Two portals to GeV sterile neutrinos : dipole versus mixing

This paper investigates the complementary sensitivity of beam-dump experiments like NA62, SHiP, and FASER2 to GeV-scale sterile neutrinos that possess both active mixing and a dipole coupling to photons, demonstrating that these facilities can probe previously unconstrained dipole moments and potentially detect signals predicted by electroweak loops.

The Gist

Imagine the Standard Model of physics as a massive, bustling city where everyone knows everyone. There are the "Active Neutrinos," which are like the city's most popular, chatty citizens. They interact with everything, but they are incredibly light and hard to pin down.

Then, there are the "Sterile Neutrinos." These are the city's ghosts. They are massive, invisible, and they don't talk to anyone in the city. They are "sterile" because they ignore the usual rules of interaction. For decades, physicists have tried to find them, assuming the only way to spot a ghost is if it accidentally bumps into a citizen (a process called mixing).

But this paper, written by Enrico Bertuzzo and Michele Frigerio, suggests there's a second, secret way to find these ghosts. It's not a bump; it's a flashlight.

The Two Portals: The Handshake vs. The Flashlight

The authors propose that these heavy sterile neutrinos have two ways to interact with our world:

1. The Mixing Portal (The Handshake): This is the old way. The sterile neutrino briefly "shakes hands" with an active neutrino. It's a weak, rare connection. If the handshake is too weak, the ghost remains invisible.
2. The Dipole Portal (The Flashlight): This is the new idea. Imagine the sterile neutrino has a tiny, magical flashlight attached to it. Even if it never shakes hands with anyone, it can still flash a beam of light (a photon) when it changes its state. This "flashlight" is a magnetic interaction with the photon.

The paper asks a crucial question: If we have both a handshake and a flashlight, which one helps us find the ghost first?

The Experiment: Hunting in the Dark

The authors focus on experiments like SHiP, NA62, and FASER2. Think of these experiments as massive, high-speed factories that smash protons together.

• The Factory: When protons smash, they create a shower of particles, including "mesons" (unstable particles that act like delivery trucks).
• The Delivery: These mesons decay. Sometimes, they drop off a sterile neutrino.
• The Journey: The sterile neutrino is a long-distance traveler. It flies hundreds of meters away from the crash site, invisible and silent.
• The Flash: Eventually, the sterile neutrino decays. If it has the "flashlight" (dipole), it emits a single, bright photon (a particle of light) right before it disappears.

The detectors are placed far away, in the dark, waiting for this single flash of light.

The Big Discovery: The "Jump" in Sensitivity

The paper's most exciting finding is about the SHiP experiment.

Imagine you are trying to hear a whisper in a noisy room.

• Old Experiments: They could only hear the whisper if the person was shouting (strong mixing) or if the room was very quiet (low background). They were limited.
• The SHiP Experiment: The authors predict SHiP will be like putting on super-hearing headphones. It will be able to detect a "flashlight" signal so faint that it was previously thought impossible to see.

They calculate that SHiP could detect a dipole strength as small as $10^{-8}$ GeV$^{-1}$. To put that in perspective, this is like detecting a signal from a new physics scale that is trillions of times heavier than the particles we currently know. It's like finding a fingerprint on a grain of dust that proves the existence of a mountain range we didn't know was there.

The Twist: The "Induced" Flashlight

Here is the clever part of the paper. Even if the sterile neutrino doesn't have a built-in flashlight (the new physics dipole), it might still flash.

Why? Because if the sterile neutrino shakes hands with an active neutrino (mixing), the laws of quantum mechanics say it must pick up a tiny, "induced" flashlight from the universe itself (via electroweak loops).

• The Analogy: Imagine the ghost is wearing a suit. Even if the suit doesn't have a built-in light, the friction of walking through the city (mixing with active neutrinos) generates a tiny static spark (the induced dipole).
• The Result: If the mixing is strong enough, this "static spark" is bright enough to be seen by SHiP, even if the "built-in flashlight" (the new physics) doesn't exist. This means SHiP could detect the ghost just by its handshake, but the signal would look like a flash.

Why This Matters

1. New Physics: If we see this flash, it proves there are heavy particles we haven't found yet. It could explain why the universe has more matter than antimatter.
2. Dark Matter: If the sterile neutrino is stable and doesn't decay, it could be a candidate for Dark Matter. The paper suggests that in some scenarios, these particles could be the invisible stuff holding galaxies together, interacting with us only through this "flashlight" mechanism.
3. The "Flavor" Problem: The paper also notes that the signal depends on which type of neutrino the ghost is talking to (electron, muon, or tau). It's like the ghost wearing a different colored hat depending on who it's shaking hands with. This helps scientists figure out exactly what kind of particle they are looking at.

The Bottom Line

This paper is a roadmap for the next generation of particle physics. It tells us that we shouldn't just look for heavy neutrinos by waiting for them to "bump" into us. We should also look for the "flashes" they might emit.

The SHiP experiment is the star of this show. It promises to be the most sensitive "flashlight detector" ever built, capable of seeing signals so faint they were previously considered invisible. Whether the ghost is holding a built-in flashlight or just generating static from a handshake, SHiP might finally catch a glimpse of the invisible world.

Technical Summary

1. Problem Statement

The paper addresses the search for Heavy Neutral Leptons (HNLs), also known as sterile neutrinos ($N$), in the mass range $0.1 \text{ GeV} \lesssim M_N \lesssim 10 \text{ GeV}$.

