Search for Cosmic-Ray Produced Dark Meson via the $U(1)_\text{D}$ Portal at JUNO

This paper investigates the potential of the JUNO experiment to detect sub-GeV dark mesons produced by cosmic rays in the atmosphere via a $U(1)_\text{D}$ vector portal, utilizing a modified Quark Combination Model for hadronization and GENIE for interaction simulation to establish projected 90% C.L. sensitivity limits on the dark gauge coupling for various dark sector masses.

The Gist

Imagine the universe is filled with a hidden, invisible world of particles, much like a secret society living right next door to our own. Scientists call this the "Dark Sector." While we know this hidden world exists because of gravity (it holds galaxies together), we've never seen a single member of this society directly.

This paper is a proposal for how to catch a glimpse of these hidden guests using a giant underground tank of liquid called JUNO (located in China) and the constant rain of particles from space called Cosmic Rays.

Here is the story of their search, explained simply:

1. The Hidden Party (The Dark Sector)

Think of our visible world as a bustling city. The "Dark Sector" is like a secret, locked-down neighborhood nearby. In this neighborhood, there are "Dark Quarks" (the citizens) that stick together to form "Dark Mesons" (the families or groups).

Usually, these two neighborhoods don't talk to each other. But the authors propose a "secret door" called the U(1)D Portal. This is a special bridge (a force-carrying particle called a $Z'$ boson) that allows the two worlds to interact, but only very weakly.

2. The Cosmic Ray "Shower" (How they get made)

High-energy particles from deep space (Cosmic Rays) are constantly crashing into Earth's atmosphere. It's like a giant, natural particle accelerator happening in the sky.

When these cosmic rays hit the air, they create a massive shower of particles. The authors calculate that this shower might also be creating "Dark Mesons" through three different methods:

• The "Skid" (Bremsstrahlung): A proton skids and emits a dark particle.
• The "Leak" (Decay): A normal particle (like a pion) decays and accidentally leaks a dark particle out.
• The "Collision" (Drell-Yan): Two particles smash together and create a dark pair.

3. The Mystery of the "Dark Glue" (Hadronization)

Here is the tricky part. When the dark particles are created, they are just loose "quarks." They need to stick together to form the "Dark Mesons" that can travel to Earth.

In our visible world, we have a rulebook (QCD) for how quarks stick together. But for the dark world, we don't have a rulebook. The authors had to invent a modified recipe (called the Modified Quark Combination Model) to guess how these dark particles group up.

• Analogy: Imagine you are trying to guess how many people will show up to a party and how they will group into tables, but you've never seen the guest list. You have to make an educated guess based on the size of the room. The authors tested different guesses (changing the "guest list" parameters) to see if their results would change drastically. They found that even if their guess was off by a factor of three, the final result didn't change much.

4. The Underground Trap (JUNO)

Once these Dark Mesons are made in the sky, they zoom down through the Earth. Most of them pass right through the planet like ghosts. However, a tiny few might bump into the atoms in the JUNO detector, which is a massive tank of liquid scintillator (a glowing liquid) buried deep underground.

• The Bump: When a Dark Meson hits an atom in the tank, it transfers a tiny bit of energy, causing the liquid to flash with a faint blue light.
• The Filter: The problem is that the Earth is also constantly bombarded by "Atmospheric Neutrinos" (ghostly particles from the sun and supernovas) that create similar flashes. It's like trying to hear a whisper in a noisy stadium.
• The Solution: The authors set up a strict filter. They only look for flashes that are:
  1. Not too weak (above 15 MeV) to avoid the noisy background.
  2. Not too strong (below 100 MeV) to avoid other types of noise.
  3. No "neutron" guests: If the event creates a neutron (a specific type of particle), they throw it out. This helps them ignore the background noise while keeping the potential dark signal.

5. The Results: What can JUNO see?

The authors ran massive computer simulations to see how many of these "Dark Meson" flashes JUNO could catch in a year.

• The Sensitivity: They found that JUNO is sensitive enough to detect these particles if the "secret door" (the coupling strength) is very weak—about 100,000 times weaker than the electromagnetic force.
• The Sweet Spot: They are most sensitive to dark particles that are very light (between 0.001 and 0.1 GeV).
• Comparison: They compared their results to the NA62 experiment (a particle accelerator in Europe). They found that JUNO is the perfect partner to NA62:
  • NA62 is great at finding heavier dark particles.
  • JUNO is the only one that can look for the lightest ones, where NA62 hits a wall.

Summary

This paper is a "blueprint" for a new way to hunt for dark matter. Instead of waiting for dark matter to drift into a detector from space (which is hard), they propose using the Earth's atmosphere as a factory to create dark matter, and then using the JUNO detector to catch the leftovers.

They proved that even with a lot of uncertainty about how these dark particles form, the JUNO detector is a powerful tool that could finally see these invisible "Dark Mesons," filling a gap that current particle accelerators cannot reach.

Technical Summary

Technical Summary: Search for Cosmic-Ray Produced Dark Meson via the U(1)D Portal at JUNO

Problem Statement
While the Standard Model (SM) successfully describes fundamental interactions, it fails to account for Dark Matter (DM). Although Weakly Interacting Massive Particles (WIMPs) have been the primary focus, null results from direct detection and collider experiments have motivated the exploration of light dark sectors in the sub-GeV mass range. A theoretically motivated class of these models involves a "Hidden Valley" or a strongly interacting dark sector characterized by a non-Abelian $SU(N)_D$ gauge group. In such scenarios, dark quarks confine at low energies to form a spectrum of dark hadrons, including stable dark mesons (dark pions) that can serve as DM candidates.

