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Search prospect for electrophilic bosons at the $\mu$ TRISTAN

This paper proposes that the asymmetric $\mu^+e^-$ collision mode of the proposed $\mu$ TRISTAN collider operating at $\sqrt{s}=346$ ~GeV offers a unique and powerful opportunity to search for electrophilic axion-like particles and $Z'$ bosons in the 5.5–300 GeV mass range, potentially improving existing coupling constraints by up to four orders of magnitude.

Original authors: Amit Adhikary, Anindya Datta, Dilip Kumar Ghosh

Published 2026-10-08✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Amit Adhikary, Anindya Datta, Dilip Kumar Ghosh

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 by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe we see around us is built on a foundation of particles and forces that physicists have mapped out with remarkable precision. This map, known as the Standard Model, successfully explains how matter interacts, from the atoms in our bodies to the stars in the sky. Yet, this map has glaring gaps. It cannot explain why the universe is filled with invisible dark matter, why neutrinos have mass, or why there is more matter than antimatter. To fill these holes, scientists suspect there are hidden particles waiting to be found. These potential new particles are often imagined as light and weakly interacting, slipping through the cracks of current experiments because they are too light for the massive machines at the Large Hadron Collider to catch, yet too heavy for the lower-energy machines that study beauty quarks to reach. This leaves a specific, unexplored zone of mass where new physics could be hiding, waiting for a machine with just the right energy and a clean environment to reveal it.

A team of researchers has proposed a way to hunt for these elusive particles using a future machine called µTRISTAN. This facility, planned for Japan, would collide a beam of muons with a beam of electrons. Muons are heavy cousins of the electron, and by smashing them together with electrons at high speeds, the machine would create a clean, quiet environment free from the chaotic noise of proton collisions. The researchers focused on a specific scenario where a new, invisible particle couples only to electrons. In this setup, the new particle would be radiated off an incoming electron, much like a photon is emitted when an electron changes speed, and then immediately decay back into a pair of an electron and a positron. The result would be a distinct signature: four charged particles flying out from the collision point, with two of them forming a pair that carries the exact mass of the new particle.

To see if this idea works, the team ran detailed computer simulations of the µTRISTAN collider operating at an energy of 346 GeV. They modeled two types of potential new particles: a pseudoscalar, similar to an axion, and a vector boson, similar to a Z boson. Both would interact only with electrons. The researchers generated millions of simulated collision events, including the rare signal of a new particle and the much more common background events that mimic the signal but come from known physics. Because the new particles would be extremely narrow and decay instantly, the challenge was to distinguish the true signal from the background noise. The team developed a sophisticated computer algorithm, a boosted decision tree, to act as a filter. This algorithm learned to identify which of the three electrons in the final state came from the new particle's decay and which was merely a bystander from the collision, allowing them to reconstruct the mass of the new particle with high precision.

The results of these simulations are promising. The researchers found that with enough data, the µTRISTAN collider could detect these new particles with a sensitivity far beyond what is currently possible. For the lightest particles they considered, with a mass of 5.5 GeV, the machine could detect couplings as weak as 6.5 × 10⁻⁵. This represents an improvement of more than four orders of magnitude over existing limits for the pseudoscalar particle and up to two orders of magnitude for the vector boson. As the mass of the new particle increases toward 300 GeV, the sensitivity naturally decreases because it becomes harder to produce such heavy objects, but the machine would still be able to probe regions of parameter space that are currently completely unconstrained. For the heaviest masses considered, this proposed collider would provide the only existing limits on these types of particles.

The study also compared the performance of the machine against the two different types of particles. While the vector boson is produced slightly more often than the pseudoscalar, leading to a modestly better reach in detecting its coupling, the overall strategy works well for both. The researchers noted that the main limitation is not the ability to spot the signal, but the sheer drop in the number of heavy particles that can be created as their mass approaches the energy limit of the machine. They also checked how errors in measurement or background estimates might affect the results. Even if the background estimates were off by five percent, the machine would still be able to set strong limits, only slightly weakening its sensitivity.

