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Searching for new physics with contact-free transitions in muonic atoms

This paper presents a feasibility study demonstrating how recent advances in quantum-sensing technologies can enable stringent comparisons between theory and experiment for contact-free transitions in muonic atoms, thereby probing new physics in spin-independent muon-proton interactions and disentangling fundamental constants from beyond-Standard-Model searches.

Original authors: Noam Burger, Ben Ohayon

Published 2026-09-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Noam Burger, Ben Ohayon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is built on a set of rules known as the Standard Model, a framework that successfully explains how particles like protons and electrons interact. However, scientists suspect this model is incomplete, hiding a deeper layer of reality that includes new, invisible forces. To find these hidden forces, researchers look for tiny discrepancies between what theory predicts and what experiments measure. One promising place to look is inside "muonic atoms." These are exotic versions of ordinary atoms where a heavy particle called a muon orbits the nucleus instead of an electron. Because the muon is much heavier, it orbits much closer to the center, making the atom incredibly sensitive to the details of the nucleus and any new forces that might be acting there. If a new, short-range force exists, it would slightly shift the energy levels of these atoms, leaving a fingerprint that current experiments might finally be able to read.

A team of researchers at the Technion in Israel has now mapped out a practical path to find these fingerprints. They propose a new way to measure the energy of light emitted by muonic atoms, focusing on specific transitions that avoid the messy complications of the atom's innermost layers. By targeting these "contact-free" transitions, they aim to compare experimental results with theoretical predictions with unprecedented precision. Their work suggests that with modern technology, it is possible to reach a level of accuracy where we can either confirm the existence of new particles or rule out vast regions of possibilities that have remained unexplored. This study does not claim to have found new physics yet; rather, it demonstrates that the tools and methods exist to search for it with a clarity that was previously impossible.

The core of the proposal relies on observing how a muon jumps between specific energy levels within an atom. When a muon falls from a higher orbit to a lower one, it releases a photon, a particle of light. The energy of this light tells scientists exactly how far the muon fell. In the past, measurements of these jumps in muonic atoms were limited by a problem known as the "proton radius puzzle," where different ways of measuring the size of the proton gave conflicting results. This uncertainty made it difficult to tell if a discrepancy in the data was caused by a measurement error or a new force of nature. The researchers realized that by choosing transitions that do not involve the lowest energy states, they could bypass the need to know the exact size of the proton. These specific jumps are less sensitive to the nucleus's physical size and more sensitive to the fundamental interactions between the muon and the proton.

To make this work, the team analyzed the theoretical calculations required to predict these energy jumps. They found that the laws of quantum electrodynamics, which describe how light and matter interact, are accurate enough to support a search for new physics, provided that certain complex corrections are accounted for. One major hurdle is the influence of the nucleus itself, which can wiggle and change shape in response to the muon. The researchers calculated that for lighter elements, such as oxygen, these nuclear effects are small enough to be managed. However, for heavier elements, the uncertainty in the nuclear shape becomes a limiting factor. They suggest that by combining new theoretical calculations with existing experimental data, scientists can reduce these uncertainties to a level where a new force would stand out clearly.

Another critical piece of the puzzle is the environment in which these atoms are created. Muonic atoms are usually formed in gases, but the presence of electrons from the gas atoms can interfere with the measurement. The researchers showed that by carefully selecting the gas pressure and using advanced detectors, they can determine exactly how many electrons are present and correct for their influence. They propose using microcalorimeters, a type of detector that measures the heat generated by a single photon to determine its energy with extreme precision. These detectors can distinguish between different energy levels that were previously blurred together. The study estimates that with a beam of muons and these detectors, it would take about ten to fifteen days of data collection to achieve the necessary precision for light elements like oxygen.

The researchers identified two specific targets for this search: oxygen and argon. Oxygen is ideal for the highest precision because its theoretical calculations are simpler and its nuclear structure is well understood. A measurement of oxygen could reach an accuracy of one part per million, which is sensitive enough to probe for new forces with masses between 0.1 and 1 million electron volts. This range is currently unexplored by other experiments. For heavier forces, the team suggests looking at argon. While the measurements for argon would be slightly less precise due to the complexity of its nucleus, they would still open up a new window into the universe, allowing scientists to test for forces with masses up to 3 million electron volts.

This work represents a feasibility study, a blueprint for how to conduct the experiment rather than the experiment itself. The authors have shown that the theoretical uncertainties are small enough and the experimental technology is advanced enough to make this search viable. They have identified the specific challenges, such as the need for better calculations of nuclear shapes and the management of electron interference, and proposed concrete ways to overcome them. By focusing on these contact-free transitions, the scientific community can finally disentangle the search for new physics from the uncertainties of fundamental constants. If new forces exist in the mass ranges they target, this method offers a clean, direct way to find them, potentially rewriting our understanding of the forces that hold the universe together.

Technical Summary: Searching for New Physics with Contact-Free Transitions in Muonic Atoms

Problem Statement
The physics community seeks to identify phenomena beyond the Standard Model (BSM), often manifested as discrepancies between measured atomic energy level spacings and theoretical predictions. In the nonrelativistic limit, new spin-independent interactions mediated by a boson $X$ (mass $m_X$ , couplings $g_X$ ) can be modeled as an effective Yukawa potential. While existing constraints on muon-neutron interactions ( $g_X^\mu g_X^n$ ) are stringent, constraints on muon-proton interactions ( $g_X^\mu g_X^p$ ) remain less explored, particularly for mediators with masses $m_X \gtrsim 50$ keV.

