Top Quark Interactions Under the Microscope

Author: Denis Avetisyan

New CMS results at the LHC probe the subtle ways top quarks interact, seeking evidence of physics beyond the Standard Model.

The search for <span class="katex-eq" data-katex-display="false"> \text{CP} </span> violation in <span class="katex-eq" data-katex-display="false"> t\bar{t}Z </span> and <span class="katex-eq" data-katex-display="false"> Zq\bar{q} </span> production reveals sensitivity to both linear and quadratic effective field theory contributions, demonstrated by likelihood scans across the <span class="katex-eq" data-katex-display="false"> (c^{I}_{tW}, c^{I}_{tZ}) </span> plane, and highlighting a landscape where deviations from the Standard Model - marked by a specific cross - are actively sought within a complex parameter space. — The search for $\text{CP}$ violation in $t\bar{t}Z$ and $Zq\bar{q}$ production reveals sensitivity to both linear and quadratic effective field theory contributions, demonstrated by likelihood scans across the $(c^{I}_{tW}, c^{I}_{tZ})$ plane, and highlighting a landscape where deviations from the Standard Model – marked by a specific cross – are actively sought within a complex parameter space.

The analysis uses effective field theory to constrain CP violation and anomalous electroweak couplings in top quark decays.

Despite the Standard Model’s continued success, subtle deviations in top quark interactions may hint at new physics beyond our current understanding. The recent study, ‘EFT results in the top quark sector in CMS’, presents a comprehensive analysis of top quark production and decay using data from the CMS experiment at the LHC, interpreted within the framework of the Standard Model Effective Field Theory (SMEFT). These results constrain potential new physics contributions to CP violation and electroweak couplings, combining Run 2 measurements and employing advanced machine learning techniques. Will future high-luminosity LHC data reveal definitive evidence of these deviations, ultimately reshaping our understanding of fundamental particle interactions?

The Standard Model’s Prophecy of Failure

Despite its extraordinary predictive power, the Standard Model of particle physics remains incomplete when confronted with cosmological observations. Phenomena such as the observed abundance of dark matter and dark energy, the matter-antimatter asymmetry in the universe, and the origin of neutrino masses all fall outside the model’s explanatory reach. These discrepancies suggest the existence of undiscovered particles and interactions, prompting physicists to explore theoretical frameworks that extend beyond the Standard Model. While the model accurately describes the known fundamental forces and particles, its inability to account for these large-scale cosmological puzzles indicates a deeper, more comprehensive understanding of the universe is required – a quest driving ongoing research and experimentation in high-energy physics.

Charge-Parity (CP) symmetry posits that the laws of physics should remain unchanged if a particle is swapped with its antiparticle and its spatial coordinates are inverted-essentially a mirror image. While extensively tested, the Standard Model predicts only a limited amount of CP violation, insufficient to explain observed imbalances in the universe, such as the prevalence of matter over antimatter. Consequently, any additional CP violation beyond the Standard Model’s predictions would signal the existence of new particles or forces. Experiments, particularly those involving heavy quarks and leptons, meticulously analyze particle decays, searching for discrepancies between the behavior of a particle and its antimatter counterpart. These subtle asymmetries, if detected with sufficient statistical significance, provide compelling evidence for physics beyond our current understanding and offer crucial clues to unraveling some of the universe’s most profound mysteries.

The search for physics beyond the Standard Model increasingly focuses on meticulously measuring violations of Charge-Parity (CP) symmetry, and interactions involving heavy particles, such as the top quark, represent a particularly promising avenue. These massive particles exhibit a stronger coupling to potential new phenomena, amplifying subtle signals that would otherwise remain hidden. By precisely analyzing the decay patterns of top quarks, physicists aim to detect discrepancies from Standard Model predictions, effectively creating a map of this unexplored territory. Any observed deviation would indicate the presence of new forces or particles, potentially shedding light on long-standing mysteries like the matter-antimatter asymmetry in the universe and the nature of dark matter. This pursuit necessitates not only high-energy particle collisions but also sophisticated data analysis techniques to isolate these rare events and extract meaningful information from the complex background noise.