A critical challenge in probing these composite dark sectors is the non-perturbative nature of the hadronization process (the transition from dark quarks to dark mesons). Previous studies often rely on phenomenological scaling of SM QCD parameters, which may not accurately extrapolate to different confinement scales. Furthermore, while high-energy cosmic rays interacting with the Earth's atmosphere provide a permanent source of sub-GeV dark sector particles, the application of this mechanism to composite dark sectors remains underexplored due to these modeling complexities.

Methodology
This work investigates the atmospheric production and subsequent detection of sub-GeV dark mesons within a framework where a confining dark $SU(N)_D$ sector couples to the SM via a leptophobic $U(1)_D$ vector portal (mediated by a $Z'$ boson). The study proceeds through three main stages:

1. Theoretical Framework and Hadronization Modeling:

   • The authors construct a low-energy effective Lagrangian based on Chiral Perturbation Theory (ChPT) to describe dark pion dynamics.
   • To address the hadronization challenge, they implement a Modified Quark Combination Model (MQCM). Unlike generic scaling approaches, this model uses a shifted-Poisson law for multiplicity and a Longitudinal Phase Space Approximation (LPSA) for kinematics.
   • The model introduces a phenomenological parameter $\beta$ governing multiplicity scaling, which is rescaled by a factor $\kappa_\beta$ (tested at $1/3, 1, 3$) to assess robustness against order-one variations in the hadronization prescription.

2. Atmospheric Flux Calculation:

   • The flux of dark mesons is calculated by convolving the cosmic-ray proton spectrum with three distinct production channels:
     • Proton Bremsstrahlung: $p + N \to p + N + Z'$.
     • SM Meson Decay: Rare radiative decays of SM mesons ($\pi^0, \eta \to \gamma Z'$) followed by $Z' \to q_k \bar{q}_k$.
     • Drell-Yan Process: $q\bar{q} \to Z'^* \to q_k \bar{q}_k$.
   • The resulting dark quark pairs are hadronized into dark mesons using the MQCM. The authors note that only a fraction of the resulting meson states (specifically the "Kaon-like" states $K_D$) couple to the SM via the $Z'$ portal, imposing a $4/9$ factor on the interacting flux for their benchmark $N_f=3$ scenario.
   • Propagation effects through the atmosphere and rock overburden are estimated via optical depth calculations, concluding that attenuation is negligible for the coupling strengths of interest ($g_{SM} \lesssim 10^{-4}$).

3. Detector Simulation and Sensitivity Analysis:

   • The interaction of relativistic dark mesons with the Jiangmen Underground Neutrino Observatory (JUNO) is simulated using the GENIE generator, specifically utilizing its Boosted Dark Matter (BDM) module.
   • Scattering channels include Elastic Scattering (EL) and Deep Inelastic Scattering (DIS) off Carbon-12 and Hydrogen nuclei.
   • Signal Selection: To mitigate atmospheric neutrino backgrounds, a conservative Large-Energy-Singles (LES) inspired selection is adopted: visible energy $15 \text{ MeV} < E_{vis} < 100 \text{ MeV}$ with a veto on events containing final-state neutrons.
   • Sensitivity is derived using the Asimov median significance for a $20 \text{ kton} \cdot \text{year}$ exposure, targeting a $90\%$ C.L. upper limit.

Key Contributions

• Hadronization Model: The paper provides a detailed, event-level implementation of the MQCM for dark sector hadronization, moving beyond simple scaling approximations. It demonstrates that while the absolute normalization of the dark meson flux depends on the hadronization parameter $\beta$, the qualitative sensitivity reach is robust against order-one variations.
• Flux Composition Analysis: The study quantifies the relative contributions of bremsstrahlung, meson decay, and Drell-Yan processes. It finds that radiative decays of light pseudoscalar mesons dominate production for light mediators ($m_{Z'} \lesssim m_\eta$), while Drell-Yan processes become dominant for heavier mediators ($m_{Z'} \gtrsim 1 \text{ GeV}$).
• JUNO Sensitivity Projection: The work establishes the projected sensitivity of JUNO to the coupling strength $g_{SM}$ between the dark gauge boson and the SM sector, specifically for sub-GeV dark mesons.

Results
For a $20 \text{ kton} \cdot \text{year}$ exposure, the projected $90\%$ C.L. sensitivities to the coupling $g_{SM}$ for representative mediator masses are:

• $m_{Z'} = 0.001 \text{ GeV} \implies g_{SM}^90 \approx 6.48 \times 10^{-5}$
• $m_{Z'} = 0.01 \text{ GeV} \implies g_{SM}^90 \approx 7.75 \times 10^{-5}$
• $m_{Z'} = 0.1 \text{ GeV} \implies g_{SM}^90 \approx 2.37 \times 10^{-4}$

The analysis shows that the sensitivity is only mildly sensitive to the choice of the hadronization parameter $\kappa_\beta$. The signal is dominated by elastic scattering on Carbon nuclei. The projected reach covers couplings at or below the $10^{-4}$ level for much of the sub-0.1 GeV region.

Significance and Claims
The paper claims that large-volume neutrino detectors like JUNO offer a complementary and powerful probe for sub-GeV dark sector particles, particularly in mass regions where accelerator-based searches (such as NA62) face kinematic limitations or background challenges.

• Complementarity: JUNO is sensitive to low mediator masses where NA62 loses coverage due to kinematic thresholds and missing-photon backgrounds. Conversely, JUNO remains competitive at higher masses where the atmospheric flux falls off but NA62 is kinematically limited.
• Robustness: The results demonstrate that the sensitivity of such detectors is not driven by finely tuned hadronization parameters, lending credibility to the use of modified QCM approaches for composite dark matter searches.
• Feasibility: The study confirms that even with conservative background rejection strategies (neutron vetoes and energy cuts), JUNO can probe couplings significantly below current experimental limits for light dark mesons produced by cosmic rays.