Beyond the Visible: Hunting for Hidden Dimensions at the LHC

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Author: Denis Avetisyan

A new analysis reveals that subtle interactions between the Higgs boson and a potential particle from an extra dimension could dramatically improve the chances of detecting these hidden realms.

Current and projected limits on the inverse symmetry breaking scale for Axion-Like Particles (ALPs) and Radions-derived from LHC light-by-light scattering searches-demonstrate an inverse relationship between experimental sensitivity and coupling strength, with stronger couplings manifesting as smaller symmetry breaking scales Ī›, as evidenced by the exclusion regions for ALPs and the translated limits for Radions with varying mixing parameters Ī¾.
Current and projected limits on the inverse symmetry breaking scale for Axion-Like Particles (ALPs) and Radions-derived from LHC light-by-light scattering searches-demonstrate an inverse relationship between experimental sensitivity and coupling strength, with stronger couplings manifesting as smaller symmetry breaking scales Ī›, as evidenced by the exclusion regions for ALPs and the translated limits for Radions with varying mixing parameters Ī¾.

Higgs-Radion mixing enhances the detectability of Radion excitations in light-by-light scattering, offering a novel search strategy within the Randall-Sundrum model.

While extra-dimensional models offer compelling solutions to fundamental physics puzzles, detecting their excitations remains a significant challenge due to inherent limitations in coupling strength. This paper, ‘Searches for extra-dimensional excitations in light-by-light scattering’, presents a detailed analysis of the Radion particle within the Randall-Sundrum framework, revealing that mixing with the Higgs boson can dramatically enhance its production rate in light-by-light scattering at the LHC. By leveraging forward proton tagging and reinterpreting existing limits on Axion-Like Particles, we derive the first exclusion contours for the Radion, demonstrating that current LHC data are beginning to constrain viable mixing scenarios. Could this mixing mechanism provide a pathway to finally observe evidence of these hidden dimensions?

The Hierarchy Problem: A Crack in Reality

The Standard Model of particle physics, despite decades of experimental verification and predictive power, presents a significant conceptual challenge known as the Hierarchy Problem. This arises from the vast discrepancy between the electroweak scale – around 100 GeV, governing interactions like radioactive decay – and the Planck scale, approximately 10^{19} \text{ GeV}[/latex>, which characterizes gravity. Quantum corrections to the Higgs boson mass, responsible for particle masses, are incredibly sensitive to contributions from high-energy physics, theoretically driving its mass to values close to the Planck scale unless extraordinarily precise cancellations occur. Such ā€˜fine-tuningā€™ seems unnatural and suggests the Standard Model is an incomplete description of reality, implying the existence of new physics at higher energy scales to stabilize the Higgs mass and resolve this fundamental tension.

The vast gulf between the electroweak scale – governing the masses of fundamental particles like the Higgs boson – and the Planck scale, where gravity is expected to become quantum mechanical, represents a profound challenge to modern physics. This discrepancy, spanning roughly sixteen orders of magnitude, isn’t simply a matter of large numbers; it implies a fundamental incompleteness in the Standard Model. Current theories struggle to explain why the Higgs bosonā€™s mass remains so much smaller than the Planck mass, requiring increasingly complex and seemingly arbitrary adjustments to avoid predictions of enormous quantum corrections. This suggests that the physics governing the universe at very high energies – and potentially at the earliest moments after the Big Bang – extends beyond the established framework, demanding new particles, forces, or even dimensions to bridge this enormous gap and provide a more natural explanation for the observed scales.

The persistent challenge in theoretical physics lies in the difficulty of explaining the vast disparity between the electroweak scale – governing the masses of fundamental particles like the Higgs boson – and the Planck scale, where gravity is expected to become quantum mechanical. Current frameworks, when attempting to reconcile these scales, often require an extraordinary degree of fine-tuning – adjustments to parameters with seemingly impossible precision to avoid results that contradict observation. This isn’t necessarily an indication of incorrect predictions, but rather a suggestion that the underlying theory requires parameters to be set to values so improbable that they appear ā€˜unnaturalā€™. For example, calculating the Higgs bosonā€™s mass using quantum corrections leads to values vastly larger than observed unless counterbalancing terms are added with extreme accuracy. This reliance on unnatural fine-tuning isnā€™t a fatal flaw, but it signals that current theoretical foundations may be incomplete, prompting a search for more elegant and self-consistent explanations that avoid such improbable coincidences.

