⚛️ phenomenology

Rethinking search signatures: Hadronic decays of GeV-scale feebly coupled particles

This paper proposes a new hadronization model tuned to electromagnetic scattering data and conservation laws to correct the inaccuracies of standard Pythia simulations for GeV-scale feebly coupled particles, revealing that their dominant experimental signatures are multiparticle decays rather than the commonly targeted two-particle modes.

Original authors: Viktor Kryshtal, Maksym Ovchynnikov

Published 2026-09-16

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Viktor Kryshtal, Maksym Ovchynnikov

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 landscape of particle physics, scientists are hunting for a new kind of resident: a particle that is heavy enough to be felt but so shy that it barely interacts with the rest of the universe. These "feebly interacting" particles are a leading candidate for dark matter, the mysterious substance that holds galaxies together but refuses to shine. To find them, researchers build massive detectors and wait for these elusive particles to decay, or break apart, into the ordinary matter we can see. The most common strategy has been to look for a very specific, simple signature: a single parent particle splitting into exactly two charged tracks, like a pair of electrons or a pair of pions. This approach is clean and easy to spot, much like looking for a single pair of footprints in fresh snow.

However, this simplicity relies on a computer program called Pythia to predict what happens when these new particles decay into heavier, more complex forms. Pythia is a standard tool used by physicists to simulate how quarks and gluons—the fundamental building blocks of matter—snap together to form particles like protons and pions. For decades, this program has been tuned using data from high-energy collisions at the Large Electron-Positron collider, where particles were moving at speeds close to the speed of light. The assumption was that the rules governing how these particles break apart at high energies would hold true even for the lighter, slower particles scientists are now hunting. But as the energy scale drops to the range of a few billion electron volts, a region where the rules of the quantum world become messy and crowded, that assumption may have been wrong.

A team of researchers at CERN and the University of Kyiv has realized that relying on the standard settings of this simulation tool is leading experiments to look in the wrong place. They found that when a feebly interacting particle with a mass of a few billion electron volts decays, it does not usually split into a neat pair of charged particles as the standard software predicts. Instead, it tends to shatter into a chaotic spray of many particles, a mix of charged tracks and neutral particles like photons that leave no track at all. The standard simulation, they argue, is blind to this reality, generating impossible combinations of particles and missing the most likely outcomes. By building a new, more careful model that respects the strict laws of symmetry and conservation, they have rewritten the map for where these particles should be found.

The researchers began by testing the standard simulation against real data from electron-positron collisions, which serve as a perfect laboratory for understanding how matter forms. They discovered that the default settings of the software were producing states that nature simply forbids, such as certain combinations of particles that violate fundamental symmetry rules. Even worse, the software was vastly overestimating the number of simple two-particle decays while severely underestimating the complex, multi-particle explosions that actually occur. It was as if a weather forecast, calibrated on clear summer days, was being used to predict a blizzard, and it kept insisting the sky would remain blue. The standard tool was failing to capture the true complexity of the hadronic world at these lower energies.

To fix this, the team constructed a new model that acts as a guide for the simulation. They took the known, precise measurements of how particles decay into specific groups, such as three pions or four pions, and used those as fixed anchors. Then, they applied a simple, data-driven rule to predict how these probabilities change as the energy increases. Crucially, they added a set of strict filters that reject any computer-generated outcome that violates the laws of physics, such as conservation of charge or specific quantum numbers. This new approach, which they have packaged into a tool called exHad, forces the simulation to respect the reality of the data rather than the habits of the software.

When they applied this new model to the SHiP experiment, a proposed facility designed to hunt for these hidden particles, the results were startling. The standard search strategy, which looks for exactly two charged tracks, was found to be looking for a ghost. In the simulations using the new model, the probability of finding a clean two-particle decay dropped dramatically. Instead, the dominant signature became a messy event containing multiple charged tracks mixed with neutral photons. For a particle with a mass of two billion electron volts, the chance of seeing a simple two-track event was suppressed by a factor of fourteen compared to the old predictions. Meanwhile, events with at least four charged particles, or a mix of charged tracks and photons, became the most common way these particles would reveal themselves.

