Peering Inside Jets for Hidden Particles

Author: Denis Avetisyan

A new technique using energy correlations promises to reveal subtle signals of new physics lurking within the debris of high-energy collisions.

The study establishes projected limits, at a 95% confidence level, on the coupling-mass plane (<span class="katex-eq" data-katex-display="false">g_q^\prime, m_{Z^\prime}</span>) for a hadrophilic <span class="katex-eq" data-katex-display="false">Z^\prime</span> boson, derived through extrapolation of the CMS energy correlator measurement in dijet events, and thus defines the boundaries within which such a resonance might exist. — The study establishes projected limits, at a 95% confidence level, on the coupling-mass plane ( $g_q^\prime, m_{Z^\prime}$ ) for a hadrophilic $Z^\prime$ boson, derived through extrapolation of the CMS energy correlator measurement in dijet events, and thus defines the boundaries within which such a resonance might exist.

This review details the application of energy correlators as a model-independent method to search for resonant new particles and probe the underlying dynamics of jet substructure.

The search for physics beyond the Standard Model increasingly relies on subtle probes of high-energy collisions. This paper, ‘Bump Hunting Inside Jets with Energy Correlators’, introduces a novel approach utilizing energy correlators to sensitively scan for new resonant phenomena within the complex environment of particle jets. By leveraging the well-understood scaling of energy correlators, deviations from expected behavior can signal the presence of new particles, effectively transforming the search into a “bump hunt”. Could this technique unlock previously inaccessible constraints on models featuring, for example, hadrophilic $Z'$ bosons, and ultimately reveal the nature of new interactions?

The Elusive Echo: Probing the Structure of Hadronic Decay

The pursuit of undiscovered, massive particles at the Large Hadron Collider faces a fundamental hurdle: these particles rarely travel far enough to be directly observed before decaying into a cascade of other, more stable particles. This decay process typically results in what physicists call “hadronic jets” – sprays of particles moving in roughly the same direction. The challenge arises because these jets, originating from the decay of a potential new particle, can appear remarkably similar to jets produced by standard, well-understood processes. Distinguishing a jet signaling new physics from the background of ordinary jets requires extremely precise measurements and innovative techniques, as the information about the original, massive particle is largely encoded within the complex structure of its decay products. Consequently, physicists must cleverly dissect these jets to unveil subtle differences that might betray the presence of something entirely new.

At the Large Hadron Collider, the immense energies generated frequently result in the creation of highly relativistic particles that decay into collimated sprays of hadrons, known as jets. However, when these particles are exceptionally energetic – or ‘boosted’ – the decay products become compressed, merging into a single, complex signature indistinguishable from the background noise. Traditional particle identification techniques, relying on the isolation and precise measurement of individual decay products, falter in these scenarios. The resulting ambiguity makes it incredibly difficult to reconstruct the original particle’s properties, hindering the search for new, massive particles beyond the Standard Model. This merging effect necessitates the development of innovative approaches focused on characterizing the internal architecture – or ‘substructure’ – of these highly boosted jets to tease out the signals of new physics.

The search for new particles at the Large Hadron Collider increasingly relies on characterizing the intricate patterns within hadronic jets, a technique known as jet substructure analysis. When massive particles decay, their energy is often so high that the resulting spray of particles coalesces into a single, powerful jet, obscuring the characteristics that would normally identify its origin. By meticulously examining the internal composition of these jets – the types, energies, and angles of the constituent particles – physicists can effectively ‘dissect’ the original decay process. This detailed analysis allows them to distinguish between the jets produced by standard model processes and those originating from the decay of new, heavier particles, even when those particles themselves are undetectable. Consequently, jet substructure has become an indispensable tool in the quest to unravel the mysteries beyond the Standard Model, offering a pathway to discover physics hidden within seemingly impenetrable cascades of particles.

The distributions of event energy flow (<span class="katex-eq" data-katex-display="false">p_{T}</span>) reveal distinct patterns in jet mass windows of 30 GeV ± 20% (left) and 50 GeV ± 20% (right), indicating how energy is distributed within these jets. — The distributions of event energy flow ( $p_{T}$ ) reveal distinct patterns in jet mass windows of 30 GeV ± 20% (left) and 50 GeV ± 20% (right), indicating how energy is distributed within these jets.

Mapping the Energy Flow: A Novel Observational Approach

Energy correlators function by analyzing the spatial distribution of energy deposition within a hadronic jet, providing insights into the originating particle’s properties and the underlying jet substructure. These techniques measure the correlation between energy deposits in multiple calorimeters, effectively creating a map of energy flow. Deviations from expected patterns, such as those predicted by standard jet models, can indicate the presence of new physics or provide constraints on jet production mechanisms. The strength and shape of these correlations are sensitive to the jet’s initiating particle – whether a quark, gluon, or other exotic entity – and the details of the parton shower evolution, thus allowing for jet tagging and improved event reconstruction.

