Probing Neutrino Compositeness with Invisible and Displaced Signals

This paper proposes that neutrinos may couple to an interacting sterile sector, leading to "dark jet" signatures such as displaced vertices and emerging jets in high-energy neutrino beams, which offer unique sensitivity to neutrino compositeness beyond current constraints from meson, electroweak, and Higgs decays.

The Gist

Imagine the universe is like a massive, bustling city. We know the "citizens" of this city well: electrons, protons, and the famous neutrinos (ghostly particles that barely interact with anything). But what if there's a hidden, secret neighborhood just next door that we can't see? This paper explores the possibility that neutrinos are actually the "doorways" or "portals" to this secret neighborhood, which the authors call the Dark Sector.

Here is the breakdown of their exciting new theory, explained with everyday analogies.

1. The Big Idea: Neutrinos aren't just Ghosts; they are "Composite"

Usually, scientists think of neutrinos as fundamental, indivisible particles (like a single, solid marble). This paper suggests a different idea: What if a neutrino is actually a "composite" object?

Think of a neutrino not as a single marble, but as a bundle of straws tied together. Inside this bundle, there are tiny, invisible particles interacting with each other in a very strong, chaotic way (like a crowd of people in a mosh pit). The authors call this the "Composite Heavy Neutral Lepton Portal."

2. The "Dark Jet" Analogy: The Exploding Firework

When a high-energy neutrino (from a powerful beam in a lab) smashes into a target, something amazing happens. Instead of just bouncing off, the "bundle of straws" (the neutrino) breaks apart.

• The Old View: If you hit a marble, it just bounces.
• The New View: If you hit this "bundle," it explodes into a spray of new, invisible particles. The authors call this a "Dark Jet."

Imagine throwing a firework into a dark room. When it hits the wall, instead of just making a sound, it bursts open and releases a shower of tiny, glowing sparks that fly off in a tight, focused stream. That stream is the "Dark Jet."

3. Two Ways to See the Invisible

Since these new particles are invisible to our eyes, how do we know they are there? The paper proposes two clever ways to spot them, depending on how long the "sparks" last before disappearing.

Scenario A: The "Long-Lived" Ghosts (Invisible Signals)

Sometimes, the sparks from the firework are very long-lived. They fly through the detector without hitting anything, disappearing into the darkness.

• The Clue: In a normal collision, you expect a certain balance between "charged" hits (like a car crash) and "neutral" hits (like a whisper). If these invisible sparks are stealing energy, the balance shifts. The paper predicts we will see more "neutral" events than expected. It's like hearing a room get quieter than it should be because someone is secretly sucking the sound out.

Scenario B: The "Delayed" Fireworks (Displaced Signals)

Sometimes, the sparks don't disappear immediately. They travel a few meters inside the detector before they finally decay (explode) into visible particles like electrons or muons.

• The Clue: This creates a "Displaced Vertex." Imagine a magician throwing a ball. You see the ball leave their hand (the collision), but then, a few feet away, a second ball suddenly appears out of thin air.
• The "Smoking Gun": If the neutrino is truly composite, it doesn't just release one spark. It releases a whole shower of them. So, instead of seeing one delayed explosion, you might see multiple explosions happening at different spots in the detector. This is called an "Emerging Jet." It's like seeing a whole flock of birds suddenly appear in different parts of a forest, rather than just one. This multi-explosion signature is the unique fingerprint of this theory.

4. Where to Look? (The Experimental Hunt)

The authors suggest we need to look in specific places to catch these "Dark Jets":

• The "Near" Future (DUNE & FPF): These are massive neutrino experiments. DUNE is like a giant underwater camera in a mine, and FPF is a detector placed far down the tunnel from the Large Hadron Collider (LHC). They are perfect for catching these "Delayed Fireworks" because they have huge detectors where the sparks can travel a bit before exploding.
• The "Flavor" Factories (LHCb & Belle II): These machines smash particles to create heavy "B-mesons." These heavy particles are like unstable eggs that might crack open and release our invisible sparks.
• The "Future" Giant (FCC-ee): This is a proposed future collider. It would be the ultimate microscope, capable of seeing the tiniest details of how the "Z boson" (a heavy particle) decays. If the Z boson ever leaks energy into our secret neighborhood, this machine will find it.

