⚛️ phenomenology

Probing CP violation in dark scalar decays at the SHiP experiment

This paper proposes using the SHiP experiment to probe CP violation in GeV-scale dark scalar bosons by analyzing the ratio of three-meson to two-meson decay events, which arise from pseudoscalar and scalar couplings respectively, alongside complementary two-muon and di-photon channels.

Original authors: Mayumi Aoki, Takashi Shimomura

Published 2026-10-09

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CC BY 4.0

Original authors: Mayumi Aoki, Takashi Shimomura

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

In the vast, invisible landscape of the universe, there is a persistent mystery that the known laws of physics cannot fully explain: why does the cosmos contain more matter than antimatter? According to our current understanding, the Big Bang should have created equal amounts of both, which would have annihilated each other instantly, leaving behind a universe filled only with light. The fact that we exist, that stars shine and planets form, suggests that something tipped the scales in favor of matter. Physicists call this imbalance a violation of a fundamental symmetry known as CP violation. While we have observed this phenomenon in a few specific, rare particle interactions, the known sources are not strong enough to account for the entire universe's existence. This gap in our knowledge has led scientists to look for new, hidden sources of this asymmetry, often theorizing the existence of a "dark sector"—a realm of particles that interact very weakly with the ordinary matter we see every day.

One promising candidate for a resident of this dark sector is a dark scalar boson, a type of particle that is invisible to our eyes but could be produced in high-energy collisions. If such a particle exists, it might be a "mixture" of two different states: one that behaves like a mirror image of itself and one that does not. Determining whether this particle is a pure mirror image, a pure non-mirror image, or a blend of both is crucial. If it is a blend, it would be direct evidence of a new kind of CP violation, potentially solving the mystery of why the universe is made of matter. However, because these particles interact so weakly, they are incredibly difficult to catch, and their behavior is subtle.

A team of researchers has proposed a clever way to hunt for this specific type of particle using two upcoming experiments designed to catch long-lived particles: SHiP, located at CERN in Europe, and FASER2, situated at the Large Hadron Collider. The researchers focused on a dark scalar boson with a mass roughly between one and two billion electron volts, a scale that is heavy enough to be interesting but light enough to be produced in large numbers. Their strategy relies on watching how this invisible particle decays, or falls apart, into other, more familiar particles. The key insight is that the way the particle breaks apart depends entirely on its internal nature. If the particle is a pure mirror-image state, it will almost exclusively break apart into pairs of mesons, which are particles made of a quark and an antiquark. If it is a pure non-mirror state, it will almost exclusively break apart into groups of three mesons.

The researchers realized that if the dark scalar is a mixture of both states, it would be a smoking gun for new physics. In this scenario, the particle would decay into both pairs and triplets of mesons simultaneously. To test this, the team simulated the conditions of the SHiP and FASER2 experiments, calculating how many of these particles would be produced from the decay of heavier B-mesons and how many would survive long enough to reach the detectors. They found that for a wide range of possible masses and mixing angles, the experiments would see a significant number of events where the dark scalar decays into two mesons, and a separate, distinct number of events where it decays into three mesons. By comparing the ratio of these two types of events, scientists could determine the exact nature of the dark scalar's CP violation.

The study also looked at other ways the particle might decay, such as into pairs of muons or pairs of photons. While these channels are also useful, the researchers found that the comparison between the two-meson and three-meson channels offers the most sensitive probe. Their simulations suggest that if the dark scalar exists with the properties they modeled, the SHiP experiment, which is designed to be exceptionally sensitive, could observe thousands of these decay events. Even if the particle interacts slightly more weakly than their most optimistic estimate, the signal would still be strong enough to distinguish between a pure state and a mixed state. The FASER2 experiment, while smaller and seeing fewer events, could still contribute valuable data, particularly for particles with masses around the mass of a specific meson called the eta-prime.

What makes this approach particularly powerful is that it does not rely on measuring complex angles or subtle correlations that require perfect detector precision. Instead, it relies on a simple count: are there particles breaking into twos, and are there particles breaking into threes? If the answer is yes to both, it proves the dark scalar is a CP-mixed state. The researchers confirmed that this signal would stand out clearly against the background noise expected in these experiments. They also checked that their conclusions held true even if the particle did not interact with electrons or muons, a scenario that would change how long the particle lives before decaying. In all cases, the ratio of the decay modes remained a reliable indicator.

This work provides a clear roadmap for the next generation of particle physics experiments. It moves beyond the theoretical possibility of a dark sector to a concrete, testable prediction. If the dark scalar boson is discovered, the very first question will be to determine its identity. By simply counting the number of particle pairs versus particle triplets in the debris of a collision, scientists will be able to answer whether this hidden particle holds the key to the universe's matter-antimatter imbalance. The proposed method turns the complex problem of quantum symmetry into a straightforward counting exercise, offering a realistic path to uncovering one of the deepest secrets of the cosmos.

Technical Summary: Probing CP Violation in Dark Scalar Decays at the SHiP Experiment

Problem Statement
The origin of the baryon asymmetry of the Universe and the nature of CP violation beyond the Standard Model (SM) remain open questions. A potential source of new CP-violating interactions lies in a "dark sector" containing new scalar degrees of freedom. A critical question is whether a neutral spin-zero dark scalar boson ( $\phi$ ) possesses a definite CP quantum number (CP-even or CP-odd) or exists as a CP-mixed state. While direct searches for CP violation via angular distributions or comparisons with CP-conjugate states are possible, they face challenges when couplings to SM particles are small or when event samples are limited. This paper addresses the challenge of identifying CP violation in a GeV-scale dark scalar sector, specifically focusing on scenarios where the scalar is a long-lived particle (LLP) produced in fixed-target or forward experiments.

