Neutrino Physics at Future Colliders

This paper reviews collider phenomenology, highlighting how current and future colliders serve as ideal testing grounds for (sub)TeV-scale neutrino mass models by directly probing associated messenger particles and leveraging recent LHC observations of TeV-scale neutrinos to test the limits of the Standard Model.

The Gist

The Big Picture: The Ghost in the Machine

Imagine the Standard Model of particle physics as a highly successful, nearly perfect instruction manual for how the universe works. It explains almost everything we see, from the atoms in our bodies to the stars in the sky. However, there is one tiny, stubborn glitch in the manual: Neutrinos.

According to the original manual, neutrinos should be weightless ghosts. But scientists have discovered they actually have a tiny bit of weight (mass). This is like finding a feather that weighs a ton; it breaks the rules. This paper argues that to fix this glitch, we need to look beyond the current manual. The best place to look? The world's biggest particle smashers, or colliders, like the Large Hadron Collider (LHC).

1. Catching the Ghosts (Seeing Neutrinos)

Usually, neutrinos are so shy they pass through the Earth like light through a window. In a collider, they just disappear, leaving behind "missing energy."

• The Analogy: Imagine a massive highway (the collider beam) where cars (particles) crash. Most debris flies everywhere, but some tiny, invisible dust (neutrinos) shoots straight ahead in a tight beam.
• The New Trick: Scientists realized that if they build a detector far down the road, past where the highway curves, they can catch this "dust." New experiments like FASER and SND@LHC have done exactly this, catching neutrinos for the first time in a collider setting.
• Why it matters: It's like finally getting a sample of the dust to study its composition. This helps us understand how particles interact at energies we've never seen before and improves our maps of how protons are built inside.

2. The Mystery of the Mass: Are They Twins or Clones?

The big question is: How do neutrinos get their mass?

• Dirac Neutrinos: Like a person with a left hand and a right hand (distinct partners).
• Majorana Neutrinos: Like a person who is their own twin (the particle is its own antiparticle).

The Smoking Gun:
To prove they are "twins" (Majorana), we need to see a process that breaks the "law of conservation of lepton number" (a rule about particle balance).

• The Analogy: Imagine a bank vault where money usually stays balanced. If you see a transaction where money vanishes from one side and reappears on the other without a record, you know the rules have been broken.
• The Collider Approach: Instead of waiting for a rare event in a rock deep underground (like the double-beta decay experiments), we can smash particles together at high speeds to create heavy "messenger" particles. If these messengers decay in a way that breaks the balance, we know neutrinos are their own twins.

3. The "Sterile" Neutrino: The Invisible Cousin

The paper suggests that to give neutrinos mass, there might be a hidden, "sterile" cousin that doesn't interact with normal matter at all.

• The Analogy: Think of a party where everyone is dancing (active neutrinos). But there's a shy guest in the corner (the sterile neutrino) who never dances with anyone. However, they are related. If the shy guest steps out for a moment, they might leave a trace.
• The Search: Colliders can create these heavy, shy cousins. If they are heavy enough, they might live just long enough to travel a tiny distance inside the detector before decaying. This creates a "displaced vertex"—a crash that happens a few millimeters away from the main explosion, which is a huge clue that something new is happening.

4. Beyond the Basics: New Forces and Loops

The paper explains that the universe might have more "gears" than we thought.

• New Forces: Maybe there are new forces (like a new kind of magnetism) that connect to these sterile neutrinos. If so, colliders could produce them directly, like turning on a new switch, rather than hoping they appear by accident.
• The Loop Trick: Sometimes, neutrinos get their mass not from a direct hit, but through a complex "loop" of quantum interactions.
  • The Analogy: Imagine you want to bake a cake (neutrino mass). The standard recipe says you can't. But maybe you can make it by baking a cake inside a cake inside a cake (quantum loops). These "loop" models predict new particles (like extra Higgs bosons) that future colliders could find.

