Sub-GeV dark matter and multi-decay signatures from dark showers at beam-dump experiments

The Gist

Imagine the universe as a giant, bustling city. We know a lot about the "visible" citizens of this city—the atoms, stars, and people we can see and touch. But physicists suspect there's a hidden neighborhood, a "Dark Sector," where the residents interact with each other very strongly but barely interact with us at all.

This paper is a blueprint for how to catch a glimpse of these hidden residents using a specific type of experiment called a "beam-dump." Here is the story of what they are looking for and how they plan to find it.

The Hidden Neighborhood and Its Residents

Think of the Dark Sector as a secret club with its own rules. Inside this club, there are particles called Dark Quarks. Just like regular quarks in our world stick together to form protons and neutrons, these Dark Quarks stick together to form "Dark Mesons."

The paper focuses on two specific types of these Dark Mesons:

1. Dark Pions: These are the "ghosts" of the club. They are stable, meaning they don't break down. They are the candidates for Dark Matter, the invisible stuff that holds galaxies together.
2. Dark Rho Mesons: These are the "messengers." They are heavier and unstable. Eventually, they decay (break apart) and turn into particles we can see, like electrons or muons.

The "Shower" Analogy

Usually, when we smash particles together in a collider, we might expect to see just one or two new particles pop out. But in this Dark Sector model, the rules are different.

Imagine throwing a single stone into a calm pond. You get a few ripples. Now, imagine throwing a stone into a chaotic, crowded mosh pit. The stone hits one person, who bumps into three others, who bump into ten more, creating a massive, cascading wave of movement.

In the paper's model, when we smash protons together, we might create a pair of Dark Quarks. Because they interact so strongly with each other, they don't just sit there. They immediately "hadronize" (stick together) and fragment into a Dark Shower. This shower is a cascade that produces many Dark Mesons at once, not just one.

The Detective Work: Finding the Clues

The scientists are looking at experiments like SHiP (at CERN), NA62, and Belle II. These are like massive, high-tech traps set up to catch these elusive particles.

Here is the challenge: The Dark Rho Mesons are "long-lived." This means they travel a bit of distance before they decay. When they finally do decay, they leave a "displaced vertex"—a spot where a particle suddenly appears out of nowhere, far away from where the collision happened.

The "Smoking Gun" Signature:
Most theories about Dark Matter suggest that if you see a signal, it's usually just one particle decaying in one spot.

• The Old Theory (Dark Photons): Imagine a factory that makes one toy at a time. If you see a toy, it's just one toy.
• This Paper's Theory (Dark Showers): Imagine a factory that dumps a whole box of toys at once. If you see three or four toys appearing in the same event, you know it's not the "one-toy" factory.

The authors argue that if an experiment like SHiP sees multiple decay points (multiple "toys") in a single collision event, it would be a "smoking gun" proving the existence of this strongly interacting Dark Sector, ruling out simpler models.

What They Found

The team ran complex computer simulations to see how many of these "Dark Showers" these experiments could catch.

1. The Sweet Spot: They found that SHiP is incredibly powerful. It can detect these particles even if they are quite heavy (up to 5 GeV) and interact very weakly with our world.
2. The Multi-Decay Bonus: Crucially, they found that in a large chunk of the possible scenarios, SHiP wouldn't just see one decay; it would see two or even three decays happening in the same event.
3. Connecting the Dots: This is important because it helps explain the "Dark Matter" mystery. If the Dark Pions (the ghosts) are to make up the right amount of Dark Matter in the universe, the math suggests the Dark Rho Mesons must have a specific mass. SHiP is perfectly tuned to look for particles in exactly that mass range.

The Bottom Line

This paper is essentially saying: "Don't just look for one lonely particle decay. Look for a party."

If the SHiP experiment at CERN starts seeing events where multiple hidden particles decay at the same time, it won't just prove that Dark Matter exists; it will prove that the Dark Sector is a busy, complex neighborhood with its own strong interactions, rather than a quiet, empty room. It's a new way to look for the invisible, using the chaos of a "shower" as the key to unlocking the secrets of the universe.

Technical Summary

Technical Summary: Sub-GeV Dark Matter and Multi-Decay Signatures from Dark Showers at Beam-Dump Experiments

Problem and Motivation
Strongly interacting dark sectors, characterized by a non-Abelian gauge group and dark quarks that confine into dark mesons, offer viable dark matter candidates and distinct collider signatures. While the stability of dark pions ($\pi_D$) can account for dark matter relic abundance via $3 \to 2$ number-changing processes, the phenomenology of the unstable vector mesons (dark rho mesons, $\rho_D$) remains less explored in the context of beam-dump experiments. A critical gap exists in distinguishing these models from minimal dark photon scenarios. In minimal dark photon models, the production of multiple dark photons in a single event is negligible. Conversely, strongly interacting dark sectors predict "dark showers" where a single collision produces a high multiplicity of dark mesons. The paper aims to evaluate the sensitivity of current and future experiments (specifically SHiP, NA62, BaBar, and Belle II) to these multi-decay signatures and to determine the parameter space where SHiP can observe multiple displaced vertices in a single event, thereby providing a unique handle on the dark sector's structure.

