Composite top partners in exotic colour representations

This contribution systematically investigates the phenomenology of fermionic top partners in exotic color-sextet representations within composite Higgs models, derives their decay patterns, and establishes current LHC exclusion limits up to 2.5 TeV as well as the projected sensitivity of the HL-LHC near 3 TeV.

The Gist

Imagine the universe is built like a giant, complex Lego set. For a long time, physicists have been trying to figure out how the pieces fit together, particularly those responsible for the mass of particles (like the Higgs boson). A popular idea suggests that these particles are not simply individual building blocks but are actually made of smaller, hidden components called "hyperfermions," held together by an ultra-strong force known as "hypercolor."

This article is a detective story about a specific, exotic Lego piece predicted by this theory: the color-sextet top partner.

Here is the breakdown of the article's story, using simple analogies:

1. The Hidden Family (The Model)

In this theory, the "top quark" (a heavy particle in our current understanding) is actually a mixture of a regular particle and a heavy, composite particle. These heavy composite particles are called "top partners."

• The Usual Suspects: Most physicists have been looking for top partners that appear in groups of three (like a trio) or groups of eight (like an octet).
• The New Discovery: This article says: "Wait a minute! The math also predicts a group of six." These are the color sextets. They are like a hexagon of interconnected particles. The authors argue that if the theory is correct, these six-member groups must exist, yet no one has specifically searched for them at the Large Hadron Collider (LHC) before.

2. The Unleashed (How They Decay)

These heavy sextet particles are unstable. They do not last long; they decay immediately into lighter particles. The article maps exactly how they decay, depending on which "family" they belong to:

• The "Top-Rich" Party: In most scenarios, the sextet decays and releases a cascade of other heavy particles, eventually culminating in a final explosion of top quarks and bottom quarks. Imagine a heavy box opening and spilling out a dozen smaller, heavy boxes. This creates a "messy" final state with many jets (sprays of particles) and missing energy.
• The "Missing Energy" Trick: In a specific version of the theory, the sextet decays into a pair of bottom quarks and a "ghost" particle (a singlet hyperbaryon) that does not interact with detectors at all. This looks like a pair of bottom quarks appearing out of nowhere, while a large amount of invisible energy is missing from the picture.

3. The Hunt (LHC Searches)

The authors scoured the LHC data archives (the world's largest particle accelerator) to see if anyone had already caught these sextets.

• The Strategy: Since no one has a specific "wanted poster" for sextets, the authors used a clever trick. They took existing searches developed for supersymmetry (another theory that predicts heavy, messy particle decays) and asked: "Could these results also catch our sextets?"
• The Results:
  • They found that current data has not yet discovered them but has pushed them into hiding.
  • If these sextets exist, they must be very heavy—between 2 and 2.5 TeV (about 2,000 times heavier than a proton).
  • When considering the entire group of five different sextet types together, the limit becomes even stricter, pushing the mass boundary up to 2.6 TeV.

4. The Future (HL-LHC)

The article looks ahead to the "High-Luminosity LHC" (HL-LHC), which will be a supercharged version of the current accelerator running with much more data.

• The Projection: With this new, massive amount of data, detectors should be able to discover these sextets if they are up to 3 TeV heavy.
• The Conclusion: The authors conclude that these "color-sextet" particles represent a powerful, largely unexplored way to test whether this specific theory of the universe is correct. They are like a hidden door in the Lego set that, if opened, would confirm the theory.

Summarizing Analogy

Imagine the Standard Model of physics as a puzzle. Most people are trying to insert the standard pieces (triplets and octets). This article says: "The instructions for this puzzle also show a hexagon piece."

The authors created a map of what this hexagon piece looks like, how it decays, and where it might be hiding. They checked the current puzzle box (LHC data) and said: "It is not yet in the range below 2.5 TeV." But they promise that if we get a bigger, brighter flashlight (the HL-LHC), we should be able to find it up to 3 TeV. If we find it, it confirms the theory; if we do not find it, we may have to discard the instructions.

Technical Summary

Technical Summary: Composite Top Partners in Exotic Color Representations

Problem and Motivation
Composite Higgs Models (CHM), based on partial compositeness, offer a symmetry-based solution to the electroweak hierarchy problem. In these frameworks, the Higgs boson arises as a pseudo-Nambu-Goldstone boson (pNGB) from a strongly coupled "hypercolor" sector. While phenomenological studies have comprehensively addressed color-triplet and color-octet top partners, the existence of fermionic color-sextet resonances is a robust prediction of several ultraviolet-complete hypercolor constructions (particularly those involving two species of hyperfermions). Despite their theoretically well-founded motivation and their enhanced QCD pair-production cross-sections due to the non-minimal color representation, color-sextet fermions have remained largely unexplored in the literature and at the Large Hadron Collider (LHC). This work closes the gap in systematic studies of these states by deriving their characteristic decay patterns and establishing current experimental constraints.

Methodology
The authors conduct a systematic analysis of color-sextet hyperbaryons within minimal CHM classes (C1, C2, and C3), defined by specific hypercolor gauge groups and hyperfermion representations.

