⚛️ phenomenology

Probing the chromo-electric dipole moment of top quark near the toponium production threshold at LHC

This paper investigates the impact of the top quark's chromo-electric dipole moment (CEDM) on toponium production near the $t\bar{t}$ threshold at the LHC by combining resonant and continuum amplitudes to construct lepton angular asymmetries, ultimately deriving expected exclusion limits on the CEDM parameter.

Original authors: Kai Ma, Tong Li

Published 2026-10-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kai Ma, Tong Li

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

In the vast, invisible world of subatomic particles, the top quark holds a unique and fleeting position. It is the heaviest known elementary particle, a building block of matter so massive that it behaves differently from its lighter cousins. Because it is so heavy, it decays almost instantly after it is created, breaking apart before it can ever settle down to form a stable structure with other particles. For decades, physicists believed this speed meant the top quark could never form a bound pair, a kind of atomic nucleus made of two top quarks orbiting each other. However, recent observations at the Large Hadron Collider, a massive machine that smashes protons together at nearly the speed of light, have hinted that something unexpected is happening. When the energy of the collision is just right to create a pair of top quarks, there is a noticeable bump in the data, suggesting that these particles briefly stick together in a short-lived, quasi-bound state before flying apart. This phenomenon, often called toponium, offers a rare window into the forces that hold matter together.

Beyond simply understanding how these particles bind, scientists are also searching for a deeper mystery: why the universe is made of matter rather than antimatter. The laws of physics generally treat matter and antimatter as mirror images, but the universe clearly favors matter. To explain this imbalance, physicists look for subtle violations in the symmetry of nature, specifically in how particles interact with the strong force that binds quarks. One way this symmetry could be broken is if the top quark possesses a specific type of internal twist, known as a chromo-electric dipole moment. This is not a physical shape you can see, but rather a property that would cause the top quark to interact with the gluons—the carriers of the strong force—in a way that distinguishes between left and right. If such a property exists, it would be a sign of new physics beyond our current understanding, potentially shedding light on the origins of the universe itself.

A team of researchers has now turned its attention to this fleeting toponium state to see if it can reveal the presence of this hidden twist. They focused their study on the moment when top quarks are created near the minimum energy required for their existence. In this specific region, the particles move slowly relative to each other, creating a calm environment where the effects of their internal properties are easier to detect than in the chaotic, high-speed collisions that usually dominate the data. The researchers built a detailed simulation of what happens when two protons collide and produce these top quark pairs. They included the possibility of the top quark having this anomalous dipole moment and calculated how it would change the way the particles are produced and how they decay.

The study revealed that simply counting the number of top quark pairs produced is not enough to spot this subtle effect. The total number of events changes very little even if the dipole moment is present. Instead, the researchers looked at the angles at which the decay products fly away. When a top quark decays, it often produces a charged lepton, a particle similar to an electron. The direction in which this lepton travels carries a precise record of the spin, or internal rotation, of the parent top quark. By analyzing the specific angles of these leptons from both the top and anti-top quarks, the team constructed a set of asymmetries. These are measurements that compare how often particles fly in one direction versus the opposite direction. In a world where the laws of physics are perfectly symmetric, these measurements would average out to zero. However, if the top quark has the suspected dipole moment, these angles would show a distinct, non-zero pattern.

The researchers found that these angular measurements are incredibly sensitive to the presence of the dipole moment. While the total number of particles might look the same, the pattern of their flight paths would shift in a way that is directly proportional to the strength of the dipole moment. Using the data expected from the Large Hadron Collider, they calculated how precisely this method could constrain the size of the effect. Their simulations suggest that with the current amount of data collected, and even more so with the larger datasets expected in the future, scientists could rule out a dipole moment larger than a specific, very small value. They determined that if such a property exists, it must be smaller than approximately 9.6 times 10 to the negative 5 inverse GeV. This result does not prove that the dipole moment exists, but it sets a new, rigorous boundary for where physicists must look next.