Current limitations in probing the $g_X^\mu g_X^p$ parameter space stem from the "proton radius puzzle" and the tension between experimental measurements and theoretical extractions of fundamental constants (specifically the proton radius) derived from electronic systems. Traditional spectroscopy in muonic atoms often relies on $s$ - or $p_{1/2}$ -states, which are highly sensitive to nuclear size and shape, thereby entangling the search for new physics with uncertainties in nuclear structure and fundamental constants.

Methodology
This paper presents a feasibility study for probing new physics using contact-free transitions in muonic atoms, specifically focusing on the $3d \to 2p_{3/2}$ manifold. These transitions are termed "contact-free" because they do not involve $s$ -states (which have non-zero probability density at the nucleus) or $p_{1/2}$ -states, thereby reducing sensitivity to nuclear size effects and allowing for a cleaner extraction of fundamental constants.

The study employs a multi-faceted approach:

Theoretical Uncertainty Analysis: The authors estimate the precision of Bound-State Quantum Electrodynamics (QED) calculations for light muonic systems ( $Z \le 20$ ). They quantify uncertainties from uncalculated higher-order terms, including three-loop electronic vacuum polarization (eVP), light-by-light (LBL) scattering, hadronic vacuum polarization (hVP), and self-energy corrections.
Nuclear Structure Modeling: The study evaluates uncertainties arising from nuclear polarization (NP) and finite nuclear size (FNS). It distinguishes between the root-mean-square charge radius ( $r_C$ ) and the nuclear shape parameter ( $r_{CC}/r_C$ ), noting that while $r_C$ is well-constrained, the shape parameter dominates theoretical uncertainty.
Experimental Feasibility: The authors analyze the impact of electron screening in non-dilute gases, which can shift energy levels by several ppm. They propose using microcalorimeters to measure multiple transitions simultaneously to infer electron configurations.
Detector and Calibration Strategy: The study evaluates state-of-the-art microcalorimeters (e.g., maXs-30 and maXs-100) for their energy resolution and stopping power. It outlines a calibration strategy using well-characterized X-ray fluorescence (XRF) lines and radioactive $\gamma$ -ray sources to minimize systematic uncertainties.

Key Contributions and Results

Theoretical Precision: The authors estimate that the combined relative uncertainty from uncalculated QED terms for the $3d-2p$ centroid energy reaches approximately 0.5 ppm for $Z=20$ . This suggests that pure QED effects will not hinder new physics searches at the targeted accuracy level.
Nuclear Uncertainties: The study identifies the nuclear shape parameter ( $r_{CC}/r_C$ ) as the dominant source of theoretical uncertainty. While a conservative 10% uncertainty in this parameter would exceed the 1 ppm goal, the authors argue that recent work suggests this uncertainty can be reduced to $\sim 1\%$ for light nuclei, keeping the total uncertainty below 1 ppm for $Z < 14$ .
Experimental Resolution: The dominant experimental broadening mechanism is attributed to Coulomb explosion in molecular gases, estimated at $10^{-4}$ of the transition energy. This remains smaller than the intrinsic resolution of modern microcalorimeters (5–8 eV FWHM).
Feasible Candidates:
- Light Nuclei ( $Z=6-12$ ): Specifically $^{16}$ O is identified as a prime candidate. Its transitions occur around 24.9 keV, flanked by well-known calibration lines. Theoretical calculations are simplified by its low charge and closed-shell configuration. The authors estimate a measurement time of 10–15 days to achieve 1 ppm precision.
- Heavier Nuclei ( $Z \approx 18$ ): To probe higher mediator masses ( $m_X > 3$ MeV), heavier targets like $^{40}$ Ar are proposed. While uncertainties increase, a measurement targeting 2 ppm precision is deemed feasible over $\sim 12$ days, provided nuclear polarization and shape theories are improved.

Significance and Claims
The paper claims that precision spectroscopy of contact-free transitions in muonic atoms offers a "clean and complementary route" to test short-range, spin-independent interactions between muons and protons.

Decoupling Constants from New Physics: A primary significance is the ability to decouple new physics searches from interpretations of the proton (and deuteron) radius puzzle. By avoiding $s$ -states, the method alleviates the requirement for precisely determined radii from electronic systems, enabling a complete separation of fundamental constant extractions from BSM physics interpretations.
Exploration of Unconstrained Parameter Space: The proposed measurements aim to access regions of the $g_X^\mu g_X^p$ vs. $m_X$ parameter space that are currently unconstrained, particularly for mediator masses between 0.1 MeV and 1 MeV (via light nuclei) and above 3 MeV (via heavier nuclei).
Realistic Accuracy: The authors assert that achieving $\sim 1$ ppm accuracy is realistic given current microcalorimeter technology and reasonable muon beam rates, provided that electron screening is controlled via multi-line measurements and systematic errors in calibration are managed.

In conclusion, the paper posits that with targeted improvements in ab initio nuclear shape calculations and the utilization of microcalorimeter technology, muonic atom spectroscopy can provide stringent, model-independent constraints on new physics in the MeV mass range.

Technical Summary: Searching for New Physics with Contact-Free Transitions in Muonic Atoms

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