The search for new physics frequently encounters signals buried beneath the threshold of current detection capabilities, necessitating increasingly sophisticated methodologies. Physicists are developing novel analysis techniques – including advanced multivariate statistical methods and machine learning algorithms – to extract faint signatures from the overwhelming background noise inherent in high-energy collision data. Simultaneously, theoretical frameworks are being refined to more accurately predict the subtle manifestations of CP violation beyond the Standard Model, guiding experimental efforts toward the most promising avenues of investigation. These combined advancements aren’t simply about building more powerful detectors; they represent a fundamental shift in how scientists approach data analysis and theoretical modeling, crucial for unveiling the universe’s hidden symmetries and ultimately, expanding our understanding of fundamental laws.

Analysis of multilepton final states reveals best-fit values and confidence intervals for weak coupling (WC) parameters, with heavy-quark couplings scaled for clarity, demonstrating the precision achievable in determining these parameters through profiled fits.

Mapping the Unknown: The SMEFT Framework

The Standard Model Effective Field Theory (SMEFT) addresses the limitations of searching for new physics at specific mass scales by parameterizing deviations from the Standard Model through the addition of higher-dimensional operators to the Lagrangian. These operators, constructed from Standard Model fields and their derivatives, are suppressed by a characteristic energy scale Λ, representing the mass of the new, heavy particles influencing the observed physics. Rather than directly searching for these particles, SMEFT focuses on measuring the coefficients of these operators, which effectively encode the indirect effects of the heavy particles without requiring knowledge of their specific mass or decay modes. The use of higher-dimensional operators, starting with Dimension-6, provides a systematic and model-independent framework for analyzing potential new physics contributions, allowing for a comprehensive assessment of deviations from the Standard Model predictions.

Dimension-6 operators, when added to the Standard Model Lagrangian, represent deviations from the predictions of the Standard Model arising from interactions with higher-mass particles. These operators are constructed from Standard Model fields and their derivatives, organized by their dimensionality, with Dimension-6 being the lowest order at which new physics effects can manifest while remaining gauge-invariant and respecting the Standard Model symmetries. Specifically, these operators modify the interactions between Standard Model particles, altering cross-sections and decay rates. The effects are suppressed by a scale Λ representing the mass of the new heavy particles, meaning the magnitude of the deviations is inversely proportional to $\Lambda^2$ . This allows for a parameterized description of new physics effects without needing to specify the exact nature of the underlying heavy particles.

Wilson Coefficients quantify the size and impact of Dimension-6 operators within the Standard Model Effective Field Theory (SMEFT) framework. These coefficients represent the strength of new physics effects, parameterized by higher-dimensional operators added to the Standard Model Lagrangian. Each operator modifies Standard Model interactions, and its corresponding Wilson Coefficient dictates the magnitude of this modification; larger coefficients indicate a stronger deviation from Standard Model predictions. Consequently, experimental searches for new physics at colliders and in precision measurements primarily focus on constraining the values of these Wilson Coefficients, providing a model-independent way to assess the presence and characteristics of Beyond the Standard Model physics. The determination of non-zero Wilson Coefficients would signal the need for a more complete UV-completion of the SMEFT.

Effective Field Theory (EFT) expansion is a perturbative approach utilized in the Standard Model Effective Field Theory (SMEFT) to systematically organize calculations based on the mass scale of new physics. This involves constructing an infinite series of operators, ordered by their dimensionality, and truncating the expansion at a given order – typically Dimension-6 – as contributions from higher-dimensional operators are suppressed by powers of Λ, where Λ represents the mass scale of the new physics. By focusing on the lowest-dimensional operators, the EFT expansion isolates the most significant modifications to the Standard Model, reducing the number of free parameters and simplifying the analysis while retaining sensitivity to potential new physics effects. This systematic approach allows for model-independent constraints on Wilson coefficients, which parameterize the strength of these operators, without needing to specify the details of the underlying UV completion.

