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Examining possible doubly topped baryon configurations

This paper utilizes two-point QCD sum rules to theoretically predict the ground state masses of doubly topped baryon configurations ( $\Xi_{ttu}$ , $\Xi_{ttd}$ , $\Omega_{tts}$ , $\Omega_{ttc}$ , and $\Omega_{ttb}$ ), finding them slightly above the sum of their constituent quark masses to provide a reference for future experimental searches at the LHC and FCC.

Original authors: M. Shekari Tousi, K. Azizi

Published 2026-07-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: M. Shekari Tousi, K. Azizi

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

Imagine the universe as a giant, cosmic Lego set. The tiniest, most fundamental bricks in this set are called quarks. Usually, these bricks snap together in groups of three to build particles called baryons—like the protons and neutrons that make up the atoms in your body. Most of these bricks are light and easy to handle, but there is one "super-heavy" brick called the top quark. It is so massive that it weighs about as much as a gold atom, yet it is incredibly unstable. Think of it as a Lego piece made of unstable jelly; the moment you try to grab it, it melts away in a flash of energy, lasting for only a fraction of a second. For a long time, scientists thought this "melting" happened so fast that the top quark could never be glued into a stable Lego structure with other bricks.

However, the rules of the quantum world are tricky. Recently, experiments at the world's biggest particle smashers (the LHC) have spotted some strange behavior near the point where top quarks are created, hinting that maybe, just maybe, these heavy bricks can stick together for a split second before dissolving. This has sparked a big question: If two of these super-heavy top quarks can briefly hold hands, what kind of new, super-massive particle could they build? Scientists are curious because finding such a particle would be like discovering a new, impossible color in the Lego set, helping us understand the glue (called the strong force) that holds the universe together at its most extreme levels.

In this paper, two researchers, M. Shekari Tousi and K. Azizi, decided to play a game of "theoretical prediction" to see what would happen if they tried to build baryons using two of these super-heavy top quarks. They didn't smash atoms in a lab; instead, they used a powerful mathematical toolkit called "QCD sum rules." You can think of this toolkit as a very sophisticated calculator that uses the known laws of physics to estimate the weight of a particle that hasn't been seen yet. They focused on five specific blueprints for these particles, naming them things like $\Xi_{ttu}$ , $\Xi_{ttd}$ , $\Omega_{tts}$ , $\Omega_{ttc}$ , and $\Omega_{ttb}$ . In plain English, these are just names for different combinations: two top quarks plus one other lighter quark (like an up, down, strange, charm, or bottom quark).

The researchers ran their calculations to predict the mass (or weight) of these hypothetical particles. Their results suggest that these "doubly topped" baryons would be incredibly heavy, weighing in at around 345 to 350 GeV (gigaelectronvolts). To put that in perspective, a single top quark weighs about 172 GeV, so these new particles are roughly twice as heavy as a single top quark, plus a tiny bit more for the third, lighter brick. The authors found that the predicted weight of these particles is just a tiny bit heavier than simply adding up the weights of the three individual quarks inside them.

Now, you might wonder: "If the particle weighs more than the sum of its parts, does that mean it's not really stuck together?" The authors explain that this small difference isn't a sign that the particle is falling apart. Instead, it's likely just a quirk of their mathematical method. Because the top quark is so short-lived and the calculations involve many complex, fuzzy variables, the numbers wiggle a little bit. The authors are careful to say that while their central numbers are slightly above the simple sum, the "uncertainty bands" (the range of error in their math) actually dip below that sum. This means it is still very possible that these particles are tightly bound together, held by the strong force, even if the math isn't precise enough to say exactly how tight the hug is.

The paper explicitly argues against the idea that these particles are impossible to form just because the top quark decays so fast. While the top quark's life is incredibly short (about $10^{-25}$ seconds), the authors suggest that the time it takes for these three quarks to "click" into a color-singlet state (a stable, neutral configuration) might be fast enough to happen before the top quarks melt away. They do not claim to have found these particles or to have proved they exist; rather, they provide a theoretical map and a set of target weights for future experiments.

In the end, this study serves as a guide for the next generation of particle hunters. The authors hope that when scientists at the Large Hadron Collider (LHC) or future facilities like the FCC look for these heavy configurations, they will know exactly what mass to look for. If these "doubly topped" baryons exist, they would be the heaviest baryons ever discovered, offering a unique window into how the universe behaves at the very edge of energy and time. For now, they remain a fascinating possibility, waiting for the next big experiment to confirm if nature has indeed built these super-heavy Lego structures.