Jet substructure analysis utilizing energy correlators relies on precise calorimetry to determine particle trajectories within the jet cone. Multiple calorimeters, strategically positioned around the interaction point, measure the energy deposited by hadrons and other particles produced in the jet. By comparing energy depositions in different calorimeters, the algorithms can resolve the angles of these particles relative to the jet axis. This reconstruction is not a direct measurement of particle tracks, but rather an inference based on the total energy flow and the known calorimeter geometry. The resolution of this reconstruction is directly proportional to the granularity and energy resolution of the calorimeters, and is crucial for distinguishing different jet origins and internal structures.

The two-point energy correlator serves as a fundamental measurement, quantifying the relationship between energy deposits in two calorimeters and establishing a baseline for jet substructure analysis. Extensions to three-point configurations, incorporating a third calorimeter measurement, significantly enhance sensitivity by providing additional angular information and reducing combinatorial backgrounds. This increased precision allows for improved discrimination between different jet origins and internal structures, as the three-point correlator can resolve finer details in particle trajectories and energy flow compared to the two-point version. The improvement stems from the ability to more accurately constrain the direction and momentum of the originating particles within the jet, leading to a more robust and detailed reconstruction of the jet’s internal dynamics.

Unitarity constraints on the two-point energy correlator spectrum reveal multiple resonance states for spins 1 and 2, arising from specific choices of spinning coefficients.

Simulating the Decay: Modeling Hadrophilic Z’ Bosons

Realistic event samples for hadrophilic Z’ boson studies are generated using Monte Carlo simulation frameworks such as MadGraph and Pythia 8. MadGraph handles the initial hard scattering process, calculating the probability of Z’ boson production based on defined theoretical models and parameters. The output of MadGraph, representing partons, is then passed to Pythia 8, which simulates the subsequent evolution of these partons into observable hadrons through a process called hadronization. This includes modeling the effects of quantum chromodynamics (QCD) – specifically, the strong force interactions – and incorporating the fragmentation functions that describe how partons split into hadrons. Accurate simulation requires careful parameter tuning and validation against available experimental data to ensure the generated samples accurately reflect expected detector signatures.

Monte Carlo simulations of Hadrophilic Z’ Boson production and decay necessitate modeling strong interaction physics through Quantum Chromodynamics (QCD). These simulations incorporate QCD dynamics to accurately represent the initial parton interactions and subsequent radiation. Furthermore, the process of hadronization – where quarks and gluons form observable hadrons – is a critical component. Accurate hadronization models, typically implemented using algorithms within programs like Pythia 8, are essential for predicting the final state particles detected in experiments, including the distribution of energy and momentum among the resulting jets and leptons. The simulation must account for both initial-state and final-state radiation, as well as the complex interplay of quarks and gluons within the proton and the formation of hadronic showers.

The strong coupling constant, $\alpha_s$ , quantifies the strength of the strong interaction within the Standard Model and directly impacts the precision of Monte Carlo simulations modeling hadrophilic Z’ boson production and decay. Its value, approximately 0.118 at the energy scale relevant to LHC experiments, governs the probability of quark-gluon interactions and therefore influences the modeling of Quantum Chromodynamics (QCD) radiation and hadronization. Accurate determination of $\alpha_s$ – typically achieved through analyses of jet production rates or the tau decay width – is crucial for correctly predicting cross-sections and final-state particle multiplicities in these simulations. Variations in $\alpha_s$ can lead to systematic uncertainties in the predicted signal rates and kinematic distributions, potentially obscuring or mimicking the signature of the Z’ boson.

Analysis of <span class="katex-eq" data-katex-display="false">Z^{\prime} \rightarrow q\bar{q}</span> decay channels and recasting of a CMS search for low-mass resonances produced with a photon constrain the coupling strength <span class="katex-eq" data-katex-display="false">g_{q}^{\prime}</span> to values represented by the 1 and 2 standard deviation bands shown. — Analysis of $Z^{\prime} \rightarrow q\bar{q}$ decay channels and recasting of a CMS search for low-mass resonances produced with a photon constrain the coupling strength $g_{q}^{\prime}$ to values represented by the 1 and 2 standard deviation bands shown.

Unveiling Resonances: The Echo of New Physics

The intricate patterns formed by particles emerging from a high-energy jet collision offer a unique window into potential new physics, specifically the possible existence of a Z’ boson. Rather than simply measuring the energy and momentum of the jet as a whole, scientists analyze the angular distribution – the way constituent particles are spread out in relation to the jet’s axis. A Z’ boson, if produced, would decay into pairs of particles, creating a characteristic resonant structure within this angular landscape. These resonances aren’t random; the angles at which decay products emerge are dictated by the fundamental properties of the Z’ boson itself. By meticulously mapping these angular patterns, researchers can effectively ‘scan’ for the telltale signature of a Z’ boson’s decay, distinguishing it from the background noise of standard model processes and providing compelling evidence for its existence.