The pursuit of physics beyond the Standard Model demands a dual strategy of theoretical innovation and experimental investigation. Researchers are actively developing new frameworks – such as supersymmetry, extra dimensions, and string theory – each attempting to resolve the Hierarchy Problem and predict observable phenomena. These theoretical advances are not sufficient, however, without corresponding experimental efforts to validate or refute them. High-energy colliders, like the Large Hadron Collider, continue to search for direct evidence of new particles, while precision measurements of known particles and sensitive searches for rare processes – like neutrinoless double beta decay – aim to reveal indirect signatures of physics at higher energy scales. The synergy between these theoretical and experimental fronts is crucial; each informs and refines the other, driving the field toward a more complete understanding of the universeā€™s fundamental laws and potentially revealing a new paradigm in particle physics.

Warped Dimensions: Bending the Rules of Spacetime

The Randall-Sundrum model postulates the existence of an additional spatial dimension beyond the three conventionally observed. This dimension is not infinite in size but is constrained and warped, meaning that the geometry of spacetime is altered such that distances are not uniform throughout the extra dimension. Specifically, the model proposes a five-dimensional Anti-de Sitter (AdS) space, characterized by a negative cosmological constant. This warping arises from a potential governing the extra dimension, leading to an exponential change in metric along the extra dimensionā€™s coordinate y . The strength of this warping is determined by a parameter, k , which dictates the curvature of the extra dimension and is central to the modelā€™s predictions.

The Hierarchy Problem arises from the vast discrepancy between the electroweak scale and the Planck scale – the energy at which quantum gravity effects become significant. The Randall-Sundrum model resolves this by introducing an extra spatial dimension with a warped geometry. This warping creates a geometric suppression of the effective Planck scale \Lambda_{eff} \approx \Lambda_{true} / L , where \Lambda_{true} is the true Planck scale and L is the size of the extra dimension. Because L can be significantly smaller than the electroweak scale, the effective Planck scale observed at lower energies is exponentially reduced, thereby alleviating the need for extreme fine-tuning to explain the weakness of gravity compared to other forces.

The Randall-Sundrum models predict the existence of the Radion, a scalar field originating from the fluctuations in the position of the brane separating the five-dimensional bulk from our observed four-dimensional spacetime. As a consequence of the warped geometry, the Radion appears as a nearly massless particle in the effective four-dimensional theory, with its mass inversely proportional to the size of the extra dimension. The Radion interacts with all Standard Model particles, with the strength of the interaction determined by the particles’ localization within the warped dimension; particles more strongly localized will have larger couplings to the Radion. Consequently, searches for the Radion often focus on deviations from Standard Model predictions in precision measurements and resonant production at colliders, where it can manifest as a narrow resonance in various decay channels.

The Radion, as a dynamical degree of freedom arising from the extra dimension in warped geometry models, directly influences and is influenced by interactions with Standard Model particles. Its mass is not inherently fixed at zero but is generated through interactions, primarily via the gravitational sector, with both matter and gauge fields; the precise mass depends on the details of these interactions and the specific model parameters. Furthermore, the Radion couples to the energy-momentum tensor, leading to Radion emission from energetic processes and modifications to gravitational interactions. The strength of these couplings is inversely proportional to the scale of extra dimensions, \Lambda , making the Radion a potential mediator between our 4D world and the higher-dimensional space. These interactions result in observable effects such as deviations from Newtonian gravity, modifications to particle masses, and potentially detectable signals in high-energy collisions.