Probing the Top Quark: A Window to New Physics

The processes of ‘ttZ production’ and ‘tZq production’ represent key channels for probing top quark interactions at the Large Hadron Collider. ‘ttZ production’ involves the simultaneous creation of a top quark-antiquark pair ( $t\overline{t}$ ) and a Z boson, while ‘tZq production’ refers to the production of a single top quark alongside a Z boson and a light quark. These processes are sensitive to couplings between the top quark, Z boson, and other Standard Model particles, providing a means to test the Standard Model and search for deviations indicative of new physics. Studying these production mechanisms requires identifying the decay products of the top quarks and Z boson, typically through analyses of their respective leptons and jets.

Multilepton final states, resulting from the decay of top quarks and Z bosons into leptons (electrons, muons, and tau leptons), provide a clean signature for reconstructing these particles’ interactions at the Large Hadron Collider. The full reconstruction of the $t\bar{t}Z$ and $tZq$ decay chains is possible due to the relatively low background contribution from processes that also produce multiple leptons. Precise measurements of kinematic variables – such as lepton momenta, invariant masses, and angular distributions – are then used to test the Standard Model predictions for the couplings between top quarks and Z bosons, and to search for deviations that might indicate new physics. The number of leptons produced allows for effective suppression of backgrounds through optimized event selection criteria and provides sufficient statistical power to observe rare processes.

The High-Luminosity Large Hadron Collider’s Run 2 dataset, comprising 138 fb⁻¹ of data used in multiple analyses and 173 fb⁻¹ specifically for searches involving CP violation, represents a significant increase in proton-proton collision statistics. This large integrated luminosity yields a correspondingly high event rate; however, the production of rare processes like top quark-Z boson interactions is often dwarfed by Standard Model background processes. Consequently, sophisticated analysis techniques, including multivariate statistical methods and boosted decision trees, are essential to effectively reduce background noise and accurately reconstruct signal events, allowing for precise measurements of top quark couplings and searches for new physics.

Physics-informed machine learning techniques are utilized to create CP-odd observables, which are specifically designed to enhance the visibility of potential new physics signals in top quark interactions. These methods integrate established theoretical constraints from the Standard Model into the machine learning algorithms, improving the robustness and interpretability of the resulting observables. By focusing on CP-odd quantities-those that change sign under the simultaneous inversion of spatial coordinates and charge conjugation-analyses can isolate effects not predicted by the Standard Model, as these interactions are typically suppressed or absent within its framework. The increased sensitivity achieved through this approach is crucial for analyzing the large datasets from Run 2 of the Large Hadron Collider, allowing for a more precise search for deviations from Standard Model predictions in processes like ttZ and tZq production.

Beyond Precision: The Future of Particle Physics

The identification of highly energetic particles presents a significant challenge in high-energy physics, particularly when analyzing events stemming from hadronically decaying bosons. These bosons, upon decay, produce sprays of particles-known as jets-that merge together at high energies, making individual particle identification impossible with traditional methods. This necessitates the implementation of ‘boosted analysis’ techniques, which focus on the collective properties of these jets rather than individual particles. By examining jet substructure – patterns within the spray of particles – physicists can reconstruct the original decaying boson and infer its properties, even when energies are extremely high and particles overlap. This approach is essential for probing beyond the Standard Model, as new, massive particles often manifest themselves as highly boosted resonances within these complex hadronic events, demanding sophisticated analysis tools for their detection and characterization.