5. Why Does This Matter?

If we find these signals, it changes everything.

1. It proves the Dark Sector exists: We would finally have direct evidence of a hidden world of particles.
2. It explains Neutrino Mass: It might finally tell us why neutrinos are so incredibly light compared to other particles.
3. It's a New Kind of Physics: It suggests that the "strong force" (which holds atoms together) might also be at work in this hidden dark world, creating these chaotic "Dark Jets."

Summary

Think of the universe as a house with a locked basement. We've always suspected the basement is there because the floorboards creak (neutrinos have mass). This paper suggests that if we hit the floor hard enough with a specific tool (high-energy neutrino beams), the floorboards won't just creak; they will shatter, revealing a hidden room filled with a chaotic, invisible storm of particles.

If we see multiple delayed explosions in our detectors, we'll know we've finally broken into the basement.

Technical Summary

1. Problem Statement

The paper addresses the theoretical possibility that neutrinos are not fundamental particles but composite states coupled to a strongly interacting "Dark Sector" (DS). While the existence of neutrino masses suggests new physics, standard models often assume weakly coupled extensions (e.g., Heavy Neutral Leptons or HNLs). This work explores a distinct regime where the sterile sector is strongly coupled and characterized by a confinement scale $\Lambda_{IR}$.

The core challenge is determining how to experimentally distinguish a composite sterile sector from a weakly coupled one. Standard searches for HNLs often rely on mixing angles that suppress signal rates when lifetimes are long enough to produce displaced vertices. The authors investigate whether the unique dynamics of a composite sector (specifically, the production of "dark jets" rather than single particles) can overcome these limitations and provide observable signatures at current and future facilities.

2. Methodology and Theoretical Framework

The Composite Portal

The authors model the interaction between the Standard Model (SM) and the Dark Sector via a non-renormalizable portal operator:
$$\mathcal{L} \supset \frac{y_\ell}{\Lambda_{UV}^{\Delta_N - 3/2}} \tilde{H} L_\ell O_N$$
where:

• $O_N$ is a fermionic composite operator with scaling dimension $\Delta_N$.
• $\Lambda_{UV}$ is the UV cutoff scale.
• $\Lambda_{IR}$ is the confinement scale of the DS ($1 \text{ MeV} \lesssim \Lambda_{IR} \lesssim 100 \text{ GeV}$).
• The authors focus on $\Delta_N \geq 5/2$ to ensure calculability within the conformal regime.

Conformal Regime and Dark Jets

In the energy range $\Lambda_{IR} < E < \Lambda_{UV}$, the theory is approximately conformal. Instead of producing a single heavy neutrino, the interaction produces a Dark Sector (DS) jet.

• Hadronization: The DS jet fragments into a spray of light resonances (dark hadrons) on a timescale $\tau \sim 1/\Lambda_{IR}$.
• Multiplicity: In the strongly coupled limit, the number of fragments scales as $N_f \sim p_D / \Lambda_{IR}$, leading to high-multiplicity final states ("emerging jets").
• Lifetime: The fragments decay back to SM particles via the same portal. Their lifetimes depend on $\Lambda_{UV}$, $\Lambda_{IR}$, and $\Delta_N$, ranging from prompt to macroscopic (displaced).

Production Mechanisms

The paper calculates production rates for three main channels:

1. Neutrino Deep Inelastic Scattering (DIS): Neutrinos scatter off nucleons, disintegrating into a DS jet and a SM jet.
2. SM Particle Decays: Mesons ($\pi, K, D, B$), $Z$, $W$, and Higgs bosons decay into a DS jet (often accompanied by a neutrino or lepton).
3. Beam Dump Experiments: Secondary mesons produced in proton targets decay into DS jets.

UV Completions

The authors analyze two benchmark scenarios for the UV behavior:

1. Unbroken Conformal Window: The conformal regime extends up to the electroweak (EW) scale. This scenario is tightly constrained by invisible $Z$ and Higgs decays.
2. Broken Conformal Window: The conformal regime terminates at a scale $\Lambda^* < m_Z$ (e.g., due to a heavy intermediate state). This relaxes EW constraints, opening up parameter space for neutrino experiments.
   They also consider the presence of light pseudo-Nambu-Goldstone bosons (pNGBs) from chiral symmetry breaking, which can enhance invisible decay branching ratios.