The search for new physics necessitates not only the observation of anomalous particle decays, but also verification of their theoretical consistency. Within the framework of jet substructure analysis, any observed angular resonances – patterns in the distribution of particles emanating from a decaying particle – are rigorously constrained by fundamental principles of unitarity and energy positivity. Unitarity demands that probabilities sum to one, preventing non-physical outcomes like particles disappearing or appearing from nowhere, while energy positivity ensures that the energy of the system remains non-negative, preventing instabilities and upholding causality. These constraints effectively define the permissible shapes and strengths of resonant features, acting as a critical filter against spurious signals and ensuring that any observed resonance genuinely reflects a physically viable decay process. By adhering to these principles, researchers can confidently interpret observed angular patterns as evidence for new particles, such as the $Z'$ boson, and distinguish them from statistical fluctuations or artifacts of the analysis.

Statistical analysis, when focused on a specific range of jet masses, provides a rigorous method for evaluating the strength of any observed resonant structures and determining the probability that these signals represent a true discovery rather than a statistical fluctuation. This technique achieves a level of sensitivity competitive with established search methods, allowing for independent verification and bolstering confidence in potential findings. Importantly, this approach offers distinct systematic advantages, potentially mitigating uncertainties inherent in alternative analyses and providing a complementary pathway to explore the decay products of particles like the Z’ boson – a crucial step in extending the Standard Model and uncovering new physics beyond it.

This analysis demonstrates a discovery potential rivaling that of current CMS searches for new physics, notably while maintaining a model-agnostic approach – meaning it doesn’t rely on pre-defined theoretical expectations about the Z’ boson’s properties. Improvements in sensitivity are achieved by focusing the search within a restricted jet mass window, effectively magnifying the signal; however, this refinement introduces a trade-off, increasing the theoretical uncertainties associated with the analysis. Despite this increased complexity in modeling, the technique remains a powerful complement to existing strategies, providing an independent pathway for uncovering potential resonant structures indicative of beyond-the-Standard-Model physics.

The search for new physics benefits directly from increased data availability, and this analysis demonstrates a predictable scaling of sensitivity with luminosity. Projections indicate substantial improvements are achievable with 300 fb⁻¹ and even more dramatically with 3 ab⁻¹ of proton-proton collision data, enhancing the ability to discern resonant structures indicative of new particles. Furthermore, the methodology employs an extended perturbative window, defined by $x_L < 0.35$ , which allows for a broader range of jet substructure configurations to be considered, ultimately bolstering the statistical power of the search without compromising theoretical consistency.

Applying a <span class="katex-eq" data-katex-display="false">30 \pm 20</span> GeV jet mass window to the signal and background distributions for transverse momentum between 400 and 500 GeV enhances signal separation. — Applying a $30 \pm 20$ GeV jet mass window to the signal and background distributions for transverse momentum between 400 and 500 GeV enhances signal separation.

The pursuit of identifying resonant signals within the complex substructure of jets, as detailed in this work, mirrors a fundamental principle of systems-their inevitable evolution. This study, employing Energy Correlators as a novel probe, doesn’t attempt to force discovery, but rather to observe the inherent dynamics at play. As Bertrand Russell noted, “The difficulty lies not so much in developing new ideas as in escaping from old ones.” The researchers allow the data to speak, resisting preconceived models and embracing a model-independent approach. This patient observation-using ECs to map the energy flow-acknowledges that sometimes understanding how a system ages gracefully is more valuable than accelerating its decay, or prematurely imposing a structure upon it. The power lies in letting the internal resonances reveal themselves.

The Horizon of Resolution

The pursuit of resonance, as detailed within this work, isn’t a search for permanence, but an attempt to briefly arrest decay. Each iteration of analysis-each refinement of energy correlators-simply sharpens the inevitable erosion of statistical significance. The paper establishes a method, a tool for momentarily illuminating substructure, but the universe rarely offers clear outlines. Future work will undoubtedly focus on extending the reach of these correlators, probing lower mass ranges, and confronting the complexities of background estimation – an exercise in perpetually chasing diminishing returns.

The real challenge isn’t simply finding a hadrophilic Z’, but understanding what its existence implies about the underlying architecture of fundamental forces. Signals will emerge, transiently, from the noise, but interpreting them requires a critical acknowledgement of the limitations inherent in any model. Unitarity, after all, is a constraint, not a guarantee.

The power of energy correlators lies in their model independence, yet even this freedom carries a cost. It shifts the burden of interpretation, demanding a more nuanced understanding of QCD dynamics and a willingness to accept that some resonances may remain stubbornly ambiguous, fading into the background like whispers lost to time.

Original article: https://arxiv.org/pdf/2605.28934.pdf

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

The Elusive Echo: Probing the Structure of Hadronic Decay

Mapping the Energy Flow: A Novel Observational Approach

Simulating the Decay: Modeling Hadrophilic Z’ Bosons

Unveiling Resonances: The Echo of New Physics

The Horizon of Resolution

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