⚛️ phenomenology

Effective kinematic variables for searching for dark matter mediators in single top quark production processes

This paper proposes and validates through full Monte Carlo simulation effective kinematic variables in the rest frame of the top-quark and mediator decay cluster to search for, classify, and measure the masses of dark matter mediators in single top quark production processes at the LHC.

Original authors: E. E. Boos, V. E. Bunichev, L. V. Dudko

Published 2026-09-30

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CC BY 4.0

Original authors: E. E. Boos, V. E. Bunichev, L. V. Dudko

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

The universe is filled with a mysterious substance known as dark matter. It does not shine, reflect light, or interact with the world in ways we can easily see, yet its gravity holds galaxies together. Because we cannot observe it directly, scientists look for it by watching what happens when particles collide at incredibly high speeds inside massive machines called accelerators. In these collisions, if dark matter is created, it escapes the detector without a trace, leaving behind a gap in the energy balance known as missing energy. To understand how this invisible matter might be created, physicists often imagine a bridge, or a mediator, that connects the ordinary particles we know to the dark world we do not. This mediator could be a new type of particle, perhaps a scalar, a pseudoscalar, or a vector, each with its own unique way of interacting with the known world. The challenge is that these signals are faint and easily hidden by the background noise of ordinary particle collisions.

A team of researchers at Moscow State University has proposed a new way to find these mediators by focusing on a specific and rare event: the production of a single top quark. The top quark is the heaviest known elementary particle, and because of its immense mass, it is a likely candidate for interacting with dark matter. When a top quark is created in a single production process, it is born with a specific spin, or orientation, much like a spinning top. As it decays almost instantly, it breaks apart into other particles, including a positively charged electron and a neutrino. The researchers realized that the way these decay products fly out carries a hidden map of the interaction that created them. By analyzing the angles and energies of these particles, they can tell if a dark matter mediator was involved and, if so, what kind of particle it was.

The scientists developed a method that looks at the collision from a very specific perspective: the rest frame of a combined group of particles. Instead of trying to track every invisible particle individually, which is nearly impossible, they grouped the visible decay products of the top quark with the invisible dark matter particles into a single "cluster." By studying how the particles move relative to this cluster, they found distinct patterns that act as fingerprints for different types of mediators. For instance, if the mediator is a scalar particle, the angle between the direction of the original quark and the resulting electron follows one specific curve. If the mediator is a pseudoscalar, the curve flips in the opposite direction. A vector mediator produces a completely different, more complex pattern. These differences are subtle, but they are consistent enough to be spotted if one knows exactly where to look.

To test if this idea would work in the real world, the team ran detailed computer simulations that mimicked the conditions of the Large Hadron Collider, including the way real detectors measure and sometimes miss information. They simulated collision events, generating 50,000 events for each scenario with mediators of 400 GeV and 1500 GeV to see how the signals held up under realistic conditions. The results were promising. Even after accounting for the imperfections of real-world detectors, the distinct shapes of the angular distributions remained clear. The angle between the decay products and the original spin direction successfully separated the scalar and pseudoscalar scenarios from the vector case. Furthermore, the energy of the emitted electron shifted in a predictable way depending on the mass of the mediator, providing another clue to its identity.

Perhaps the most significant finding was a method to actually measure the mass of the invisible mediator. Since the dark matter particles escape detection, their mass cannot be weighed directly. However, the researchers discovered that by using the known energy and momentum of the visible particles and applying a specific approximation where the invisible neutrino behaves similarly to the visible electron, they could reconstruct the mass of the missing particle. In their simulations, this reconstruction method produced a sharp peak at the exact mass value used to generate the events for scalar and pseudoscalar mediators. However, for the vector mediator, the peak shifted significantly toward larger values, indicating that the kinematics of the main subprocess are violated in that specific case. This suggests that if such a particle exists and is produced in these collisions, scientists could not only detect its presence but also determine its weight with high precision for scalar and pseudoscalar types, while noting distinct deviations for vector types.

The study confirms that looking at single top quark production offers a powerful new window into the dark sector. By focusing on the spin correlations and energy distributions of the decay products within a specific reference frame, physicists can distinguish between different types of dark matter mediators and measure their masses. While these results come from simulations and have yet to be confirmed by experimental data, the proposed variables provide a clear and effective roadmap for future searches at the Large Hadron Collider. If dark matter mediators are hiding in the data of single top quark events, this new approach gives scientists the tools to find them.

Technical Summary: Effective Kinematic Variables for Searching for Dark Matter Mediators in Single Top Quark Production

Problem Statement
The identification of dark matter (DM) particles remains a central challenge in high-energy physics. While astrophysical observations confirm the existence of dark matter, accelerator experiments at the Large Hadron Collider (LHC) seek to detect production processes involving large missing transverse energy. A prevailing theoretical framework posits that interactions between Standard Model (SM) fields and dark matter are mediated by intermediate particles (mediators), which can be scalar, pseudoscalar, or vector in nature.