3. Key Contributions

A. Novel Signatures: "Dark Jets" and Emerging Jets

The paper identifies that composite neutrinos do not decay as single particles but as sprays of particles.

• Emerging Jets: If the DS fragments have macroscopic lifetimes, they decay at different points within a detector, creating a "jet" of displaced vertices (DVs) rather than a single DV.
• Smoking Gun: The observation of multiple displaced vertices (2 or more) in a single event is a unique signature of strong coupling, distinguishing it from weakly coupled HNLs which typically yield single DVs.

B. Enhancement of NC/CC Ratio

A critical theoretical result is that strongly coupled sterile sectors enhance the Neutral Current (NC) to Charged Current (CC) ratio in neutrino DIS.

• In weakly coupled HNL models, mixing suppresses inclusive cross-sections.
• In the composite model, the inclusive production of DS jets adds to the NC rate without suppressing the CC rate, leading to a measurable excess in NC events. This is a unique probe for composite neutrinos.

C. Classification of Higher-Dimensional Portals

The authors extend the analysis to the Composite $\nu$-SMEFT, classifying higher-dimensional operators (dipole, four-fermion, etc.) that could arise in UV completions. They show that four-fermion contact interactions can dominate at high energies (e.g., HL-LHC), offering complementary search strategies.

4. Results and Experimental Sensitivity

The paper maps the sensitivity of various experiments in the $(\Lambda_{IR}, \Lambda_{UV})$ plane for $\Delta_N = 5/2$ and $7/2$.

• Neutrino Experiments (DUNE, FPF):
  • DUNE: Can probe the NC/CC ratio enhancement and displaced vertices (single and multiple). In "dump mode," it can access low $\Lambda_{IR}$ via meson decays.
  • Forward Physics Facility (FPF): With high-energy neutrinos from the HL-LHC, FPF is uniquely sensitive to emerging jets (multiple DVs) due to the high boost and multiplicity of the DS fragments.
• Flavor Experiments (LHCb, Belle II):
  • Rare decays of $B$ and $D$ mesons ($B \to X \ell + \text{DS jet}$) provide clean environments to search for displaced vertices. The observation of multiple DVs in $B$ decays would be a definitive signal of compositeness.
• Beam Dump Experiments (SHiP, CHARM):
  • SHiP can improve limits on single DVs. However, the probability of observing multiple DVs is suppressed unless $\Lambda_{IR}$ is close to the kinematic threshold ($\sim 1$ GeV).
• Future Colliders (FCC-ee):
  • FCC-ee offers the ultimate sensitivity via displaced $Z$ decays. With $\sim 10^{12}$ $Z$ bosons, it can probe the compositeness scale up to $\Lambda_{UV} \sim \text{few TeV}$ (for $\Delta_N=5/2$) or higher, depending on the UV completion.
• Constraints:
  • The "unbroken" scenario is heavily constrained by current limits on invisible $Z$ and Higgs decays.
  • The "broken" scenario (conformal regime ending below $m_Z$) evades these constraints, making neutrino experiments the leading probes.

5. Significance

This work fundamentally shifts the paradigm for searching for sterile neutrinos:

1. Beyond Weak Coupling: It demonstrates that if neutrinos are composite, the phenomenology is drastically different from standard HNL searches, requiring new experimental strategies (searching for jets of displaced vertices rather than single tracks).
2. New Discovery Channels: It identifies the NC/CC ratio enhancement and emerging jets as robust, background-free signatures that are inaccessible to weakly coupled models.
3. Comprehensive Roadmap: The paper provides a concrete experimental program spanning the intensity frontier (DUNE, SHiP, LHCb) and the energy frontier (FCC-ee, HL-LHC), showing that neutrino facilities are uniquely positioned to test the compositeness of neutrinos, potentially uncovering a strongly interacting dark sector that has remained hidden from traditional searches.

In conclusion, the paper argues that high-energy neutrino beams are the premier tool for probing neutrino compositeness, capable of discovering a strongly coupled dark sector through distinctive multi-vertex and invisible signatures that standard models cannot replicate.