1. Model Construction: The study utilizes the CCWZ formalism (Coleman-Callan-Wess-Zumino) to derive the low-energy effective Lagrangian. The spectrum is determined by the symmetry-breaking patterns of hyperfermion condensates:

   • Class C1: $SU(6)/SO(6)$ with real hyperfermions.
   • Class C2: $SU(6)/Sp(6)$ with pseudoreal hyperfermions.
   • Class C3: $SU(3) \times SU(3)/SU(3)$ with complex hyperfermions.
     The authors explicitly construct the embedding of composite baryons (hyperbaryons) into the unbroken symmetry groups to identify the quantum numbers of the sextet states ($Q_6$).

2. Derivation of Interactions: Two primary sources of interactions governing sextet decays are derived:

   • Derivative Couplings: Interactions between hyperbaryons and colored pNGBs (specifically the color-octet $\pi_8$ as well as the color-sextet $\pi_6$ or triplet $\pi_3$, where applicable), resulting from the CCWZ Lagrangian.
   • Partial Compositeness: Linear mixing between elementary Standard Model (SM) quarks and composite operators, inducing couplings between sextets, pNGBs, and SM quarks.

3. Phenomenological Analysis:

   • Decay Patterns: The authors map the dominant decay channels for the sextet components (charges $Q = -5/3, -2/3, +1/3$). These depend strongly on the mass hierarchy between the sextet, the triplet partners, and the colored pNGBs.
   • LHC Reinterpretation: Since no dedicated searches for color-sextet fermions exist, the authors reinterpret existing ATLAS and CMS searches for high-multiplicity final states (typically used for Supersymmetry searches). They simulate pair production with MadGraph5_aMC@NLO, apply parton showering with Pythia8, and analyze events with MadAnalysis5.
   • Extrapolation: Current limits are derived from Run-2 data, and projections for the High-Luminosity LHC (HL-LHC) at 3 ab$^{-1}$ are performed using conservative, systematics-dominated scaling assumptions.

Main Contributions

• Systematic Classification: The work provides the first comprehensive classification of color-sextet hyperbaryons in CHMs, detailing their mass spectra, electric charge assignments, and specific decay modes for classes C1, C2, and C3.
• Decay Topologies:
  • Universal Channel: In all classes, sextets decay via the color-octet pNGB ($\pi_8$) into top-rich final states (e.g., $Q_6 \to \bar{t}\pi_8 \to \bar{t}\bar{t}t$).
  • Class C1 Specifics: In Class C1, a unique decay channel exists via the color-sextet pNGB ($\pi_6$) and a singlet hyperbaryon ($\hat{Q}_1$), leading to a $b\bar{b} + E_T^{miss}$ signature.
• Production Cross-Sections: The authors calculate leading-order pair-production cross-sections for color sextets and highlight their enhancement compared to triplets due to QCD color factors. They apply a representative K-factor of $K=3$ to estimate higher-order uncertainties and acknowledge the absence of NNLO calculations for sextets.
• Reinterpreted Limits: The study translates existing LHC searches into exclusion limits for color-sextet resonances, distinguishing between individual charge states and the entire multiplet.

Results

• Current Exclusions:
  • For individual sextet components decaying via the $\pi_8$ channel, current LHC data exclude masses up to approximately 2.0–2.4 TeV (depending on the charge state and whether a K-factor is applied). The $Q^{-5/3}_6$ state exhibits the strongest limit, due to the higher jet multiplicity in its decay chain.
  • Considering the entire sextet multiplet (five nearly degenerate states), the exclusion limit strengthens to 2.4–2.6 TeV.
  • For the specific Class C1 channel ($Q_6 \to \pi_6 \hat{Q}_1 \to b\bar{b} + E_T^{miss}$), current data exclude sextet masses up to 2.65 TeV (LO) or 2.9 TeV (with K-factor), provided the singlet $\hat{Q}_1$ is light enough to allow the decay.
• HL-LHC Projections: Conservative extrapolations to 3 ab$^{-1}$ at $\sqrt{s}=13$ TeV indicate a reach near 3 TeV for the entire multiplet in both $\pi_8$- and $\pi_6$-mediated channels.
• Comparison with Octets: The mass reach for sextets is comparable to, and in some cases stronger than, current limits for color-octet fermion resonances, despite sextets being less studied.

Significance and Claims
The authors claim that color-sextet fermions represent a "powerful and largely unexplored probe mechanism" for composite Higgs models with partial compositeness. The significance of this work lies in:

1. Completing the Spectrum: It highlights that robust UV-complete constructions predict these states, and that ignoring them leaves a substantial portion of the model parameter space untested.
2. Enhanced Sensitivity: The non-minimal color representation leads to larger production cross-sections, potentially making these states more accessible at hadron colliders than standard triplet top partners.
3. Distinctive Signatures: The identification of specific decay topologies (top-rich vs. $b\bar{b} + E_T^{miss}$) enables targeted searches distinct from standard top partner analyses.
4. Future Prospects: The results suggest that existing LHC analyses already constrain a significant portion of the multi-TeV mass range, and the HL-LHC will be capable of probing up to 3 TeV, covering the natural mass range predicted by many composite models.

The work concludes by noting the need for Next-to-Leading-Order (NLO) QCD calculations for sextet production to reduce theoretical uncertainties and calls for dedicated LHC analyses targeting the identified specific multi-top and $b\bar{b} + E_T^{miss}$ topologies.