This work highlights a specific window of opportunity in particle physics. Current experiments have largely covered the very light and very heavy ends of the spectrum for particles that talk only to electrons, leaving a middle ground largely unexplored. The µTRISTAN collider, with its unique combination of high energy and a clean electron beam, is ideally suited to fill this gap. By simulating the collision of muons and electrons, the researchers have shown that this machine could effectively scan the mass range between 5.5 and 300 GeV, potentially uncovering the first signs of new physics that explains the dark matter of the universe or the origin of neutrino masses. While these findings are based on simulations and depend on the future construction of the collider, they provide a clear roadmap for how a dedicated machine could solve one of the most persistent mysteries in modern physics.

Technical Summary: Search Prospects for Electrophilic Bosons at $\mu$ TRISTAN

Problem Statement
The Standard Model (SM) leaves several empirical questions unanswered, including the nature of dark matter, neutrino masses, and the baryon asymmetry of the Universe. Many Beyond the Standard Model (BSM) scenarios propose light, weakly coupled states rather than heavy new particles. A specific phenomenological gap exists for "electrophilic" mediators—bosons that couple predominantly or exclusively to electrons—in the mass range between $\mathcal{O}(10)$ GeV and a few hundred GeV.

Current Limitations: B-factories probe the lower end of this mass window but are kinematically limited. The Large Hadron Collider (LHC) faces overwhelming hadronic backgrounds for such searches. Existing $e^+e^-$ data and Lepton Collider (LEP) contact-interaction searches constrain the upper end but leave a significant intermediate region weakly explored.
Specific Gap: Couplings to charged leptons, particularly electrons, are less constrained than couplings to photons or gluons. Existing bounds often rely on quark couplings (absent for leptophilic mediators) or low-energy kinematic reach.

Methodology
The authors investigate the sensitivity of the proposed $\mu$ TRISTAN collider (operating at J-PARC) in its asymmetric $\mu^+e^-$ mode.

Collider Configuration: A 1 TeV muon beam collides with a 30 GeV electron beam, yielding a center-of-mass energy $\sqrt{s} = 346$ GeV and an integrated luminosity up to $1000 \text{ fb}^{-1}$ . This configuration provides a clean leptonic initial state with an electron in the beam, allowing the electrophilic mediator to be radiated directly from the incoming electron.
Theoretical Framework: The study employs a model-independent Effective Field Theory (EFT) approach for two minimal scenarios:
1. Axion-Like Particle (ALP): A pseudoscalar $a$ coupling to the electron via a Yukawa-type interaction ($gaee$).
2. $Z'$ Boson: A neutral vector boson associated with a $U(1)_X$ symmetry, coupling to the electron current ( $g_{Z'}$ ).
- Both mediators are assumed to decay exclusively to $e^+e^-$ .
- The signal process is $e^-\mu^+ \to e^- e^+ e^- \mu^+$ , where the mediator is radiated off the electron line.
Simulation and Analysis:
- Event Generation: Signal and SM background events (mediated by $\gamma/Z$ ) are generated at Leading Order (LO) using MadGraph5_aMC@NLO.
- Detector Emulation: Since no specific $\mu$ TRISTAN detector design exists, the response is emulated using Gaussian momentum smearing tuned to the International Large Detector (ILD) concept of the ILC.
- Event Selection: Events are required to have exactly three electrons and one muon. Kinematic cuts include $p_T \ge 2$ GeV and $|\eta| \le 3.5$ .
- Pairing Strategy: A critical challenge is identifying which of the three final-state electrons originates from the mediator decay versus the "spectator" electron. The authors employ a Boosted Decision Tree (BDT) trained on production-level kinematics (excluding the invariant mass of the pair to avoid bias) to tag the spectator electron.
- Resonance Search: The invariant mass of the identified $e^+e^-$ pair ( $m_{ee}$ ) is reconstructed. Signal peaks are fitted using a double-sided Crystal Ball function.
- Statistical Analysis: Exclusion limits at 95% Confidence Level (CL) are derived using the Asimov significance formula, considering integrated luminosities of 100, 300, 500, and $1000 \text{ fb}^{-1}$ , with and without 5% systematic uncertainty.