The work highlights the power of looking at the details of particle decay rather than just the total count of events. By focusing on the near-threshold region where top quarks move slowly, and by using the charged leptons as precise probes of the top quark's internal state, the researchers have identified a clear path to testing one of the most fundamental questions in particle physics. Their findings confirm that the toponium state, once thought to be too short-lived to be useful, is actually an ideal laboratory for probing the deepest symmetries of nature. As the Large Hadron Collider continues to collect data, these angular measurements will serve as a critical tool, helping to either discover new physics that explains the matter-antimatter imbalance or to tighten the constraints on the theories that attempt to do so.

Technical Summary: Probing the Chromo-Electric Dipole Moment of the Top Quark Near the Toponium Production Threshold at LHC

Problem Statement
Recent observations by the CMS and ATLAS collaborations indicate a significant excess in $t\bar{t}$ production near the kinematic threshold, consistent with the formation of a color-singlet, S-wave quasi-bound state of top and anti-top quarks (toponium). While the top quark's short lifetime ( $\tau_t \approx 10^{-25}$ s) traditionally precludes bound state formation, the non-relativistic nature of the $t\bar{t}$ system near threshold allows for a resonant enhancement governed by QCD potentials. Concurrently, the search for CP violation in the top quark sector remains a critical probe for physics beyond the Standard Model (SM). While CP-violating anomalous couplings (such as the chromo-electric dipole moment, CEDM) have been studied at high invariant masses ( $m_{t\bar{t}} \gg 2m_t$ ), their impact near the kinematic threshold—where the momentum scale is minimal and non-perturbative QCD effects dominate—has not been systematically investigated. This work addresses the gap in understanding how the top quark's CEDM influences toponium formation and whether threshold observables can provide enhanced sensitivity to CP violation compared to high-energy regimes.

Methodology
The authors employ a framework combining Non-Relativistic QCD (NRQCD) with effective field theory to model toponium production at the LHC.

Theoretical Framework: The CEDM interaction is introduced via a dimension-six operator in the SM Effective Field Theory (SMEFT), parameterized by the coupling $d^g_t$ . The interaction Lagrangian modifies the $t\bar{t}g$ vertex and introduces a new $gg t\bar{t}$ vertex.
Production Mechanism: The study focuses on the near-threshold region ( $330 \text{ GeV} < m_{t\bar{t}} < 360 \text{ GeV}$ $330 GeV < m_{t \overset{ˉ}{t}} < 360 GeV$ ). The production amplitude is decomposed into a short-distance hard coefficient and a long-distance non-relativistic Green's function. The authors implement the threshold enhancement by reweighting the partonic matrix elements with the ratio of the interacting NRQCD Green's function to the free Green's function.
- Dominant Channels: The primary focus is the spin-0, color-singlet S-wave state ( $\eta_t$ , $^1S_0^{[1]}$ ) produced via gluon fusion.
- Subdominant Channels: Contributions from the spin-1 color-singlet state ( $\psi_t$ , $^3S_1^{[1]}$ ) via $q\bar{q}$ annihilation and color-octet states ( $^1S_0^{[8]}$ , $^3S_1^{[8]}$ ) are calculated but found to be numerically negligible or lacking threshold enhancement due to repulsive potentials.
Simulation and Observables: Signal events are generated using MadGraph5_aMC@NLO with a custom UFO model for CEDM. The analysis utilizes the dileptonic decay channel ( $t\bar{t} \to b\ell^+\nu \bar{b}\ell^-\bar{\nu}$ ), where charged leptons serve as spin analyzers.
Asymmetry Construction: To isolate CP-violating effects, the authors construct 15 angular asymmetries ( $A_\xi$ $A_{ξ}$ ) based on the polar and azimuthal angles of the charged leptons in the $t\bar{t}$ $t \overset{ˉ}{t}$ rest frame. These are defined as $A_\xi = (N(\xi > 0) - N(\xi < 0)) / (N(\xi > 0) + N(\xi < 0))$ $A_{ξ} = (N (ξ > 0) - N (ξ < 0)) / (N (ξ > 0) + N (ξ < 0))$ .
- CP-Even Observables: Sensitive to quadratic CEDM effects.
- CP-Odd Observables: Sensitive to the interference between SM and CEDM amplitudes, yielding a linear dependence on $d^g_t$ .
Statistical Analysis: A $\chi^2$ analysis is performed using a covariance matrix derived from pseudo-experiments to account for correlations between the five most sensitive asymmetries ( $\xi_6, \xi_{10}, \xi_{11}, \xi_{14}, \xi_{15}$ ). The analysis assumes an integrated luminosity of $138 \text{ fb}^{-1}$ (LHC13) and projects to $1 \text{ ab}^{-1}$ and $3 \text{ ab}^{-1}$ (HL-LHC).