The interference landscape in the <span class="katex-eq" data-katex-display="false"></span>\(\\Lambda_r\\)-\\xi\\) plane reveals that constructive interference (darker regions, <span class="katex-eq" data-katex-display="false"></span>\\xi > 0\\) enhances the Radion signal, while destructive interference (lighter regions) suppresses it, particularly within the photophobic region marked by the dotted line, with the effect being more pronounced for <span class="katex-eq" data-katex-display="false"></span>m_{\\phi} = 600\\) GeV compared to <span class="katex-eq" data-katex-display="false"></span>m_{\\phi} = 200\\) GeV.
The interference landscape in the \(\\Lambda_r\\)-\\xi\\) plane reveals that constructive interference (darker regions, [latex]\\xi > 0\\) enhances the Radion signal, while destructive interference (lighter regions) suppresses it, particularly within the photophobic region marked by the dotted line, with the effect being more pronounced for [latex]m_{\\phi} = 600\\) GeV compared to [latex]m_{\\phi} = 200\\) GeV.</figcaption></figure> <h2>Hunting the Radion: A Glimmer in the Photon Sea</h2> <p>The Radion, a hypothetical particle arising from extra-dimensional models, interacts with the Higgs boson via kinetic mixing. This mixing introduces a term in the Lagrangian that allows the Radion field to couple to the electromagnetic field, effectively altering the Higgs bosonā€™s interactions with other particles. Specifically, the strength of the Higgs coupling to photons and other gauge bosons is modified, deviating from the Standard Model predictions. The magnitude of this modification is directly proportional to the kinetic mixing parameter, <latex>\xi</latex>, quantifying the degree of interaction between the Radion and the Higgs. Consequently, precise measurements of Higgs boson couplings provide a pathway to constrain the Radionā€™s properties and search for evidence of its existence.</p> <p>Light-by-Light (LBL) scattering, or <latex>\gamma\gamma \rightarrow \gamma\gamma</latex>, represents a sensitive probe for beyond-the-Standard-Model physics, specifically the Radion. This process, where two photons interact, is forbidden at leading order in quantum electrodynamics but can occur through quantum loop effects or the exchange of virtual particles. The extremely small cross-section for LBL scattering in the Standard Model is significantly enhanced in models containing new particles that couple to photons, such as the Radion. Experimental observation of an anomalous LBL scattering rate, or a deviation from the predicted Standard Model cross-section, would therefore provide evidence for the existence of such new particles and allow for the determination of their properties. Current analyses utilize ultra-peripheral collisions to provide a high-luminosity environment for observing this rare process.</p> <p>Light-by-Light (LBL) scattering provides a means to constrain the mass and coupling strength of the Radion due to its sensitivity to new physics modifying the Higgs sector. Analyses of LBL scattering cross-sections demonstrate that even moderate kinetic mixing <latex>\xi = 0.5</latex> between the Radion and the Higgs boson can significantly enhance the scattering rate. Specifically, current calculations indicate a cross-section increase of at least a factor of 200 compared to the predicted cross-section arising solely from gravitational interactions. This enhancement allows for more stringent limits on Radion properties through precise measurements of the LBL scattering process.</p> <p>Ultra-peripheral collisions, typically heavy-ion collisions at energies such as those achieved at the LHC, offer a unique environment for studying Light-by-Light scattering due to the limited overlap of the colliding nuclei, minimizing background processes. The addition of Forward Proton Tagging - detectors positioned downstream of the interaction point to identify protons that remain largely intact after the collision - further refines the signal by identifying events where the photons interact with the nuclei without disrupting their overall structure. This methodology allows for the observation of this exceedingly rare process and, by translating existing exclusion limits established in the search for Axion-Like Particles (ALPs) - which share similar interaction signatures - current analyses have pushed the upper limit on the Radion mass to approximately 24.2 GeV.</p> <figure> <img alt="The light-by-light scattering cross-section <span class="katex-eq" data-katex-display="false">\sigma(\gamma\gamma \to X \to \gamma\gamma)</span> reveals that while a pure trace anomaly coupling (blue, <span class="katex-eq" data-katex-display="false">\xi=0</span>) severely suppresses the signal, Higgs-Radion mixing (red, <span class="katex-eq" data-katex-display="false">\xi=0.5</span>) partially recovers sensitivity, though at a rate approximately <span class="katex-eq" data-katex-display="false">5 \times 10^{-4}</span> times lower than that of an axion-like particle (ALP) for a fixed scale of 1 TeV." src="https://arxiv.org/html/2601.03110v1/ALPradion_xs.png" style="background-color: white;"/><figcaption>The light-by-light scattering cross-section [latex]\sigma(\gamma\gamma \to X \to \gamma\gamma) reveals that while a pure trace anomaly coupling (blue, \xi=0) severely suppresses the signal, Higgs-Radion mixing (red, \xi=0.5) partially recovers sensitivity, though at a rate approximately 5 \times 10^{-4} times lower than that of an axion-like particle (ALP) for a fixed scale of 1 TeV.

Beyond the Standard Model: A Paradigm Shift on the Horizon

The detection of a Radion particle would signify a monumental leap in physics, directly validating the existence of extra spatial dimensions as proposed by theories like the Randall-Sundrum model. This hypothetical particle arises from the warping of a higher-dimensional spacetime, manifesting as a resonance in the observable four dimensions. Unlike gravitons that propagate throughout all dimensions, the Radion represents the excitation of the extra dimension itself. Its observation wouldn't merely add another particle to the Standard Model; it would fundamentally alter our understanding of the universeā€™s geometry and potentially offer a solution to the Hierarchy Problem - the unexplained disparity between the weak scale and the Planck scale. Confirmation of the Radion would necessitate a reevaluation of established cosmological models and open new avenues for exploring the nature of gravity at extremely high energies, effectively bridging the gap between particle physics and cosmology.

