The core of this transformative research lies in the innovative application of a hybrid model, a strategic amalgamation of disparate theoretical approaches designed to capture the complex phenomenology of ultra-relativistic heavy-ion collisions. Traditional models often struggle to encompass the entire lifecycle of these events, from the initial, violent impact to the eventual emergence of observable particles. By skillfully combining elements of both hydrodynamical descriptions, which excel at modeling the collective behavior of the emergent medium, and more microscopic approaches that can meticulously track the initial stages of the collision and the generation of quantum fluctuations, the scientists have crafted a potent tool. This hybrid architecture allows for a more comprehensive and accurate simulation, enabling them to disentangle the myriad of processes at play with a clarity previously unattainable. The researchers are not just creating a simulation; they are animating the very fabric of spacetime as it existed fractions of a second after the Big Bang.

What sets this work apart is the unprecedented resolution at which the physicists have analyzed the evolving state of the quark-gluon plasma (QGP), the exotic state of matter formed in these collisions. Instead of treating the QGP as a monolithic entity, the model boldly decomposes its behavior into distinct “modes,” each representing a specific characteristic or pattern of evolution. This meticulous “mode-by-mode” analysis allows for a far deeper understanding of how the plasma expands, cools, and eventually fragments into the particles we observe. It’s akin to dissecting a complex symphony, not just listening to the whole but understanding how each instrument, each melodic line, contributes to the final masterpiece. This granular approach reveals subtle correlations and dependencies that might otherwise remain hidden, shedding light on the intricate dynamics of strongly interacting matter.

The sheer energy involved in these lead-lead collisions, precisely at 5.02 TeV, is crucial. This energy scale is specifically chosen because it recreates conditions that are remarkably similar to those that prevailed in the universe mere microseconds after its birth. At these extreme energies, the protons and neutrons within the colliding lead nuclei are effectively shattered, their constituent quarks and gluons liberated from their confined states. The hybrid model then tracks the subsequent evolution of this vibrant, deconfined soup. It meticulously accounts for the strong nuclear force, which governs the interactions between quarks and gluons, and the rapid expansion and cooling that characterize this fleeting state. The precision of the simulation at this energy frontier is what allows for the direct comparison with experimental data, validating the theoretical framework and opening new avenues of inquiry.

One of the most striking revelations from this simulation is the exquisite sensitivity of the QGP’s evolution to very subtle initial conditions. Even minute variations in the way the two lead nuclei collide can lead to significantly different patterns of plasma formation and decay. The hybrid model, with its advanced computational capabilities, is capable of exploring this complex landscape of initial states and their corresponding outcomes. This finding has profound implications for our understanding of how the universe began, suggesting that the initial quantum fluctuations, however small, may have played a critical role in shaping the large-scale structure of the cosmos we observe today. The model acts as a cosmic microscope, magnifying these initial quantum whispers into observable consequences.

The research team’s success hinges on their ability to accurately model the transition from a deconfined state of quarks and gluons back into the familiar protons and neutrons that make up everyday matter. This process, known as hadronization, is incredibly complex and has long been a significant challenge for theoretical physicists. The hybrid model, by integrating various theoretical tools, offers a more nuanced picture of this critical phase, capturing the interplay between the collective expansion of the QGP and the processes that lead to the formation of new particles. It’s not a sudden transformation but a dynamic and intricate unraveling of the initial energetic state into the particles that eventually populate our universe, a testament to the dynamic nature of fundamental forces.

Furthermore, the mode-by-mode analysis allows researchers to identify specific collective phenomena within the QGP that were previously difficult to isolate. These include phenomena like “flow,” where the plasma exhibits collective motion, and “elliptic flow,” which is a specific anisotropic pattern of this motion. By tracking these modes independently, the scientists can gain a deeper appreciation for the interplay between different aspects of the QGP’s behavior, providing crucial insights into the mechanisms driving these collective effects. Understanding these collective behaviors is paramount to decoding the nature of the strong force and the properties of the quark-gluon plasma, offering a window into the fundamental interactions governing our universe.

The implications of this study extend far beyond purely academic curiosity. A profound understanding of the QGP and the conditions of the early universe is essential for developing new technologies and for addressing some of the most fundamental questions in physics, such as the nature of dark matter and dark energy. The ability to precisely simulate these extreme conditions could also inform the design of future particle accelerators and detectors, pushing the boundaries of experimental physics. This research isn’t just about understanding the past; it’s about unlocking the secrets that will shape our future technological and scientific advancements, underscoring the vital importance of fundamental research.

The meticulous validation of the hybrid model against experimental data, particularly from experiments like those conducted at CERN’s Large Hadron Collider, is a cornerstone of this achievement. The fact that the simulation’s predictions align so closely with observed outcomes lends immense credibility to the theoretical framework. This rigorous comparison process is essential for ensuring that our theoretical models accurately reflect the physical reality, allowing us to build upon a solid foundation of empirical evidence. It’s this synergy between theory and experiment that drives scientific progress, with each informing and refining the other in a continuous cycle of discovery.

The visualization capabilities inherent in this research are also noteworthy. While the scientific community primarily focuses on the numerical outputs, the underlying computational framework allows for the generation of compelling visual representations of the QGP’s evolution. These visualizations, though not explicitly featured here, are invaluable tools for communicating complex physical processes to a broader audience. They transform abstract equations and data points into tangible, albeit fleeting, glimpses of the universe’s most extreme states, making the abstract tangible and fostering wider engagement with scientific discoveries.

The collaborative nature of this research, involving physicists from different institutions and potentially different theoretical backgrounds, highlights the power of international cooperation in tackling some of the most challenging scientific questions. The pooling of expertise and resources is essential for undertaking projects of this magnitude, fostering a spirit of shared endeavor and accelerating the pace of discovery. This global approach to scientific problem-solving is vital for unlocking the universe’s deepest mysteries, demonstrating that breakthroughs often emerge from a confluence of diverse perspectives and skills.

Looking ahead, the advancements made in this study are expected to pave the way for even more sophisticated simulations. The researchers are already envisioning incorporating additional physical phenomena and exploring a wider range of collision energies and types of colliding particles. This iterative process of refinement and expansion is characteristic of scientific progress, with each breakthrough building upon previous successes to unlock deeper levels of understanding. The future of heavy-ion physics research is undoubtedly bright, fueled by the innovative approaches demonstrated in this pivotal work.

The potential for this research to inspire a new generation of physicists and engineers is immense. By pushing the boundaries of what is computationally and theoretically possible, this work serves as a powerful testament to human ingenuity and our unyielding drive to explore the unknown. The detailed, nuanced picture of the early universe emerging from this simulation is not just a scientific achievement; it’s a source of wonder and inspiration, reminding us of the profound beauty and complexity of the cosmos and our place within it.

The implications for cosmology are particularly profound. Understanding how matter behaved in the extreme conditions of the early universe has direct bearing on our models of cosmic evolution and the formation of the structures we observe today. This research provides crucial missing pieces to the puzzle, enabling cosmologists to refine their predictions and develop a more complete narrative of the universe’s journey from its fiery inception to its present, vast expanse, offering a clearer picture of our cosmic origins.

The scientific community is abuzz with the implications of this groundbreaking research. The promise of a more accurate and detailed understanding of the universe’s earliest moments, coupled with the potential for new technological advancements, has generated significant excitement. This work exemplifies the power of fundamental research to not only expand our knowledge but also to lay the groundwork for future innovations that will shape our world in ways we can only begin to imagine, igniting a spark of curiosity and wonder.

Subject of Research: The collective behavior and mode-by-mode evolution of quark-gluon plasma created in ultra-relativistic lead-lead collisions at 5.02 TeV.

Article Title: Mode-by-mode evolution of Pb–Pb collisions at 5.02 TeV in a hybrid model.

Article References:

Krupczak, R., Borghini, N. & Roch, H. Mode-by-mode evolution of Pb–Pb collisions at 5.02 TeV in a hybrid model.
Eur. Phys. J. C 85, 1232 (2025). https://doi.org/10.1140/epjc/s10052-025-14959-4

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-14959-4

Keywords: Quark-gluon plasma, heavy-ion collisions, hybrid model, relativistic heavy ions, early universe, particle physics, nuclear physics, high-energy physics, mode decomposition, collective phenomena, hadronization, Big Bang.

The strong force, mediated by gluons, is responsible for holding atomic nuclei together, overcoming the electromagnetic repulsion between positively charged protons. However, unlike electromagnetism, which is governed by a simple Abelian gauge theory with photons, QCD is a non-Abelian gauge theory. This complexity arises from the fact that gluons themselves carry the “color” charge, meaning they interact not only with quarks but also with each other. This self-interaction is the root cause of many of QCD’s most fascinating and challenging phenomena, including asymptotic freedom, where the force weakens at short distances, and confinement, where quarks and gluons are permanently bound within composite particles like protons and neutrons. Understanding these behaviors at a fundamental level requires sophisticated theoretical frameworks and rigorous computational methods.

At the heart of this new research lies the concept of the dilaton, a hypothetical particle associated with the breaking of scale symmetry in theories of fundamental forces. In the context of QCD, the researchers have developed a specific “sum rule” that connects the properties of this dilaton to the conformal anomaly form factor. A sum rule in physics is a theoretical constraint that relates different observable quantities or properties of a system, essentially acting as a consistency check for our theoretical models. The conformal anomaly, on the other hand, refers to a situation where a symmetry that is present in the classical equations of motion is broken by quantum effects. In QCD, scale invariance, which implies that the physics of the theory should be independent of the energy scale, is anomalously broken. This anomalous breaking plays a crucial role in phenomena like the mass generation of hadrons, the composite particles made of quarks and gluons.

The team’s innovative approach leverages the fact that the dilaton is expected to couple to the trace of the QCD energy-momentum tensor, a fundamental object that encapsulates the density and flow of energy and momentum within the theory. By carefully analyzing the theoretical contributions to this trace, particularly in the presence of strong interactions and at specific energy scales, they were able to derive a sum rule that precisely relates the dilaton’s properties to the conformal anomaly form factor. This connection is significant because the conformal anomaly form factor itself is difficult to calculate directly from the fundamental QCD Lagrangian, making this new sum rule a powerful indirect probe. It provides a pathway to extract information about this crucial quantity through the potentially more accessible dilaton contributions.

What makes this discovery particularly viral-worthy is its potential to bridge the gap between different approaches to understanding QCD. For decades, physicists have utilized a variety of theoretical tools to tackle the complexities of the strong force, ranging from perturbative calculations at high energies to lattice QCD simulations at lower energies. However, connecting these different regimes and ensuring consistency has been a persistent challenge. The dilaton sum rule, by providing a unified framework, offers a way to potentially reconcile results from these diverse methodologies, leading to a more coherent and complete picture of QCD. The ability to connect high-energy perturbative insights with low-energy, non-perturbative dynamics is a long-standing goal in nuclear physics.

The researchers’ calculations are performed at the order of $\alpha_s$, the strong coupling constant of QCD, which is a measure of the strength of the interaction between quarks and gluons. While $\alpha_s$ is a fundamental parameter, its value changes with energy, being small at high energies (allowing for perturbative calculations) and large at low energies (necessitating non-perturbative methods). By working at the order of $\alpha_s$, the team has effectively pinned down a significant contribution to the dilaton sum rule, providing a quantitatively precise prediction that can be tested experimentally or compared with other advanced theoretical calculations. This precision is crucial for validating theoretical frameworks.

Imagine the intricate dance of quarks and gluons within a proton, a phenomenon invisible to the naked eye and notoriously difficult to model. This new dilaton sum rule acts like a subtle conductor’s baton, guiding our understanding of this complex choreography. By focusing on the dilaton, a particle that has eluded direct detection but is theoretically predicted to exist, the researchers are indirectly probing the very essence of how the strong force shapes the behavior of matter at its most fundamental level. The implications extend beyond just understanding the proton; they influence our comprehension of nuclear structure and the forces that govern it.

The theoretical underpinnings of this work are rooted in advanced quantum field theory techniques and a deep understanding of symmetries. The team meticulously analyzed the contributions from various quantum fluctuations and interactions to the QCD energy-momentum tensor, ensuring that all relevant terms were accounted for in their derivation of the sum rule. This rigorous mathematical approach forms the bedrock of their discovery, providing a solid foundation for future experimental verification and theoretical exploration. The careful handling of renormalization group flows and operator product expansions are key ingredients in such detailed QFT calculations.

Furthermore, the research has profound implications for understanding phenomena beyond the strong force. The dilaton, and the concept of spontaneously broken scale invariance, are not unique to QCD. Similar ideas appear in other areas of physics, including cosmology and theories of gravity. This common thread suggests that the dilaton sum rule could serve as a unifying principle, connecting otherwise disparate areas of physics and potentially leading to unforeseen breakthroughs in our understanding of the universe as a whole. Identifying universal principles across different physical phenomena is a hallmark of major scientific progress.

The experimental verification of this dilaton sum rule is the next critical step. While it’s challenging to directly observe a dilaton, physicists can look for its indirect effects on other measurable quantities within particle collider experiments or through precise cosmological observations. The precise predictions derived from this sum rule provide concrete targets for experimentalists, ushering in a new era of synergy between theoretical prediction and experimental verification. The discovery of a particle or phenomenon initially predicted by a theoretical framework often ignites new avenues of experimental inquiry.

The beauty of this research lies in its elegance and its potential for broad applicability. By providing a new and powerful tool for probing the conformal anomaly in QCD, the dilaton sum rule opens up new avenues for research into the fundamental properties of matter. It’s the kind of scientific breakthrough that can redefine a field, offering a fresh perspective on long-standing mysteries and paving the way for future discoveries we can only begin to imagine. The ability to make precise predictions that can be tested across different experimental setups and theoretical approaches amplifies the impact of such work.

This new sum rule can also be instrumental in refining our understanding of heavy quarkonium physics, the bound states of a quark and antiquark, which are sensitive probes of the QCD vacuum. By linking the dilaton to the conformal anomaly, it allows for a more accurate description of the spectral properties of these systems, providing crucial data points for validating effective field theories and understanding the complex interplay of forces within them. The nuanced behavior of heavy quark bound states offers a rich playground for testing QCD predictions.

In summary, the development of this dilaton sum rule for the conformal anomaly form factor in QCD represents a significant leap forward in our quest to understand the strong nuclear force. The researchers’ meticulous theoretical work has not only provided a sophisticated new tool for probing the intricacies of QCD but has also opened up exciting possibilities for unifying our understanding of fundamental interactions across different branches of physics. This breakthrough is a testament to the power of theoretical physics to unravel the universe’s deepest secrets, inspiring a new generation of physicists to explore the fundamental forces that shape our reality. The continuous refinement of theoretical models, coupled with advancements in experimental capabilities, promises to further illuminate the fundamental workings of the universe.

The implications of this research extend to the realm of ultra-high energy physics, where the non-perturbative aspects of QCD become dominant. Understanding the behavior of matter under extreme energy densities, as is the case in relativistic heavy-ion collisions, is directly influenced by the QCD vacuum structure and its anomalies. The dilaton sum rule offers a novel avenue to investigate these conditions, potentially leading to a deeper comprehension of phase transitions in nuclear matter and the properties of the quark-gluon plasma. This plasma, a state of matter existing in the early universe and recreated in laboratories, is a crucial area for testing our understanding of QCD.

The specific numerical value of the strong coupling constant at a given energy scale is a cornerstone of QCD calculations, and this dilaton sum rule, by providing a new constraint, could help to more precisely determine its running behavior. Accurate knowledge of $\alpha_s$ is essential for almost all predictions in high-energy particle physics, from the production of Higgs bosons to the structure of protons. Therefore, any advancement that aids in its precise determination is of paramount importance to the entire field. This interconnectedness of different parameters within a theory highlights the holistic nature of scientific inquiry.

Moreover, the dilaton’s role as a potential mediator of dark energy, a mysterious component driving the accelerated expansion of the universe, adds another layer of intrigue to this research. While this specific paper focuses on QCD, the theoretical framework of dilatons and scale symmetry breaking is relevant to cosmology. This cross-disciplinary connection underscores the potential for fundamental physics discoveries to have far-reaching implications, touching upon some of the most profound unanswered questions in cosmology. The search for a unified theory of everything often involves finding connections between seemingly disparate phenomena.

Ultimately, this groundbreaking work serves as a powerful reminder that even in the most well-studied areas of physics, there are still profound mysteries waiting to be uncovered. The dilaton sum rule is a key that could unlock new levels of understanding of the strong force, and its implications are likely to resonate throughout the physics community for years to come, driving new experiments and theoretical explorations. The ongoing pursuit of knowledge, fueled by curiosity and rigorous scientific inquiry, continues to push the boundaries of our comprehension of the cosmos.

Subject of Research: Quantum Chromodynamics (QCD), Strong Nuclear Force, Conformal Anomaly, Dilaton Sum Rule.

Article Title: A dilaton sum rule for the conformal anomaly form factor in QCD at order $\alpha_s$.

Article References: Corianò, C., Lionetti, S., Melle, D. et al. A dilaton sum rule for the conformal anomaly form factor in QCD at order $\alpha_s$. Eur. Phys. J. C 85, 983 (2025). https://doi.org/10.1140/epjc/s10052-025-14686-w

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-14686-w

Keywords: QCD, Strong Force, Dilaton, Conformal Anomaly, Sum Rule, Quantum Field Theory, Particle Physics, Nuclear Physics.

The ALICE experiment, with its sophisticated detector systems, is uniquely designed to capture the intricacies of heavy-ion and proton-nucleus collisions. Its ability to track and identify the vast shower of particles emerging from these high-energy interactions allows physicists to reconstruct the events with incredible detail. In this latest publication, the focus is on the charged-particle production within a broad pseudorapidity region, a measure of the angle of a particle relative to the beam axis. By extending this analysis to wider angles, ALICE is pushing the boundaries of our understanding, moving beyond the central ‘forward’ regions typically studied in such experiments. This comprehensive view is crucial for building a complete picture of how energy is converted into matter and how particle correlations evolve in these extreme environments, providing vital data for refining theoretical frameworks that describe the early universe.

At the heart of this research lies the concept of the quark-gluon plasma (QGP). This exotic state of matter, predicted by quantum chromodynamics (QCD), consists of deconfined quarks and gluons, the fundamental constituents of protons and neutrons, that are no longer bound within individual nucleons. In the incredibly high temperatures and densities created during the LHC’s heavy-ion collisions, such as lead-lead collisions, the QGP is thought to form. However, the collisions of protons with lead nuclei, as investigated in this study, offer a complementary probe. They allow scientists to investigate how the QGP-like characteristics, or specific features that resemble QGP behavior, might emerge even in systems that are not as comprehensively “full” as lead in lead, providing insights into the role of system size and initial conditions.

The charged-particle multiplicity distribution, the statistical spread of the number of charged particles observed in each collision event, is a fundamental observable that carries deep information about the underlying physics. A wider pseudorapidity range means that ALICE is not just looking at the particles traveling almost parallel to the colliding beams, but also those emitted at more significant angles. This allows for a more holistic understanding of the particle production process, revealing how the system evolves and how the initial energy is distributed across all produced particles, irrespective of their trajectory. The precise measurement of this distribution across such a wide angular expanse is crucial for testing theoretical predictions about the initial phase of these collisions.

The choice of proton-lead (p-Pb) collisions is strategic. While lead-lead collisions are the primary laboratory for QGP studies, p-Pb collisions provide a unique stepping stone. They allow researchers to disentangle effects that are specific to the nucleus-nucleus interaction from those that might arise from the proton or be influenced by the nuclear environment. By studying p-Pb collisions, scientists can better understand the role of initial-state effects, such as the spatial distribution of nucleons within the colliding nuclei and the impact of the nuclear geometry, in shaping the final particle production. This helps in isolating the signals that are truly indicative of QGP formation and evolution.

The energy scale of 5.02 TeV per nucleon is particularly significant. At this high energy, the conditions created in the collision are expected to be more extreme, potentially leading to the formation of a hotter and denser state of matter. This increased energy allows for a greater number of particles to be produced, and thus a richer dataset for statistical analysis. Moreover, high-energy collisions are essential for pushing the boundaries of theoretical models, many of which are formulated in the context of perturbative QCD and require high energies to be applicable. The precision of the ALICE measurements at this energy is therefore critical for validating and refining these theoretical frameworks.

The ALICE collaboration’s analysis of charged-particle multiplicity distributions over this wide pseudorapidity range reveals subtle yet crucial deviations from simpler theoretical expectations. These deviations hint at the complex dynamics at play, including the interplay of color strings formed in the initial interactions, the subsequent hadronization process where quarks and gluons coalesce into observable particles, and potentially even early collective effects. The detailed shape and normalization of these distributions are sensitive to the underlying assumptions about particle production mechanisms, the density of the evolving matter, and the connectivity of the produced particles.

The pseudorapidity coverage of this study is extensive, reaching out to $|\eta| \approx 5$. This wide acceptance region is essential for capturing the full picture of particle production, as particles are emitted across a broad range of angles. Understanding particle production at forward and backward rapidities, where particles are emitted at small angles relative to the beam direction, can provide insights into the very initial stages of the collision and the structure of the colliding proton and lead nuclei. Conversely, particles at more central rapidities offer information about the bulk properties of the created matter.

One of the key insights from the ALICE data is the comparison between different collision systems and theoretical models. The charged-particle multiplicities observed in p-Pb collisions at 5.02 TeV are compared with those from proton-proton (pp) collisions at similar energies and nucleus-nucleus collisions. These comparisons allow physicists to quantify the impact of the nuclear environment and the presence of a larger number of initial interacting participants. The observed nuclear effects, such as Cronin enhancement or shadowing, are vital for understanding how the nuclear medium modifies particle production.

The ALICE experiment’s detectors, including the Time Projection Chamber (TPC) for tracking charged particles and measuring their momentum, and the Forward Multiplicity Detector (FMD) for measuring particle production at very forward angles, are crucial for achieving this wide pseudorapidity coverage. The combined information from these detectors allows for a comprehensive reconstruction of the event. The meticulous calibration and understanding of the detector efficiencies and acceptances are paramount for extracting reliable physics results from the immense amount of data collected at the LHC.

The implications of these findings extend beyond the direct measurement of particle distributions. They provide essential input for phenomenological models used to simulate various aspects of high-energy nuclear collisions. These simulations are critical for interpreting more complex observables, such as flow coefficients and particle correlations. By having precise predictions for one of the most fundamental observables, physicists can better understand the validity and limitations of these models and focus on more subtle effects that might be indicative of new physics.

Furthermore, the study of these multiplicity distributions in p-Pb collisions at high energy helps to bridge the gap between the well-understood proton-proton collisions and the more complex nucleus-nucleus collisions. It allows physicists to explore the onset of collective behavior and the transition from a gas-like system to a more liquid-like quark-gluon plasma. The systematic studies of how particle production scales with the number of participants and the system size are key to understanding the fundamental properties of nuclear matter under extreme conditions, potentially revealing signs of the Deconfinement phase transition.

The ALICE analysis reveals that the charged-particle multiplicity in p-Pb collisions at 5.02 TeV exhibits a complex dependence on pseudorapidity. The data shows a marked increase in multiplicity as pseudorapidity increases, a trend expected from the kinematic properties of particle production in high-energy collisions. However, the detailed shape of this distribution and its comparison to various theoretical models provide critical tests for our understanding of how the initial energy density is distributed and how the strong force governs the emergence of these particles.

In essence, this research is about meticulously mapping out the particle landscape of a fleeting, high-energy collision. By precisely measuring the number of charged particles produced across a vast angular range, the ALICE collaboration is providing indispensable data that challenges our current models and drives the development of new theoretical frameworks. This work is not just about counting particles; it’s about deciphering the intricate physics that governs the creation of matter from pure energy, offering a glimpse into the very earliest moments of the universe. The scientific community eagerly awaits further insights as ALICE continues to probe the mysteries of the strong interaction at the LHC.

Subject of Research: Charged-particle multiplicity distributions in proton-lead (p-Pb) collisions at $\sqrt{s_{\text{NN}}}} = 5.02$ TeV across a wide pseudorapidity range.

Article Title: Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at $\sqrt{{{\varvec{s}}}_{{\textbf {NN}}}}={\textbf {5.02}}$ TeV.

Article References:

ALICE Collaboration., Acharya, S., Agarwal, A. et al. Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at (\sqrt{{{\varvec{s}}}_{{\textbf {NN}}}}={\textbf {5.02}}) TeV.
Eur. Phys. J. C 85, 919 (2025). https://doi.org/10.1140/epjc/s10052-025-14577-0

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-025-14577-0

Keywords**: Quark-gluon plasma, High-energy physics, Particle multiplicity, Pseudorapidity, Proton-lead collisions, LHC, ALICE experiment, Quantum chromodynamics