This shift changes everything for how experiments should be designed. The researchers showed that if an experiment only looks for two charged tracks, it might miss the vast majority of these new particles entirely. The most promising signal is no longer a clean pair, but a complex cluster of debris. For the SHiP experiment, this means that the ability to reconstruct events with multiple tracks and to detect neutral photons is not just a nice-to-have feature; it is essential. The team demonstrated that by including these mixed charged-photon states in the search, the number of detectable events could increase by a factor of two to nine, depending on the type of particle being hunted.

The work does not claim to have solved the mystery of dark matter, nor does it prove that these feebly interacting particles exist. It is a simulation study, a rigorous re-evaluation of the tools used to predict what those particles would look like if they were there. The authors emphasize that their model is a better approximation of reality based on current data, but it still relies on assumptions about how particles behave at energies where direct measurements are scarce. They have not discovered a new particle; they have discovered that the map used to find one was drawn with the wrong colors. By correcting the map, they have shown that the search for these elusive particles must change its focus. The next generation of experiments will need to be ready to see the chaos of the multi-particle decay, rather than waiting for the simplicity of a single pair. The hunt is not over, but the hunters now know they must look in a different direction.

Technical Summary: Rethinking search signatures: Hadronic decays of GeV-scale feebly coupled particles

Problem Statement
Experimental searches for GeV-scale feebly interacting particles (such as Heavy Neutral Leptons, dark photons, $B-L$ vectors, axion-like particles (ALPs), and Higgs-like scalars) frequently rely on simulations of hadronic decays to estimate sensitivity. These searches often target simple final states, specifically pairs of charged particles. However, for hadronic invariant masses above $\sim 1$ GeV, the inclusive hadronic width is typically dominated by multi-hadron modes rather than two-body decays.

Current simulations rely heavily on the Lund string fragmentation model implemented in Pythia 8, which is calibrated primarily on high-energy LEP and SLD $e^+e^-$ data. The authors argue that applying these default parameters ("raw Pythia") to the few-GeV mass range constitutes an unreliable extrapolation. Quantitative and qualitative failures of this approach include:

Symmetry Violations: The generation of symmetry-forbidden states (e.g., parity-forbidden two-pseudoscalar states for ALPs, isospin-forbidden two-pion states for $B-L$ vectors).
Rate Misestimation: Misidentifying dominant decay channels by orders of magnitude.
Bias Toward Simplicity: Systematically overpredicting few-hadron final states while underpredicting multi-hadron decays.

This bias risks experiments optimizing their selection criteria for incorrect signatures, potentially missing signals or misinterpreting sensitivity limits.

Methodology
The authors develop a constrained hadronization model, implemented as a standalone package named exHad, designed to reweight Pythia's fragmentation predictions for low-mass systems. The model combines particle-specific exclusive decay calculations with a common empirical prescription constrained by electromagnetic data.

The core components of the methodology are:

Exclusive Boundary Conditions: Channel probabilities are fixed at a reference mass ( $m^*$ ) using experimental data (e.g., $e^+e^- \to$ hadrons cross-sections) or exclusive theoretical calculations specific to the particle model.
Quantum-Number Conservation: Generated hadronic states are rejected if they violate the total isospin, $C$ -parity, or $G$ -parity of the decaying particle's current. For two-body states, spin and parity compatibility with the source is also enforced.
Mass Scaling: The probability of producing a specific channel group $F$ at invariant mass squared $s$ is scaled from the reference mass $m^*$ using a power law modified by a finite-mass factor:
$P_F(s) = \frac{b_F}{N(s)} \left( \frac{m_*^2}{s} \right)^p \frac{T_F(s)}{T_F(m_*^2)}$
where $p \simeq 2$ is an empirical exponent motivated by $e^+e^- \to$ hadrons data (specifically the $s^{-3}$ scaling of multi-pion cross sections relative to the inclusive $s^{-1}$ cross section). $T_F(s)$ is a finite-mass correction factor derived from Pythia's residual mass dependence, accounting for phase-space suppression near threshold. $N(s)$ ensures probabilities sum to unity.