Processes involving the top quark are of particular interest because the interaction parameters of scalar mediators with SM fermions are proportional to fermion masses. Furthermore, in single top quark production (specifically the $t$ -channel), the top quark is produced with strong polarization due to the $(V-A)$ structure of the interaction vertices. This polarization is transferred to decay products, manifesting in energy spectra and spin correlations. However, distinguishing between different mediator types and reconstructing their masses is complicated by the presence of undetected particles (neutrinos and DM particles), which constitute the total missing four-momentum.

Methodology
The authors propose a method to analyze these processes in the rest frame of a "common cluster" formed by the top quark and the mediator decay products. Since the neutrino and DM momenta cannot be individually resolved, the cluster's four-momentum is reconstructed using the total missing four-momentum, the charged lepton momentum, and the most energetic $b$ -quark momentum.

The study employs the following steps:

Theoretical Derivation: Effective Lagrangians for scalar, pseudoscalar, and vector mediators are defined. Differential cross-sections are derived for the polarized top quark decay ( $t \to b\nu e^+$ ) within the common cluster frame. The analysis focuses on the angular dependence of the decay products relative to the top quark spin quantization axis (defined by the initial $d$ -quark direction).
Kinematic Variables: Three primary variables are investigated:
- $\cos \theta$ : The angle between the charged lepton momentum and the spin quantization axis.
- $\phi$ : The azimuthal angle in the plane perpendicular to the lepton momentum, determined by the mutual orientation of the production ( $d$ -quark) and decay ( $b$ -quark) systems.
- $E_{e^+}$ : The positron energy in the cluster frame.
- $M_\phi$ : A reconstructed mediator mass variable derived under the approximation that the neutrino momentum aligns with the positron momentum in the cluster frame for heavy mediators.
Simulation: The efficiency of these variables is tested using full Monte Carlo simulations. Parton-level calculations are performed using CompHEP, followed by parton showering and hadronization via PYTHIA, and detector response simulation using Delphes (modeling CMS detector capabilities). Two mediator mass benchmarks are used: 400 GeV (lower bound for scalar/pseudoscalar) and 1500 GeV (lower bound for vector).

Key Contributions and Results

Differentiation of Mediator Types:
- Scalar vs. Pseudoscalar: The distribution in the angle $\phi$ provides the most distinct signature. For scalar mediators, the distribution follows a $(-\cos \phi)$ profile, whereas for pseudoscalar mediators, it follows a $(+\cos \phi)$ profile. This difference arises from the geometric orientation of the production and decay systems in the cluster frame. The $\cos \theta$ distribution preserves the SM-like $(1 + \cos \theta)$ correlation for both scalar and pseudoscalar cases, making it insufficient for distinguishing between them.
- Vector Mediators: The vector mediator scenario destroys the correlation between the $d$ -quark and positron momenta in $\cos \theta$ due to contributions from diagrams involving initial quark lines and a more complex Lorentz structure. The $\phi$ distribution for vector mediators exhibits a more complex behavior and shifts significantly toward smaller $\phi$ values at higher masses.
Mass Reconstruction:
- The authors propose a mass reconstruction variable $M_\phi = \sqrt{(E_{miss} - E_{e^+})^2 - (\vec{p}_{miss} - \vec{p}_{e^+})^2}$ . This relies on the approximation that for sufficiently heavy mediators, the neutrino and positron momenta are nearly collinear in the cluster frame.
- Simulation results show that for scalar and pseudoscalar mediators, the reconstructed mass distribution peaks sharply at the true input mass (400 GeV and 1500 GeV).
- For vector mediators, the peak shifts toward larger values due to the contribution of additional diagrams that violate the kinematics of the main subprocess.
- When applied to SM samples, the method yields a peak at the $W$ -boson mass, confirming its specificity to new physics scenarios.
Robustness Against Detector Effects:
- Full simulation including detector response confirms that the characteristic behaviors of the $\phi$ distribution (distinguishing scalar from pseudoscalar) and the positron energy distribution (showing a shift to higher energies for new physics) are preserved, although slightly smeared.
- The mass reconstruction method remains accurate even after including detector effects, allowing for precise mass measurement.

Significance
The paper claims that the joint analysis of the positron energy, the angle $\phi$ , and the reconstructed mass variable $M_\phi$ in the common cluster rest frame offers an effective strategy for the LHC. These variables allow for:

The unambiguous identification of the mediator type (scalar, pseudoscalar, or vector).
The precise measurement of the mediator mass.
The separation of new physics events from SM backgrounds by imposing kinematic cuts on the reconstructed mass variable.

The authors conclude that this approach is directly applicable to LHC experiments for the search and study of dark matter particles, leveraging the unique spin correlations inherent in single top quark production.

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