5. The LHC as a Lepton Collider

Protons are messy; they are made of quarks and gluons. But, due to quantum weirdness, they also contain a few electrons and muons (charged leptons).

• The Analogy: It's like a junkyard full of scrap metal (quarks), but occasionally, you find a pristine, shiny gold coin (a lepton) hidden inside a scrap pile.
• The Opportunity: The paper notes that we can use the LHC to collide these hidden gold coins against each other. This turns the messy proton collider into a cleaner "lepton collider," allowing us to study specific interactions that are usually hard to see.

6. Connecting the Dots: Dark Matter and the Origin of Life

Finally, the paper connects these neutrino mysteries to two other huge cosmic puzzles:

• Dark Matter: The lightest "sterile" neutrino might be a candidate for Dark Matter—the invisible stuff holding galaxies together.
• Why We Exist: The same heavy neutrinos that give mass to the light ones might be responsible for why the universe is made of matter instead of antimatter (Leptogenesis).
• The Collider Role: Future colliders could produce these heavy neutrinos and watch how they decay. If the decay patterns match what is needed to explain why we exist, it would be a massive breakthrough.

Summary

This paper is a roadmap for the future. It tells us that while we have learned a lot about neutrinos from looking at them in the dark (intensity frontier), the next giant leap will come from smashing them together at high speeds (energy frontier). By building better detectors and using future colliders, we can finally "see" the invisible particles that hold the secrets to why the universe has mass, why it exists, and what the dark universe is made of.

Technical Summary

Technical Summary: Neutrino Physics at Future Colliders

Problem Statement
The Standard Model (SM) successfully describes fundamental particles and interactions but fails to account for neutrino masses, which are experimentally established to be non-zero due to neutrino oscillations. This necessitates Beyond-the-Standard-Model (BSM) physics. A central open question is the nature of neutrino mass: whether neutrinos are Dirac or Majorana fermions. Distinguishing between these possibilities is experimentally challenging because direct detection of non-relativistic cosmic relic neutrinos is currently infeasible, and low-energy probes like neutrinoless double beta decay ($0\nu\beta\beta$) face sensitivity limits and theoretical uncertainties regarding the neutrino mass ordering. Furthermore, the mechanism generating neutrino mass (e.g., tree-level seesaw vs. radiative) and its connection to other BSM phenomena like baryon asymmetry (leptogenesis) and dark matter remain unproven.

Methodology
This review adopts a phenomenological approach to evaluate the role of current and future high-energy colliders (LHC, HL-LHC, FCC-ee, FCC-hh, CEPC, ILC, CLIC, muon colliders) in probing neutrino physics. The methodology involves:

1. Direct Observation: Analyzing the production and detection of high-energy neutrinos in forward detectors (e.g., FASER, SND@LHC, Forward Physics Facility) to measure fluxes, cross-sections, and lepton universality.
2. Messenger Particle Searches: Investigating collider signatures of the "messenger" particles associated with neutrino mass generation. This includes searching for heavy neutral leptons (sterile neutrinos), $SU(2)_L$-triplet scalars and fermions, and new gauge bosons ($Z'$, $W_R$).
3. Process Analysis: Examining specific processes such as Lepton Number Violation (LNV) signatures (e.g., same-sign dileptons), displaced vertex decays of long-lived particles, and radiative mass model signatures involving lepton flavor violation (LFV).
4. Comparative Sensitivity: Contrasting collider reach with constraints from astrophysics, cosmology (BBN, CMB), and low-energy experiments ($0\nu\beta\beta$, meson decays), particularly in the sterile neutrino mass-mixing parameter space.