The model is applied to various benchmark cases: Dark Photons, $B-L$ vectors, fermion-coupled ALPs, Higgs-like scalars, and Heavy Neutral Leptons (HNLs). For each, the model integrates exclusive inputs (form factors, spectral functions) with the fragmentation prescription, ensuring continuity in rates and derivatives at matching intervals.

Key Contributions

exHad Package: A standalone decay package providing a common prescription for Pythia-based simulations, capable of handling diverse particle models while respecting their specific quantum numbers and exclusive rates.
Constrained Fragmentation Model: A method to correct Pythia's low-mass extrapolations by enforcing symmetry constraints and calibrating mass scaling to electromagnetic data, rather than relying on default high-energy tuning.
Re-evaluation of Search Signatures: A demonstration that correcting the hadronization model fundamentally alters the predicted dominant decay signatures for GeV-scale particles.

Results
The application of the tuned model yields significant shifts in predicted decay compositions compared to raw Pythia:

Suppression of Forbidden/Suppressed Modes: The model correctly eliminates or suppresses channels forbidden by symmetry (e.g., $2\pi$ for $B-L$ vectors, $2$-pseudoscalar states for ALPs), which raw Pythia erroneously populates.
Enhancement of Multi-Hadron Decays: The probability of multi-hadron final states (e.g., $3\pi$ , $5\pi$ , $\eta\pi\pi$ , $K\bar{K}\pi$ ) is significantly enhanced relative to two-body charged pairs. For a 2 GeV ALP, modes like $\eta^{(\prime)}\pi\pi$ account for $\sim 80\%$ of the hadronic width, whereas raw Pythia underestimates these.
Impact on Experimental Acceptance (SHiP Example): Using the SHiP experiment as a case study, the authors show that after applying geometric and momentum selections ( $|p| > 1$ $∣ p ∣ > 1$ GeV):
- For Dark Photons and ALPs, the "two-track" (exactly two charged particles) signature is suppressed by factors of 4 to 14 compared to raw Pythia predictions.
- Conversely, "mixed" signatures containing both charged tracks and photons (e.g., from $\pi^0 \to \gamma\gamma$ or $\eta \to \gamma\gamma$ in multi-body decays) become the dominant accepted category.
- For ALPs, the mixed charged-photon category increases the combined accepted fraction by a factor of $\sim 9$ relative to the two charged-only categories.

Significance and Claims
The paper claims that the reliance on default Pythia fragmentation for GeV-scale feebly coupled particles leads to a systematic misidentification of dominant search signatures. The authors assert that:

Search Strategies Must Evolve: Experiments should not optimize solely for charged-pair final states. The shift toward multi-hadron and mixed charged-neutral states necessitates "multitrack" searches and the reconstruction of events using both charged tracks and calorimetric photon information.
Sensitivity Reassessment: Sensitivity projections based on default fragmentation may be inaccurate. The authors provide a tool (exHad) to reassess these sensitivities.
Modest Scope of Accuracy: The authors explicitly state that a better fit to electromagnetic data alone does not guarantee higher accuracy for all new particles. True accuracy requires controlling quantum-number correlations, missing resonances, and amplitude interferences. The model is presented as a common prescription that incorporates improved exclusive descriptions where available, but it remains an empirical extension subject to the uncertainties of the underlying exclusive inputs and matching choices.

The work serves as a motivation for experimental collaborations to adopt more sophisticated hadronization models that respect the specific quantum numbers of the particles being searched for, rather than relying on generic high-energy fragmentation tunes.

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