Should experimental searches fail to detect the Radion - a potential messenger particle arising from the existence of extra dimensions as proposed by the Randall-Sundrum model - the implications are significant for theoretical physics. Stringent limits placed on the Radionā€™s mass and couplings would progressively constrict the parameter space available to this model, ultimately challenging its viability as a solution to the Hierarchy Problem - the unexplained disparity between the weak scale and the Planck scale. This would necessitate a shift in focus towards alternative theoretical frameworks, prompting further investigation into models like supersymmetry, extra-dimensional scenarios beyond Randall-Sundrum, or entirely novel approaches to address the fundamental question of why gravity is so much weaker than the other fundamental forces. The continued absence of Radion signals, therefore, doesnā€™t represent a dead end, but rather a crucial guidepost directing the search for physics beyond the Standard Model.

The predicted properties of the Radion, a potential manifestation of extra spatial dimensions, are notably susceptible to quantum loop effects - virtual particles briefly appearing and disappearing that subtly alter its behavior. These loops typically diminish the observability of the Radion signal, making detection exceedingly difficult. However, a theoretical mechanism known as kinetic mixing offers a potential solution by effectively amplifying the signal. This mixing introduces interactions between the Radion and other particles, counteracting the usual loop suppression and enhancing its detectability. Calculations reveal that kinetic mixing reduces the suppression factor to approximately 2.40e-6, a significant improvement that brings the Radion within a more realistic range for observation at future high-energy colliders and experiments designed to probe physics beyond the Standard Model.

The pursuit of physics beyond the Standard Model necessitates continued advancements in collider technology and experimental precision. Future facilities, designed to reach higher energy scales and increased luminosity, offer the potential to directly observe subtle deviations from predicted particle interactions - clues that could resolve long-standing puzzles like the Hierarchy Problem, which questions the vast disparity between the electroweak scale and the Planck scale. These experiments wonā€™t solely rely on discovering new particles; precise measurements of known particle properties, such as their masses and couplings, can also reveal indirect evidence of new physics manifesting through quantum corrections. Furthermore, innovative experimental techniques, including those leveraging advanced detector materials and data analysis algorithms, will be crucial in sifting through the immense datasets generated by these colliders, ultimately paving the way for a more complete understanding of the fundamental constituents and forces governing the universe.

Simulations of ALP (grey) and Radion (red) signals at <span class="katex-eq" data-katex-display="false">m=150</span> GeV demonstrate a close agreement in pseudorapidity separation <span class="katex-eq" data-katex-display="false">\Delta\eta</span>, validating the assumption of comparable selection efficiencies.
Simulations of ALP (grey) and Radion (red) signals at m=150 GeV demonstrate a close agreement in pseudorapidity separation \Delta\eta, validating the assumption of comparable selection efficiencies.

The pursuit within this study mirrors a fundamental tenet of scientific inquiry: the willingness to challenge established boundaries. Researchers dissect the Randall-Sundrum model, not to confirm its tenets, but to expose potential signals - the Radion - obscured by inherent limitations like loop-suppression. This methodical dismantling, searching for faint traces within light-by-light scattering, exemplifies a core principle. As Karl Popper stated, ā€œThe only statements with a scientific status are those which can be tested.ā€ The work doesnā€™t seek to prove extra dimensions, but to devise experiments capable of falsifying their existence, embracing a methodology where rigorous testing, not confirmation, defines genuine progress.

What's Next?

The enhanced sensitivity to the Radion via light-by-light scattering, stemming from Higgs mixing, presents a curious paradox. The very mechanism that allows detection-a seemingly accidental confluence of couplings-highlights how reliant the search for extra dimensions remains on loopholes in established physics. It isn't a direct observation of altered spacetime, but rather a subtle distortion within the Standard Model's framework. The best hack is understanding why it worked.

Future work must address the inherent limitations of focusing solely on this particular decay channel. The modelā€™s parameter space remains largely unexplored, and the assumptions regarding the Radion's couplings-its ā€˜personalityā€™, if one will-are far from definitive. A comprehensive search necessitates broadening the experimental landscape, examining other potential signatures-perhaps those deliberately obscured by the modelā€™s inherent complexities.

Ultimately, this investigation underscores a fundamental truth: every patch is a philosophical confession of imperfection. The continued refinement of these searches isnā€™t simply about finding the Radion; itā€™s about iteratively deconstructing the Standard Model, probing its vulnerabilities, and revealing the deeper, more elegant structure-or lack thereof-that lies beneath. The real question isn't if extra dimensions exist, but how thoroughly we must dismantle our current understanding to find them.

Original article: https://arxiv.org/pdf/2601.03110.pdf

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

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2026-01-07 17:16