Key Contributions

Threshold-Specific CEDM Study: This is the first dedicated study of CP-violating anomalous top quark couplings specifically in the toponium formation region, contrasting with previous high-mass studies.
Interference Effects: The paper demonstrates that while inclusive cross-sections are only quadratically sensitive to $d^g_t$ (due to phase space integration suppressing the interference term), CP-odd angular asymmetries retain the linear interference term, offering superior sensitivity to small CEDM values.
Green's Function Implementation: The work rigorously combines the resonant toponium contribution with the continuum $t\bar{t}$ amplitude, consistently including interference effects induced by the CEDM within the NRQCD framework.
Optimized Observables: The authors identify specific mixed polar-azimuthal correlations (e.g., $\cos\theta_{\ell^-}\sin\phi_{\ell^+}$ ) that exhibit clear distortions under CEDM influence, distinguishing them from CP-even observables which show minimal shape variation.

Results

Cross Sections: The inclusion of a benchmark CEDM coupling ( $d^g_t = 3 \times 10^{-4} \text{ GeV}^{-1}$ ) results in a modest $\sim 4\%$ enhancement in the color-singlet $\eta_t$ production cross-section and a $\sim 5-6\%$ enhancement in the color-octet channel. The color-singlet $q\bar{q}$ channel remains negligible.
Asymmetry Sensitivity:
- CP-even angular distributions show negligible sensitivity to CEDM in the near-threshold region.
- CP-odd asymmetries exhibit a linear dependence on $d^g_t$ for small values, followed by a turnover at larger values where quadratic terms dominate the normalization.
- The CP-odd asymmetries ( $\xi_{10}, \xi_{11}, \xi_{14}, \xi_{15}$ ) show significant deviation from the SM prediction (which is near zero) when CEDM is present.
Exclusion Limits: Using the combined sensitivity of five selected asymmetries and a covariance matrix to handle correlations, the authors derive an expected 95% confidence level (CL) upper limit on the top CEDM parameter:
$d^g_t \lesssim 9.6 \times 10^{-5} \text{ GeV}^{-1}$
This limit is comparable to current experimental bounds derived from high-mass $t\bar{t}$ events but is derived from a distinct kinematic regime (threshold) and a different set of observables (spin correlations).

Significance
The paper claims that the near-threshold region provides a unique laboratory for probing the spin and CP structure of top quark interactions. By leveraging the non-relativistic nature of the $t\bar{t}$ system and the specific spin-correlation properties of the color-singlet toponium state, the proposed method offers a complementary and potentially more sensitive probe of CP violation than traditional high-energy searches. The work establishes that CP-odd angular asymmetries in the dileptonic channel are powerful tools for isolating CEDM effects, as they avoid the suppression of interference terms that plagues inclusive rate measurements. The derived exclusion limit demonstrates the feasibility of constraining top CEDM using threshold data, motivating dedicated analyses of the excess observed by CMS and ATLAS.

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