The Vanishing Proton: A New Hunt for Physics Beyond the Standard Model

Author: Denis Avetisyan

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A novel search strategy at the future Electron-Ion Collider could reveal subtle signals of new particles by looking for events where a proton seemingly disappears.

This review proposes a ‘missing proton energy’ search at the EIC to probe invisible decays and explore potential signatures of axion-like particles and other beyond-the-Standard-Model physics.

Despite the Standard Model’s success, fundamental questions about dark sectors and new physics remain unanswered, motivating searches beyond established frameworks. This paper, ‘Braking protons at the EIC: from invisible meson decay to new physics searches’, proposes a novel search strategy at the future Electron-Ion Collider (EIC) – exploiting ‘missing proton energy’ signatures – to probe invisible decays of particles like axion-like particles and potentially reveal subtle deviations from known physics. By precisely reconstructing proton kinematics, the EIC could enhance bounds on invisible meson decays by up to four orders of magnitude and directly probe axion-like particle couplings up to 10⁵ GeV. Could this ‘missing energy’ approach unlock a new window into the hidden sectors of the universe?

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Unveiling the Universe’s Hidden Components

The Standard Model of particle physics, while remarkably successful in describing the fundamental forces and particles of the universe, leaves several key questions unanswered, most notably the existence of dark matter. Cosmological observations strongly suggest that approximately 85

The search for physics beyond the Standard Model often encounters the challenge of directly observing new, weakly interacting particles. Given the limitations of current detection methods, scientists are increasingly focused on identifying indirect evidence of their existence. One promising avenue involves studying particle decays that appear to violate expected conservation laws – specifically, decays into particles that are effectively ‘invisible’ to detectors. These “invisible decays” don’t produce any readily measurable signals, but their frequency – quantified by the Invisible Branching Ratio – provides a crucial signature. By precisely measuring how often a particle decays into these unseen components, researchers can infer the presence of new particles mediating the process, even if those particles themselves remain elusive. This approach allows exploration of the unseen universe by meticulously tracking what isn’t detected, offering a complementary path to direct observation.

The search for physics beyond the Standard Model hinges, in part, on meticulously quantifying how often particles decay into undetectable forms – a measurement captured by the Invisible Branching Ratio. This ratio represents the frequency with which a particle transforms into constituents that do not interact with detectors, potentially revealing the existence of dark matter or other hidden sector particles. Current experiments, such as the NA62 Collaboration, have already established stringent limits on this ratio for certain particles; for charged kaons (K^+), the upper bound stands at less than 2 x 10^-11, meaning fewer than two in ten billion decays produce these ‘invisible’ products. These precise measurements, while not yet revealing new particles, progressively constrain theoretical models and guide the development of more sensitive searches, pushing the boundaries of what can be observed and understood about the universe.

Current investigations into the unseen universe rely on meticulously measuring the decay rates of known particles, specifically searching for instances where they appear to vanish into nothing – decaying into particles undetectable by current instruments. Experiments such as NA62 and NA64 are at the forefront of these searches, establishing increasingly stringent upper limits on the ‘Invisible Branching Ratio’ – the frequency with which these ‘invisible decays’ occur – for various mesons. However, the proposed Electron-Ion Collider (EIC) promises a significant leap in sensitivity. While current limits hover around 2 x 10^{-{11}} for certain decays, the EIC is projected to achieve a sensitivity of approximately 10^{-9} for the decay of the neutral pion (π^0), potentially revealing subtle signals of new physics and shedding light on the composition of dark matter or the existence of previously unknown particles.

A New Lens for Discovery: The Electron-Ion Collider

The Electron-Ion Collider (EIC) utilizes the collision of high-energy electron beams with either polarized electron beams or heavy ion beams to probe the internal structure of nucleons – protons and neutrons. This approach allows physicists to investigate the strong force, which binds quarks and gluons within these particles, and to map the distribution of these constituents in both momentum and spin space. By varying the collision energy and utilizing different ion species, the EIC aims to create a three-dimensional picture of the nucleon, revealing how its structure evolves under different conditions and ultimately providing insights into the emergence of mass and the properties of nuclear matter. The EIC is designed to access a kinematic regime inaccessible to previous experiments, enabling precision measurements of the gluon and sea quark distributions within nucleons and investigating the role of saturation effects at high energy densities.

The Forward Proton Detector is a critical component of the Electron-Ion Collider (EIC) designed to capture protons that emerge at very small angles relative to the beam direction – termed “forward-going” protons. These protons are produced when the colliding electron interacts with a nucleon inside the ion, effectively knocking that nucleon out of the nucleus. The detector utilizes a system of silicon trackers, Cherenkov detectors, and calorimeters to precisely measure the momentum and position of these forward protons. This detailed tracking is essential for reconstructing the kinematics of the original electron-ion collision and provides a means to access information about the internal structure of the colliding ions, specifically the distribution of quarks and gluons within the nucleons.

Precise tracking of forward-going protons at the Electron-Ion Collider (EIC) allows for reconstruction of collision kinematics by measuring the proton’s momentum and direction. This reconstruction is vital for determining the initial state of the collision and identifying any imbalance in momentum, which manifests as missing energy. The ability to accurately measure this missing energy is not dependent on directly detecting the products of the decay, but rather inferred from the overall momentum imbalance. This indirect detection method enhances the EIC’s sensitivity to phenomena involving weakly interacting or invisible particles, enabling searches beyond the Standard Model and precise measurements of known particle properties.

