is currently beyond the direct reach of our machines but whose shadows are cast upon the particles we can see. The work serves as a roadmap for experimentalists, showing them exactly where to look and what to expect if the top quark is indeed hiding a second, secret door.

Technical Summary: Minimal Cascade Decay of the Top Quark through a New Scalar

Problem Statement
Despite the production of over $4 \times 10^8$ top-antitop ( $t\bar{t}$ ) pairs at hadron colliders, only the Standard Model (SM) tree-level decay mode, $t \to W^+ b$ , has been observed. This is anomalous given that all other known elementary particles heavier than the muon possess multiple measured decay modes. The paper investigates the possibility of a second, measurable decay mode for the top quark: $t \to \phi_t c$ , where $\phi_t$ is a new gauge-singlet complex scalar and $c$ is a charm quark. The authors argue that while current constraints on vectorlike quarks (VLQs) suggest a high mass scale ( $m_\chi \gtrsim 1.5$ TeV), this does not preclude a nonstandard top branching fraction at the percent level, potentially corresponding to millions of events in existing LHC datasets.

Methodology and Model Construction
The authors propose a minimal renormalizable extension of the SM involving a complex scalar $\phi_t$ and a vectorlike quark $\chi$ transforming as $(3, 1, +2/3)$ under $SU(3)_c \times SU(2)_W \times U(1)_Y$ .

Effective Operator: The interaction is mediated by a dimension-5 operator: $\frac{1}{\Lambda_5} \phi_t H \bar{q}_{3L} c_R + \text{H.c.}$ , where $q_{3L}$ is the third-generation quark doublet and $H$ is the Higgs doublet.
UV Completion: This operator arises from integrating out the heavy vectorlike quark $\chi$ at tree level, with the scale $\Lambda_5 = m_\chi / (y_{\chi\phi} y_{\chi H})$ . The Yukawa couplings $y_{\chi\phi}$ and $y_{\chi H}$ are assumed to be $\mathcal{O}(1)$ or smaller.
Decay Chain:
- Top Decay: For $M_{\phi_t} \lesssim 170$ GeV, the top decays via $t \to \phi_t c$ .
- Scalar Decay: In the mass range $M_W + m_b + m_c < M_{\phi_t} < m_t - m_c$ , the scalar decays via a 3-body process mediated by an off-shell top quark: $\phi_t \to c t^* \to c b W^+$ .
- Cascade: The full nonstandard top cascade is $t \to c \phi_t \to c c b W^+$ .
Simulation: The authors utilize FeynRules to generate UFO model files and MadGraph5_aMC@NLO for simulations. They compute Next-to-Leading Order (NLO) QCD corrections for the top decay width and perform detailed kinematic studies of the final states.

Key Contributions and Results

Branching Fraction Estimates:
The nonstandard branching fraction $\mathcal{B}(t \to \phi_t c)$ scales as $y_{\chi\phi}^2 y_{\chi H}^2 / m_\chi^2$ . Assuming $m_\chi \approx 1.5$ TeV and Yukawa couplings of order unity, the branching fraction can reach $\sim 1.5\%$ . Even with more conservative parameters ( $m_\chi \approx 2$ TeV, smaller couplings), the branching fraction remains in the sub-percent range. This implies that millions of nonstandard $t\bar{t}$ events may have already been produced at the LHC.
Scalar Decay Dynamics:
The paper provides an analytic calculation of the 3-body decay width $\Gamma(\phi_t \to W b c)$ . The width is highly sensitive to the scalar mass $M_{\phi_t}$ , increasing by three orders of magnitude as $M_{\phi_t}$ moves from 100 GeV to 150 GeV due to phase space.
- Prompt Decays: For $\Lambda_5 \lesssim 50$ TeV, the decay length is negligible ( $c\tau \ll 1$ mm), ensuring prompt decays.
- Competing Modes: The 1-loop induced 2-body decay $\phi_t \to b \bar{s}$ is calculated and found to be suppressed by factors of $m_c^2 m_b^2$ , making it negligible compared to the tree-level 3-body decay in the studied mass range.
Vectorlike Quark Signals:
The model predicts single production of the vectorlike quark in association with the scalar: $pp \to \chi \phi_t j$ . Depending on the ratio of Yukawa couplings, $\chi$ decays dominantly via $\chi \to \phi_t c$ (if $y_{\chi\phi} \gg y_{\chi H}$ ) or via SM modes ( $\chi \to h t, Z t, W b$ ). The dominant signal for the former case is a cascade yielding a final state of $3c + b\bar{b} WW j$ .
LHC Phenomenology and Sensitivity:
- Final State: The primary signal for nonstandard top decays is $t\bar{t} \to (c \phi_t)(\bar{b} W^-) \to c c b W^+ \bar{b} W^-$ , resulting in a $c\bar{c} b\bar{b} W^+ W^-$ final state.
- Kinematic Features: The authors identify distinct kinematic features:
  - The charm quark from the $\phi_t$ decay is significantly softer (average $p_T \sim 10$ GeV for $M_{\phi_t}=100$ GeV) compared to the charm from the direct top decay.
  - The lepton from the $W$ boson originating from $\phi_t$ decay is softer than the lepton from the SM $W$ decay.
  - The decay products of $\phi_t$ are more collimated than those from QCD radiation.
- Current Constraints: Re-analyzing existing CMS and ATLAS measurements of $t\bar{t} + c\bar{c}$ production, the authors find that current limits do not exclude the model. The existing analyses are optimized for QCD radiation (harder jets) and are not sensitive to the softer, more collimated signature of the $\phi_t$ decay.
- Projected Sensitivity: With Run 3 data ( $330 \text{ fb}^{-1}$ ), the signal could yield $\mathcal{O}(10^3)$ events for $\Lambda_5 \approx 1$ TeV. A dedicated search exploiting the softer kinematics and invariant mass reconstruction could probe $m_\chi$ up to $\sim 2$ TeV.

Significance and Claims
The paper claims that the search for nonstandard top decays is a crucial, yet underutilized, window into new physics at the 10 TeV scale. The authors emphasize the complementarity between direct searches for heavy vectorlike quarks and indirect searches for modified top decay properties.

Indirect Reach: Even if the vectorlike quark is too heavy for direct pair production, its indirect effects can manifest as a percent-level branching fraction in top decays, corresponding to millions of events in current datasets.
Model Specificity: The study highlights that standard search strategies (optimized for QCD radiation) may miss this signal due to the unique soft kinematics of the cascade decay.
Future Outlook: The authors suggest that dedicated searches with relaxed $p_T$ thresholds for charm tagging and specific reconstruction of the $W b \bar{c}$ invariant mass could significantly improve sensitivity. They also note that future colliders (FCC-ee, FCC-hh, muon colliders) would be well-suited to probe the specific mass ranges and couplings discussed.

The work concludes that while the nonstandard branching fraction may be small, the sheer volume of top quarks produced makes this a viable and necessary avenue for discovering physics beyond the Standard Model.

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