A detailed examination of the transverse momentum distribution of Z bosons provides a powerful avenue for probing physics beyond the Standard Model. The transverse momentum, a measure of momentum perpendicular to the beam axis, is particularly sensitive to the influence of new, massive particles that might subtly alter the production dynamics of these bosons. By precisely mapping how frequently Z bosons are produced with varying transverse momenta, researchers can identify deviations from theoretical predictions based solely on known physics. These deviations, even if slight, could indicate the presence of undiscovered particles or interactions, allowing scientists to refine their search for new phenomena and establish increasingly stringent limits on potential modifications to established theories. This approach effectively uses $p_{T}$ as a magnifying glass, enhancing the ability to detect the faint signatures of new physics hidden within the complex landscape of particle collisions.

This analysis establishes stringent constraints on the values of Wilson Coefficients, parameters that quantify potential deviations from the Standard Model of particle physics. Specifically, the study determines that $c_{tWI}$ falls within the range of -2.7 to 2.5, while $c_{tZI}$ is limited to between -0.2 and 2.0, both at a 95% confidence level. Notably, the data exhibits a local significance of 2.5 standard deviations favoring a value for $c_{tZI}$ different from the Standard Model prediction, hinting at possible new physics contributions to the interactions of W and Z bosons. These precise limits serve as crucial benchmarks for future studies and theoretical models aiming to refine understanding of fundamental particle interactions.

The precision of current analyses benefits significantly from synergistic combinations, achieving a 10% enhancement in the constraints placed on potential new physics. Future prospects are even more promising, as the forthcoming High-Luminosity Large Hadron Collider (LHC) is anticipated to dramatically improve sensitivity – projections indicate a two to four-fold increase compared to the constraints established during Run 2. This leap in performance stems from the increased data volume and collision rate, allowing for more detailed investigations into subtle deviations from the Standard Model and offering a powerful pathway towards discovering or excluding beyond-the-Standard-Model phenomena. The combined effect of optimized analysis techniques and the upgraded LHC facilities positions particle physics for a new era of precision measurements and discovery.

The search for deviations from the Standard Model, as detailed in this analysis of top quark interactions, isn’t about finding definitive answers, but rather mapping the contours of uncertainty. Monitoring these subtle discrepancies-the places where theory and experiment diverge-is the art of fearing consciously. The pursuit isn’t to prove the Standard Model wrong, but to understand how it might fail, and where the next revelation lies. As Blaise Pascal observed, “The eloquence of angels is silence.” Similarly, the most profound insights often emerge not from strong signals, but from the meticulous measurement of what isn’t there – the faint echoes of physics beyond our current grasp. true resilience in this endeavor begins where certainty ends; the ability to adapt to the unexpected revelations within the data.

What’s Next?

The pursuit of new physics in the top quark sector, as documented here, isn’t a search for completion, but a refinement of the questions. Each constrained dimension-6 operator doesn’t eliminate possibility-it merely shifts the locus of the unknown. The Standard Model, even when stretched by increasingly precise measurements, remains a remarkably resilient scaffolding, and this work serves as another iteration in that stress test. It is not a confirmation of emptiness, but a mapping of the remaining dark matter.

Future iterations will undoubtedly require a departure from the assumption that deviations will manifest as simple modifications of established couplings. The elegance of the effective field theory approach lies in its generality, but also in its potential to obscure more complex phenomena. A guarantee of discovery isn’t possible, only an increasing precision with which to define the boundaries of ignorance. The search for CP violation, in particular, may reveal itself not as a direct signal, but as a subtle reshaping of decay topologies.

Stability, as demonstrated by the continued success of this approach, is merely an illusion that caches well. The system will evolve, and any attempt to build a complete theory is an exercise in predicting the precise nature of its eventual failure. The real work, then, isn’t to find the answer, but to cultivate the ecosystem in which more interesting questions can emerge. Chaos isn’t failure-it’s nature’s syntax.

Original article: https://arxiv.org/pdf/2601.05282.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Standard Model’s Prophecy of Failure

Mapping the Unknown: The SMEFT Framework

Probing the Top Quark: A Window to New Physics

Beyond Precision: The Future of Particle Physics

What’s Next?

See also: