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Reggeon Model: Massive Singularities Discovered.

December 13, 2025
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Unveiling the Cosmic Dance: New Physics Insights Emerge from Exotic Particle Models

In a breakthrough that promises to reshape our understanding of the fundamental forces governing the universe, physicists have delved deep into the enigmatic realm of particle theory, unearthing groundbreaking revelations that challenge long-held assumptions and open new avenues for research. A recent study, published in the prestigious European Physical Journal C, meticulously explores a sophisticated theoretical framework known as the reggeon model, which incorporates two particularly intriguing entities: the pomeron and the odderon. These theoretical constructs, crucial for describing particle interactions at high energies, have been re-examined with a novel approach, focusing on their “singularities with non-zero masses.” This intricate work, spearheaded by a trio of brilliant minds, M.A. Braun, E.M. Kuzminskii, and M.I. Vyazovsky, suggests that our current models of particle behavior might be incomplete, hinting at underlying dynamics that have eluded detection until now. The implications of this research are vast, potentially impacting everything from the behavior of matter in extreme cosmic environments to the very fabric of spacetime itself.

The reggeon model, in essence, provides a powerful mathematical tool to describe how subatomic particles interact when they collide at incredibly high energies, such as those generated in particle accelerators like the Large Hadron Collider or observed in the most violent cosmic events. It postulates the existence of “reggeons,” which are theoretical particles or excitations that mediate these interactions. Within this model, the pomeron and the odderon stand out due to their unique properties. The pomeron is associated with elastic scattering, where particles bounce off each other without changing their internal state, and it is thought to be responsible for the increasing strength of proton-proton collisions observed experimentally. The odderon, on the other hand, is a more elusive entity, responsible for charge-conjugation violating processes, which are critical for understanding the subtle asymmetries in particle interactions and potentially shedding light on the matter-antimatter imbalance in the universe.

Traditionally, the pomeron and odderon have been treated as massless singularities, meaning their theoretical description implies they don’t possess any intrinsic mass. However, the new research boldly ventures into uncharted territory by exploring the consequences if these singularities were to possess non-zero masses. This seemingly small divergence from established theory has profound implications. It suggests that at certain energy scales, these fundamental mediators of force might behave in ways we have not anticipated, leading to observable phenomena that current models fail to predict. The inclusion of mass introduces a new dimension to their behavior, influencing how they propagate and interact, and thus altering the outcomes of particle collisions.

This exploration into massive pomeron and odderon singularities is not merely an academic exercise; it is a critical step towards reconciling theoretical predictions with experimental observations that have, at times, presented puzzling discrepancies. Physicists have long grappled with inconsistencies in high-energy scattering data, and the hypothesis of massive singularities offers a potential resolution to some of these lingering questions. By introducing mass, the model gains a new parameter that can be adjusted to fit experimental results more precisely, potentially leading to a more accurate and unified description of particle interactions across a wider range of energies. The intricate mathematical machinery employed in this study allows for a rigorous examination of these mass effects, providing concrete predictions that can be tested.

The concept of singularities in physics often refers to points where a mathematical function or a physical quantity becomes infinite or undefined. In the context of the reggeon model, these singularities in the complex plane of energy and momentum transfer are crucial for understanding the behavior of scattering amplitudes. The traditional assumption of massless singularities implies a certain behavior of these amplitudes, particularly at high energies. However, if these singularities are endowed with mass, their location and influence on the scattering amplitude shift, thereby altering the predicted interaction strengths and patterns. This shift can manifest as subtle deviations from expected cross-sections or the appearance of entirely new interaction channels that were previously unaccounted for.

One of the most exciting aspects of this research lies in its potential to shed light on the nature of the strong force, which binds quarks together to form protons and neutrons, and is responsible for the interactions described by the reggeon model. The strong force is famously complex, exhibiting a property called “asymptotic freedom” at very high energies (where it becomes weaker) and “confinement” at low energies (where it becomes stronger). The pomeron and odderon are key players in understanding this behavior, and by introducing mass, Braun, Kuzminskii, and Vyazovsky are probing the very foundations of quantum chromodynamics (QCD), the theory of the strong force. The ability to describe these high-energy interactions with greater fidelity has far-reaching consequences for cosmology and astrophysics.

Furthermore, the odderon, with its connection to charge-conjugation violation, opens up a fascinating avenue for exploring fundamental symmetries in nature. Charge conjugation (C) is an operation that flips the sign of all charges in a system. C-violation means that a process is not identical when all its charges are reversed. While C-violation is known to occur in weak interactions (leading to phenomena like parity violation), its role in strong interactions, particularly at high energies, is less understood. A massive odderon could provide a mechanism for observable C-violating effects in high-energy collisions, offering direct experimental probes of these subtle asymmetries and potentially contributing to the cosmic mystery of why the universe is dominated by matter rather than antimatter.

The mathematical framework developed in this paper is highly sophisticated, involving advanced techniques from quantum field theory and complex analysis. The authors likely employed methods such as Mellin transforms and analyticity properties of scattering amplitudes to investigate the impact of massive singularities on their behavior. The concept of “analyticity” in physics refers to the property of a function being differentiable in a region, which is a fundamental assumption for describing scattering amplitudes. By studying how the location of these singularities in the complex plane is affected by mass, the researchers can map out the predicted interaction behavior across a wide range of kinematic variables.

The implications for particle accelerator experiments are particularly significant. Facilities like the LHC are constantly pushing the boundaries of energy and precision. The predictions arising from this new theoretical framework, particularly those concerning measurable deviations from standard models, will be crucial for guiding future experimental searches. Scientists will be able to design experiments specifically looking for the subtle signatures that a massive pomeron or odderon might produce. This could involve meticulous measurements of scattering cross-sections, angular distributions, or the production of specific particle states that are sensitive to these exotic interactions.

Moreover, the study’s findings could have profound implications for our understanding of cosmic rays and ultra-high-energy astrophysical phenomena. When cosmic rays, energetic particles from outer space, interact with the Earth’s atmosphere, they undergo high-energy collisions similar to those studied in particle accelerators. The behavior of these interactions is governed by the same fundamental principles, and the reggeon model plays a significant role in simulating these events. If the pomeron and odderon have mass, their influence on these interactions could be more pronounced at ultra-high energies than currently assumed, potentially explaining some puzzling observations in cosmic ray physics, such as the energy spectrum or composition of these enigmatic particles.

The paper’s examination of “singularities with non-zero masses” can be visualized as introducing a new fundamental characteristic to these theoretical entities. Instead of being points of infinite strength with no inherent properties beyond their interaction, they are now described as having a certain “size” or “energy scale” associated with their existence. This mass term acts as a regulator, preventing infinities from appearing too abruptly and dictating how their influence on particle interactions evolves with energy. It’s akin to saying that instead of a perfect, dimensionless point particle, we are considering a tiny, massive sphere, which obviously would interact differently.

The theoretical underpinning of this work is deeply rooted in the S-matrix theory, a cornerstone of quantum field theory that focuses on the properties of scattering amplitudes rather than the explicit construction of fields. The reggeon calculus, an extension of this theory, provides a framework to sum up infinite series of Feynman diagrams that become dominant at high energies. The inclusion of massive singularities within this calculus significantly alters the summations, leading to novel predictions for the behavior of scattering amplitudes as a function of energy and momentum transfer. This advanced mathematical treatment allows for a detailed probing of the asymptotic behavior of quantum chromodynamics.

The potential for this research to become “viral” within the scientific community stems from its ability to address long-standing mysteries and offer predictive power. The pursuit of a unified theory of fundamental forces and the quest to comprehend the early universe are central drivers of modern physics. When theoretical advancements provide concrete, testable predictions that can help resolve experimental anomalies or unlock deeper insights into these grand challenges, they tend to generate immense excitement and widespread interest, sparking new collaborations and research directions. The elegance of the mathematical framework, combined with the profound physical implications, makes this study a prime candidate for such a ripple effect.

In conclusion, the work by Braun, Kuzminskii, and Vyazovsky on the reggeon model with massive pomeron and odderon singularities represents a significant leap forward in theoretical particle physics. It offers a compelling new perspective on high-energy interactions, with the potential to resolve existing experimental puzzles, guide future research at particle accelerators, and deepen our understanding of the fundamental forces that shape our universe. This theoretical innovation promises to ignite a new wave of research, pushing the boundaries of our knowledge and potentially revealing the hidden mechanisms that govern the cosmos.

Subject of Research: Theoretical Particle Physics, Quantum Field Theory, High-Energy Interactions, Strong Force Dynamics, Pomeron and Odderon Behavior.

Article Title: On the reggeon model with the pomeron and odderon: singularities with non-zero masses.

Article References: Braun, M.A., Kuzminskii, E.M. & Vyazovsky, M.I. On the reggeon model with the pomeron and odderon: singularities with non-zero masses.
Eur. Phys. J. C 85, 1415 (2025). https://doi.org/10.1140/epjc/s10052-025-14941-0

Image Credits: AI Generated

DOI: https://doi.org/10.1140/epjc/s10052-025-14941-0

Keywords: Reggeon Model, Pomeron, Odderon, Non-zero Mass Singularities, High-Energy Scattering, Quantum Chromodynamics, Particle Physics, Theoretical Physics.

Tags: advanced particle interaction modelsbreakthroughs in theoretical physicscosmic implications of particle behaviorexotic particle models researchfundamental forces in the universehigh-energy particle collisionsimplications for extreme cosmic environmentsmassive singularities in particle theorynon-zero mass singularitiespomeron and odderon interactionsReggeon model in particle physicsreshaping our understanding of spacetime
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