Key Contributions and Results

• Collider Neutrino Experiments: The paper highlights that colliders produce collimated beams of neutrinos accessible via forward detectors. Experiments like FASER and SND@LHC have already observed collider neutrinos. Future facilities (FPF) will enable precision measurements of neutrino interaction cross-sections at TeV energies, probe forward hadron production dynamics, reduce Parton Distribution Function (PDF) uncertainties, and potentially observe rare SM events like tau tridents.
• Sterile Neutrinos and LNV: The review details the search for heavy sterile neutrinos ($N$) in the GeV–TeV range.
  • Production: $N$ can be produced via active-sterile mixing ($W/Z$ decays) or, in extended models, via new gauge interactions ($Z'$, $W_R$).
  • Signatures: The "smoking gun" for Majorana nature is the Keung-Senjanović process ($pp \to N\ell^\pm \to \ell^\pm\ell^\pm jj$). However, in minimal scenarios with large mixing, LNV is often suppressed because sterile neutrinos behave as pseudo-Dirac particles. Exceptions include resonant enhancement when mass splitting equals decay width, or sterile-antineutrino oscillations resolvable in long-lived particle searches.
  • Constraints: Current limits from LHC (ATLAS, CMS, LHCb) and future projections (FCC-ee, MATHUSLA, SHiP) cover a vast region of the mass-mixing plane. Future lepton colliders are particularly sensitive to long-lived sterile neutrinos, potentially reaching the theoretical seesaw limit.
• Beyond Minimal Seesaw: The paper discusses non-minimal scenarios where collider phenomenology is enriched:
  • Gauge Extensions: $U(1)'$ and Left-Right symmetric models allow direct production of sterile neutrinos via new gauge bosons, bypassing mixing suppression.
  • Type-II Seesaw: Involves $SU(2)_L$-triplet scalars ($\Delta$). The "smoking gun" is the production of doubly-charged scalars ($\Delta^{\pm\pm}$) decaying into same-sign dileptons.
  • Radiative Models: Models like the Zee, Zee-Babu, and KNT models generate neutrino masses at loop levels. These predict heavy particles (charged scalars, neutral Higgs) with Lepton Flavor Violating (LFV) couplings. Future lepton colliders (e.g., $\mu$TRISTAN, ILC) can probe parameter spaces excluded by current LFV and $(g-2)_\mu$ constraints.
• LHC as a Lepton Collider: The paper notes that proton PDFs contain charged leptons, allowing the LHC to function as a lepton collider. This enables resonant production of leptoquarks and leptophilic Higgs bosons, offering a unique probe for radiative neutrino mass models.
• Connections to Cosmology: The review connects collider searches to leptogenesis and dark matter. Low-scale variants of leptogenesis (resonant/freeze-out and ARS/freeze-in) are testable at colliders. Additionally, keV-scale sterile neutrinos (warm dark matter) or light $SU(2)_R$-triplet scalars could be produced at colliders, complementing astrophysical X-ray/gamma-ray searches with mono-photon or mono-jet signals.

Significance and Claims
The paper asserts that high-energy colliders provide a crucial, complementary avenue to intensity-frontier experiments for understanding the neutrino sector. Its primary significance lies in:

1. Direct Probing of Mass Mechanisms: Colliders can directly access the messenger particles (fermions, scalars, gauge bosons) responsible for neutrino mass generation, rather than inferring them indirectly.
2. Testing Majorana Nature: By searching for LNV signatures and specific messenger particles, colliders offer an alternative path to determining the Majorana nature of neutrinos, independent of the challenges facing $0\nu\beta\beta$ experiments (such as normal mass ordering).
3. Broadening the Search: The review emphasizes that a "broad net" approach is necessary, as different models (tree-level vs. radiative, minimal vs. extended gauge sectors) require different experimental strategies.
4. Interdisciplinary Links: Future collider data can simultaneously address the origin of matter (leptogenesis) and the nature of dark matter, linking the neutrino sector to the broader BSM landscape.

The author concludes that while the SM is empirically successful, the neutrino sector remains the least understood part of it. Future colliders offer an unprecedented opportunity to transition from indirect evidence to direct observation of the physics governing neutrino masses.