Key Contributions

First Sensitivity Study for $\mu$ TRISTAN: This work provides the first dedicated sensitivity analysis for electrophilic ALPs and $Z'$ bosons at the proposed $\mu$ TRISTAN facility.
Optimized Pairing Algorithm: The authors demonstrate that simple kinematic prescriptions (e.g., angular proximity or momentum ordering) fail to maintain high efficiency across the full mass range (5.5–300 GeV). They introduce a BDT-based tagger that maintains a correct pairing efficiency between 70% and 96% across the entire mass spectrum.
Comprehensive Mass Coverage: The analysis covers the "blind spot" between B-factory reach and LEP contact-interaction limits, specifically targeting the 5.5 to 300 GeV range.

Results

ALP Scenario ($gaee$):
- For $L = 1000 \text{ fb}^{-1}$ and no systematics, the projected 95% CL upper limits on the coupling $gaee$ range from $\sim 6.5 \times 10^{-5}$ at $m_a = 5.5$ GeV to $\sim 2.7 \times 10^{-3}$ at $m_a = 100$ GeV.
- For heavier masses ($150-300$ GeV), the reach degrades to $5.5 \times 10^{-3} - 1.7 \times 10^{-2}$ .
- These limits improve upon existing perturbative unitarity bounds and indirect ATLAS constraints (which probe $gaee$ via loop-induced $ga_{\gamma\gamma}$ couplings) by more than four orders of magnitude at the low-mass end and up to two orders of magnitude at the high-mass end. The analysis targets a region of parameter space that is currently unconstrained by direct searches.
$Z'$ Scenario ( $g_{Z'}$ ):
- For $L = 1000 \text{ fb}^{-1}$ , the projected limits on $g_{Z'}$ range from $\sim 4.2 \times 10^{-5}$ at 5.5 GeV to $\sim 1.8 \times 10^{-3}$ at 100 GeV.
- At higher masses ($150-300$ GeV), limits are $3.5 \times 10^{-3} - 1.1 \times 10^{-2}$ .
- The $\mu$ TRISTAN sensitivity improves upon LEP mono-photon, LEP-2 contact interaction, and IceCube constraints by factors of 15 to 150 in the intermediate mass region. Above $m_{Z'} \approx 220$ GeV, this analysis provides the only constraint on this parameter space.
Cross-Section Limits: The exclusion limits on the production cross-section $\sigma(\mu^+e^- \to \mu^+e^+e^-e^-)$ are remarkably flat at low masses ( $\sim 0.03$ fb) and degrade gradually to $\sim 0.12-0.19$ fb at higher masses due to phase-space suppression.
Systematics: Including a 5% systematic uncertainty on the background relaxes the coupling limits by at most 25%, with the largest impact occurring where the background yield is highest (e.g., near the $Z$ pole at 90 GeV).

Significance and Claims
The paper claims that the asymmetric $\mu^+e^-$ mode of $\mu$ TRISTAN is uniquely well-suited to probe the intermediate-mass window for electrophilic mediators.

Unique Reach: It offers the only projected constraint for electrophilic ALPs and $Z'$ bosons in the mass range above B-factories but below the kinematic reach of LEP contact interactions, specifically for direct searches (noting that indirect ATLAS constraints exist for ALPs via loop-induced couplings).
Sensitivity Improvement: The study demonstrates that $\mu$ TRISTAN can improve existing bounds by more than four orders of magnitude for pseudoscalars and up to two orders of magnitude for vectors in specific mass regions.
Robustness: The results are robust against systematic uncertainties and rely on a clean leptonic final state that minimizes hadronic backgrounds, a distinct advantage over hadron colliders.
Caveats: The authors note that the analysis is performed at the parton level with emulated detector resolution. They acknowledge that a dedicated detector design and a full assessment of beam-induced backgrounds (specific to stored muon beams) are required for a realistic experimental proposal. Furthermore, the comparison with existing constraints is indicative, as the external limits rely on different statistical treatments and assumptions (e.g., neutrino couplings for $Z'$ ).

In summary, the paper establishes that a dedicated high-energy lepton collider like $\mu$ TRISTAN can effectively fill a critical gap in the search for weakly coupled, electron-specific new physics.

Technical Summary: Search Prospects for Electrophilic Bosons at μ\muμTRISTAN

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Technical Summary: Search Prospects for Electrophilic Bosons at $\mu$ TRISTAN