Methodology
The authors adopt an effective Lagrangian approach to describe the interaction of a dark scalar $\phi$ with SM fermions and gauge bosons. The interaction is parameterized by scalar ( $\xi^s_f$ ) and pseudoscalar ( $\xi^p_f$ ) couplings, which are expressed in terms of an overall coupling strength $\epsilon$ and a CP-violating phase $\theta$ (where $\xi^s_f = \epsilon \cos \theta$ and $\xi^p_f = -\epsilon \sin \theta$ ).

Hadronic Decays: For dark scalar masses in the GeV range ( $m_\phi \lesssim 2$ GeV), the relevant degrees of freedom are hadrons. The authors utilize Chiral Perturbation Theory ( $\chi$ PT) to derive the decay amplitudes. A key theoretical insight utilized is that CP-even interactions predominantly induce decays into even numbers of mesons (e.g., two-meson final states like $\pi\pi$ , $K\bar{K}$ ), while CP-odd interactions induce decays into odd numbers of mesons (e.g., three-meson final states like $\pi\pi\pi$ , $\pi K\bar{K}$ ).
Production Mechanism: The dark scalar is assumed to be produced primarily through the decays of heavy $B$ mesons ( $B \to X_s + \phi$ ). The production rate depends on the mixing of the dark scalar with the SM Higgs and the specific CP structure of the couplings.
Experimental Setup: The study evaluates the sensitivity of two dedicated LLP experiments: SHiP (at CERN) and FASER2 (at the LHC). The analysis calculates the expected number of signal events by integrating the production cross-section, the decay branching ratios (including mixing effects with $\pi^0, \eta, \eta'$ ), and the probability of the dark scalar decaying within the detector volume.
Signal Definition: The primary signal strategy involves the simultaneous observation of two-meson (even) and three-meson (odd) decay channels. Complementary channels include two-muon ( $\mu\mu$ ) and di-photon ( $\gamma\gamma$ ) decays.

Key Contributions and Results

CP-Violation Probe via Decay Multiplicity: The paper proposes that the simultaneous observation of both two-meson and three-meson final states serves as a direct probe of CP violation. If the dark scalar were a pure CP eigenstate, only one class of decays (even or odd meson numbers) would be dominant. The presence of both requires non-zero values for both $\xi^s_f$ and $\xi^p_f$ , implying a CP-mixed state.
Quantitative Sensitivity at SHiP:
- For benchmark coupling strengths of $\epsilon = 10^{-5}$ and $5 \times 10^{-6}$ , the authors find that SHiP can detect a sufficient number of events for dark scalar masses $m_\phi \gtrsim 0.9$ GeV.
- The ratio of three-meson to two-meson events ( $N_{3m}/N_{2m}$ ) is shown to be highly sensitive to the CP-violating phase $\theta$ . This ratio varies from $10^{-2}$ to $100$ over the range $\pi/8 \lesssim \theta \lesssim 7\pi/8$ .
- Specific dominant channels identified are $K\bar{K}$ for two-meson decays and $\pi K\bar{K}$ for three-meson decays in the mass range above 1 GeV.
- The analysis confirms that even with reduced couplings ( $\epsilon = 5 \times 10^{-6}$ ) or in leptophobic scenarios (where couplings to leptons are set to zero), the ratio of event types remains robust for probing CP violation.
Complementary Channels: The two-muon channel is identified as a useful reference because its width is largely independent of $\theta$ for $m_\phi \gg m_\mu$ . The di-photon channel, while loop-suppressed, shows $\theta$ -dependence through pseudoscalar meson mixing and can provide complementary information, particularly near the $\eta'$ mass threshold.
FASER2 Prospects: The study extends the analysis to FASER2. While the expected event rates are lower than at SHiP due to the smaller detector size, the experiment still retains sensitivity to two-meson decays in the mass range $m_{\eta'} \leq m_\phi \leq 2$ GeV and three-meson decays for $m_\phi \geq 1$ GeV and $\pi/4 \lesssim \theta \lesssim 3\pi/4$ .
Constraints: The chosen parameter space ( $\epsilon \sim 10^{-5}$ , $1 \text{ GeV} \leq m_\phi \leq 2 \text{ GeV}$ ) is shown to evade current constraints from LHCb (for CP-even scalars), CHARM (for CP-odd scalars), and Electron Electric Dipole Moment (EDM) measurements.

Significance and Claims
The paper claims that the proposed strategy offers a robust method to determine the CP nature of a GeV-scale dark scalar boson without relying on complex angular correlation measurements or large event samples for angular resolution. By focusing on the multiplicity of the final state mesons (even vs. odd), the method directly tests the existence of both scalar and pseudoscalar interactions.
The authors emphasize that this approach is applicable to a broad class of models, including those with extended Higgs sectors or specific UV completions that generate the effective Lagrangian used. Furthermore, the study highlights the utility of these experiments in distinguishing a CP-violating dark scalar from other dark sector candidates, such as dark vector bosons (dark photons), which might mimic certain decay signatures but possess different CP properties. The work concludes that the SHiP experiment, in particular, has the potential to probe a wide range of the CP-violating parameter space for dark scalars around the GeV scale.

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