Methodology
The authors analyze a specific model: an $SU(3) \times U(1)'$ gauge extension of the Standard Model (SM) with two Dirac dark quarks. The dark sector confines at a scale $\Lambda_D$, producing stable dark pions and unstable dark rho mesons. The interaction between the dark sector and the SM is mediated by a heavy $Z'$ boson (integrated out), resulting in an effective dimension-6 operator coupling dark quarks to the SM electromagnetic current.

• Model Parameters: The phenomenology is reduced to three independent parameters: the dark pion mass ($m_{\pi_D}$), the dark rho meson mass ($m_{\rho_D}$), and the suppression scale of the effective interaction ($\Lambda_{\text{eff}}$). The ratio $r \equiv m_{\rho_D}/m_{\pi_D}$ is fixed to 1.5 and 1.9 to satisfy the condition $m_{\rho_D} < 2m_{\pi_D}$, ensuring $\rho_D$ decays exclusively to SM states. All other sector properties (e.g., coupling $g_{\pi\rho}$, decay constants) are inferred from lattice QCD simulations.
• Production Mechanisms: The study considers two primary production modes at the CERN SPS (400 GeV proton beam):
  1. Dark Showers: Perturbative production of dark quark pairs followed by hadronization and fragmentation into multiple dark mesons. This is simulated using MadGraph and Pythia (Hidden Valley module). To address Pythia's limitations with sub-GeV masses, the authors employ a rescaling technique where masses and energies are scaled by a factor $\chi$, preserving dimensionless distributions.
  2. Dark-Photon-Like Modes: Standard production channels such as meson decays, proton bremsstrahlung, and Drell-Yan processes. The authors note significant theoretical uncertainties in bremsstrahlung and fragmentation mixing; consequently, they exclude bremsstrahlung from their yield calculations but include initial-state radiation in fragmentation to avoid excessive conservatism.
• Experimental Analysis: The authors utilize two computational approaches:
  1. Semi-analytic (SensCalc): Used for single-decay constraints, treating events with $N$ dark rhos as $N$ independent decays.
  2. Monte Carlo (EventCalc): An importance-sampling tool used to calculate rates for $n$-decay events ($n > 1$) by processing events individually.
     Experiments analyzed include past/current beam dumps (BEBC, CHARM, NA62), the proposed SHiP facility (15-year run, $6 \times 10^{20}$ protons on target), and $e^+e^-$ colliders (BaBar, Belle II).

Key Contributions

1. Multi-Decay Signatures: The paper establishes that observing multiple displaced vertices in a single event is a robust discriminator between strongly interacting dark sectors and minimal dark photon models. While minimal models rarely produce multiple dark photons, dark showers can yield events with 2 or 3 decaying $\rho_D$ mesons.
2. Updated Sensitivity Projections: The authors provide updated constraints and sensitivity projections for NA62, BaBar, and Belle II, incorporating improved dark shower simulations and lattice-derived parameters.
3. Rescaling Technique: A practical method is detailed for simulating sub-GeV dark showers in Pythia by rescaling mass and energy scales, ensuring reliable kinematic distributions for masses below 1 GeV.
4. Kinematic Discrimination: The study demonstrates that the total invariant mass ($m_{\text{inv}}$) of the decaying system in multi-decay events provides a secondary discriminant. Unlike dark photon pair production from heavy meson decays (which peaks at the parent mass), dark shower events exhibit a broad invariant mass distribution extending from the kinematic threshold $n \cdot m_{\rho_D}$.

Results

• Production Dominance: Dark shower production dominates the $\rho_D$ flux for masses $m_{\rho_D} \lesssim 0.8$ GeV at SPS energies, contributing significantly up to $\approx 3$ GeV. For heavier masses, Drell-Yan production becomes dominant.
• SHiP Sensitivity: SHiP is projected to probe a large, unconstrained parameter space, reaching $m_{\rho_D} \approx 5$ GeV and $\Lambda_{\text{eff}} \approx 20$ TeV.
  • Single-Decay: The primary sensitivity comes from single-decay events.
  • Multi-Decay: SHiP is predicted to observe events with two decaying $\rho_D$ mesons up to $m_{\rho_D} \approx 2$ GeV and three decaying mesons up to $m_{\rho_D} \approx 1$ GeV.
• Dark Matter Connection: The probed parameter space overlaps with the region required for dark pion dark matter to achieve the correct relic abundance via $3\pi_D \to \pi_D \rho_D$ conversions. SHiP can probe nearly the entire range of $\Lambda_{\text{eff}}$ where this mechanism is not limited by the interaction strength with the SM.
• Constraints: Current constraints from NA62 and BaBar are limited to $m_{\rho_D} \lesssim 0.5$ GeV (NA62) and up to $\approx 1.6$ GeV (BaBar), primarily due to geometric acceptance and trigger requirements.

Significance
The paper claims that SHiP offers a unique discovery potential for strongly interacting dark sectors that is complementary to $e^+e^-$ colliders like Belle II. While single-decay searches are standard, the ability of SHiP to detect multiple displaced vertices in a single event is highlighted as a crucial feature. Such an observation would immediately exclude minimal dark photon models. Furthermore, the measurement of the invariant mass spectrum in these multi-decay events allows for differentiation from non-minimal dark photon models that allow pair production. The authors conclude that SHiP is uniquely positioned to not only discover light, long-lived particles in the GeV/sub-GeV regime but also to elucidate the underlying structure of the dark sector through multiplicity and kinematic signatures.