Technical Summary: Examining Possible Doubly Topped Baryon Configurations

Problem Statement
The paper addresses the theoretical possibility of baryonic states containing two heavy top quarks ( $t$ ), a configuration that has remained largely unexplored due to the top quark's exceptionally short lifetime ( $\sim 10^{-25}$ s) and large decay width ( $\Gamma_t \simeq 1.4$ GeV). While the Standard Model (SM) traditionally suggests that the top quark decays before it can hadronize, recent experimental observations by CMS and ATLAS of a pseudoscalar excess near the $t\bar{t}$ threshold have reignited interest in near-bound top dynamics. Motivated by these findings and the prior discovery of the doubly charmed baryon $\Xi_{cc}^{++}$ , the authors investigate whether baryons composed of two top quarks and one light quark ( $u, d, s$ ) or a second heavy quark ( $c, b$ ) can form. Specifically, the study targets the masses of the $\Xi_{ttu}$ , $\Xi_{ttd}$ , $\Omega_{tts}$ , $\Omega_{ttc}$ , and $\Omega_{ttb}$ systems.

Methodology
The authors employ the method of QCD Sum Rules, a non-perturbative approach derived directly from the QCD Lagrangian, to calculate the ground state masses of these doubly topped baryons. The analysis proceeds through the following steps:

Interpolating Currents: Suitable interpolating currents ( $\eta(x)$ ) are constructed for each baryon channel. For the $\Xi_{ttu}$ , $\Xi_{ttd}$ , and $\Omega_{tts}$ systems (two identical top quarks and a light quark), symmetric currents involving the top ( $Q$ ) and light ( $q$ ) fields are defined with a mixing parameter $\beta$ . For the triply heavy $\Omega_{ttc}$ and $\Omega_{ttb}$ systems, currents are constructed using top, charm/bottom, and top fields.
Two-Point Correlation Function: The correlation function $\Pi(q)$ is defined as the vacuum expectation value of the time-ordered product of these currents.
Dual Representations:
- Phenomenological Side: The correlator is expressed in terms of hadronic parameters (mass $m_B$ and coupling $\lambda$ ) by inserting a complete set of hadronic states, isolating the ground state pole.
- Theoretical (OPE) Side: The correlator is expanded using the Operator Product Expansion (OPE). This includes perturbative contributions and non-perturbative effects up to dimension eight condensates. The expansion utilizes explicit expressions for heavy and light quark propagators in coordinate space, incorporating gluon field strength tensors and vacuum condensates (e.g., $\langle \bar{q}q \rangle$ , $\langle g_s^2 G^2 \rangle$ ).
Sum Rule Extraction: By equating the phenomenological and OPE representations via quark-hadron duality and applying a Borel transformation, the authors derive sum rules. The mass is extracted by taking the ratio of the Borel-transformed invariant amplitudes associated with the $\not{q}$ and identity Lorentz structures.
Stability Analysis: The reliability of the results is ensured by determining working windows for the Borel mass parameter ( $M^2$ $M^{2}$ ) and the continuum threshold ( $s_0$ $s_{0}$ ). These windows are constrained by requiring:
- Pole contribution dominance ( $\geq 50\%$ ).
- OPE convergence (dimension-8 contributions $\leq 5\%$ ).
- Stability of the extracted mass against variations in $M^2$ , $s_0$ , and the mixing parameter $\beta$ .

Key Results
The study provides the first quantitative mass predictions for the five specified doubly topped baryon configurations using QCD sum rules. The extracted central masses and their associated uncertainties are:

$\Xi_{ttu}$ : $345.20^{+1.10}_{-1.11}$ GeV
$\Xi_{ttd}$ : $345.20^{+1.10}_{-1.11}$ GeV
$\Omega_{tts}$ : $345.22^{+1.11}_{-1.13}$ GeV
$\Omega_{ttc}$ : $346.88^{+1.19}_{-1.17}$ GeV
$\Omega_{ttb}$ : $350.00^{+1.21}_{-1.18}$ GeV

The authors compare these results to the sum of the constituent quark masses for each system. They find that the central predicted masses are slightly above the constituent mass sums. However, the authors explicitly note that the lower bounds of the uncertainty intervals extend below these sums. They interpret this not as evidence of a physical negative binding energy or deeply bound states, but rather as a reflection of the systematic uncertainties inherent to the QCD sum rule method, particularly the sensitivity to the Borel mass and continuum threshold parameters.

Significance and Claims
The paper positions these results as a theoretical reference rather than a definitive prediction of existence. The authors claim:

First-Principle Estimates: The work provides the first first-principle theoretical mass estimates for baryons containing two top quarks, filling a gap between theoretical speculation and experimental capability.
Experimental Guidance: These quantitative predictions serve as benchmarks for future experimental searches at the Large Hadron Collider (LHC) and sensitivity studies for next-generation facilities like the Future Circular Collider (FCC).
Theoretical Context: The study supports the theoretical interpretation of recent $t\bar{t}$ threshold excesses by exploring the possibility of multi-top baryonic configurations, suggesting that if such states exist, their masses would be in the range of 345–350 GeV.

The authors remain modest regarding the physical realization of these states, acknowledging that the top quark's rapid decay is a significant barrier. They suggest that while the QCD sum rule framework allows for the calculation of such masses, the actual formation of these baryons depends on complex quantum correlations and collective effects that require further theoretical refinement and, crucially, dedicated experimental input to confirm.

Technical Summary: Examining Possible Doubly Topped Baryon Configurations

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