The detection of missing energy at the Electron-Ion Collider (EIC) serves as a key signature for identifying particle decays where the decay products are not directly observed. Specifically, the EIC’s instrumentation is designed to achieve a sensitivity below 4.4 \times 10^{-9} for the neutral pion (\pi^0) decay, a process that commonly occurs but is difficult to detect due to the lack of charge and limited interaction cross-section of its decay products. Precise measurement of missing transverse momentum, resulting from undetected decay products, allows for the reconstruction of these invisible decays and provides crucial data for understanding particle physics beyond the Standard Model.

Tracing the Vanishing: Pseudoscalar Mesons and Hidden Particles

The Electron-Ion Collider (EIC) will investigate the phenomenon of invisible decays of pseudoscalar mesons – specifically the neutral pion (π⁰), eta (η), and eta prime (η’) – where the decay products are not directly detectable by the experimental apparatus. These mesons are produced copiously in proton-proton collisions at the EIC, and their subsequent decay provides a potential avenue for searching for physics beyond the Standard Model. The “missing proton energy” search will reconstruct the energy and momentum of the initial proton and measure any apparent energy deficit, indicative of undetected decay products. Precise measurement of the decay branching ratios for these mesons into invisible final states is critical, as any deviation from Standard Model predictions could signal the presence of new, weakly interacting particles.

Axion-Like Particles (ALPs) are hypothetical neutral bosons proposed as potential components of dark matter and extensions to the Standard Model. Unlike the photon, which is massless, ALPs are predicted to have a small, but non-zero, mass. Their primary interaction is through coupling to two photons, allowing for potential decay channels of pseudoscalar mesons like π⁰, η, and η’ into undetectable particles. The strength of this coupling is parameterized by a constant, and measurements of meson decay rates into these ‘invisible’ final states can constrain the ALP coupling strength and mass. Current experimental bounds, such as those from the NA64h experiment, place limits on the branching ratios for η and η’ decaying into invisible particles, providing initial constraints on the parameter space for ALPs.

The Electron-Ion Collider (EIC) will investigate the decay products of pseudoscalar mesons-specifically, instances where the expected visible decay products are absent, indicating decay into invisible particles. This search is predicated on the possibility that these decays are mediated by beyond-the-Standard-Model particles, most notably Axion-Like Particles (ALPs). By precisely measuring the branching ratios and kinematic properties of these ‘invisible’ decays – where energy and momentum appear to be missing – the EIC can establish the existence of these new particles. Detecting a statistically significant excess of invisible decays, and characterizing their properties, would constitute direct evidence for physics beyond the current Standard Model, and could reveal the nature of dark matter candidates like ALPs.

Analysis of pseudoscalar meson decays at the EIC offers a pathway to determine the coupling strength of Axion-Like Particles (ALPs). Projected sensitivity for detecting ALPs through these decay rates is expected to reach ma\sqrt{fa/ga\chi} > 10 \text{ GeV}, where m_a is the ALP mass, f_a is the decay constant, and g_aχ is the coupling to dark matter. Current experimental bounds, established by the NA64h experiment, place limits on the branching ratios for invisible decays of the η and η’ mesons at BR(η->inv) < 1.1 x 10^-4 and BR(η’->inv) < 2.1 x 10^-4, respectively. Precise measurement of these branching ratios will refine these bounds and potentially reveal evidence for ALP interactions.

The proposed ‘missing proton energy’ search at the Electron-Ion Collider represents a distillation of experimental strategy. It acknowledges the inherent limitations of direct detection and shifts focus to inference-detecting absence as a signal. This approach mirrors a commitment to parsimony, seeking meaningful data from what is not observed. As John Stuart Mill stated, “It is better to be a dissatisfied Socrates than a satisfied fool.” The pursuit of new physics, particularly signals beyond the Standard Model like axion-like particles, demands this level of intellectual dissatisfaction – a relentless questioning of assumptions and a willingness to explore the implications of apparent anomalies. The search isn’t for what is there, but for what should be, and isn’t.

Beyond the Vanishing Point

The proposition of a ‘missing proton energy’ search at the EIC represents a subtraction, not an addition. It does not demand more complex detectors, nor intricate reconstruction algorithms. Instead, it acknowledges the inherent limitation of detection – that absence of evidence, when properly considered, is evidence. The true challenge lies not in seeing more, but in accurately accounting for what remains unseen. A system that requires ever-increasing complexity to interpret its null results has, by definition, failed to achieve simplicity.

The focus on axion-like particles, while a pragmatic starting point, should not become a constraint. The methodology – identifying signatures through incomplete momentum transfer – is broadly applicable. Any weakly coupled particle decaying invisibly, or any process violating momentum conservation in a subtle manner, becomes a potential target. The EIC, thus conceived, shifts from a machine for confirming known physics to one for exposing its absences.

Ultimately, the success of this approach will be measured not by the discovery of a specific particle, but by the refinement of the question itself. Clarity is courtesy; the ideal search is one that, upon finding nothing, reveals the fundamental structure of nothingness. A truly elegant theory requires no instruction manual.

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Original article: https://arxiv.org/pdf/2601.00068.pdf

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

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2026-01-05 14:36