• The Challenge: Traditional searches rely on the mixing portal, where sterile neutrinos mix with active Standard Model (SM) neutrinos ($\theta$). However, experimental bounds on this mixing are extremely tight in the GeV mass range.
• The Alternative: Sterile neutrinos can also couple to the photon via a dipole portal (a dimension-5 operator, $d$). This interaction allows for the production and decay of sterile neutrinos into photons ($N \to \nu \gamma$ or $N_2 \to N_1 \gamma$).
• The Gap: Previous studies often treated the dipole and mixing portals independently or assumed negligible mixing. This paper investigates the interplay between the two. Specifically, it analyzes how active-sterile mixing induces an irreducible dipole coupling via electroweak (EW) loops, and how a fundamental dipole operator between sterile states generates an active-sterile dipole. The goal is to determine the sensitivity of upcoming experiments (NA62, SHiP, FASER2) to the dipole coupling $d$ when both portals are active.

2. Methodology

Theoretical Framework

• Model: The authors introduce a minimal model with two sterile Weyl fermions ($N'_1, N'_2$) and a dimension-5 dipole operator coupling them to the hypercharge field strength ($B_{\mu\nu}$).
  • Lagrangian includes kinetic terms, Majorana masses, Yukawa couplings to SM Higgs/leptons (generating mixing $\theta$), and the dipole term $d N'_1 \sigma_{\mu\nu} N'_2 B^{\mu\nu}$.
• Mass Diagonalization: The model is diagonalized to find mass eigenstates ($N_1, N_2$) and the mixing matrix $U$. The mixing angles $\theta_{i\alpha}$ (where $i=1,2$ and $\alpha=e,\mu,\tau$) are constrained by existing experimental data.
• Dipole Generation:
  1. Direct: The fundamental dipole $d$ induces a transition between sterile states ($N_2 \to N_1 \gamma$) and, via mixing, between active and sterile states ($N \to \nu \gamma$).
  2. Induced (EW Loops): Even if the fundamental dipole $d$ is zero, electroweak loops involving $W$ bosons and charged leptons generate an irreducible active-sterile dipole ($d_{EW}$). The paper calculates this contribution explicitly.
• Flavor Structure: The analysis considers mixing with specific lepton flavors ($e, \mu, \tau$) and combinations thereof, respecting constraints from neutrino oscillation data and lepton-flavor-violating processes.

Phenomenological Analysis

• Production Mechanisms: Sterile neutrinos are produced primarily via meson decays ($M \to N \ell$ or $M \to N_1 N_2$) in beam-dump experiments (NA62, SHiP) and proton-proton collisions (FASER2).
  • Production can be driven by mixing (e.g., $D \to \mu N$) or the dipole (e.g., $\rho \to N_1 N_2$).
• Decay Channels: The paper calculates decay widths for:
  • $N_2 \to N_1 \gamma$ (driven by the sterile-sterile dipole).
  • $N_k \to \nu_\alpha \gamma$ (driven by the active-sterile dipole, which is a sum of the NP contribution and the EW loop contribution).
• Experimental Simulation:
  • The authors simulate event rates for NA62, SHiP, and FASER2, as well as past experiments (CHARM-II, BEBC).
  • They define signal regions based on the detection of a mono-photon in a distant detector.
  • They categorize events into five populations based on where the production and decay occur (e.g., $N_2$ produced at the target, decaying to $N_1$ before the detector, which then decays to $\nu \gamma$ inside the detector).
• Constraints: The study incorporates bounds from:
  • Direct searches (mixing limits).
  • Cosmology (Big Bang Nucleosynthesis - BBN).
  • Astrophysics (Supernova cooling).

3. Key Contributions

1. Interplay of Portals: The paper provides the first comprehensive analysis of the correlation between the mixing angle $\theta$ and the dipole coupling $d$. It demonstrates that in many regions of parameter space, the dipole dominates production while mixing dominates decay (or vice versa), creating complex sensitivity patterns.
2. Irreducible EW Contribution: A crucial finding is that the electroweak loop-induced dipole ($d_{EW}$) is significant. Even if the new physics dipole $d \to 0$, the EW contribution can generate a detectable photon signal for sterile neutrinos in the mass range $0.3 \text{ GeV} \lesssim M_N \lesssim 3 \text{ GeV}$, provided there is non-zero mixing. This creates a "vertical" sensitivity region in the $(M_N, d)$ plane where the experiment is sensitive even to vanishingly small $d$.
3. Flavor-Dependent Sensitivity: The analysis highlights how sensitivity varies drastically depending on whether the sterile neutrino mixes with the electron, muon, or tau flavor.
   • Tau mixing: Allows larger mixing angles but has higher mass thresholds (due to the heavy $\tau$ mass), limiting production at lower $M_N$.
   • Muon/Electron mixing: Lower thresholds allow production at lower masses, but mixing angles are more tightly constrained.
4. SHiP's Leap in Sensitivity: The paper quantifies the dramatic improvement expected from the SHiP experiment compared to current and near-future facilities.

4. Key Results

• Sensitivity Reach:
  • SHiP is projected to probe dipole couplings as small as $d \sim 10^{-8} \text{ GeV}^{-1}$ (for $M_N \sim 1 \text{ GeV}$), which corresponds to new physics scales well above the electroweak scale (up to $\sim 10^3$ TeV).
  • In the presence of mixing near current bounds, SHiP could detect the EW-induced dipole signal, effectively testing the standard model prediction for neutrino magnetic moments in the GeV range.
  • NA62 and FASER2 are sensitive to $d \gtrsim 10^{-6} \text{ GeV}^{-1}$ for masses $M_N \lesssim 0.3 \text{ GeV}$.
• Dominance Regions:
  • The paper maps out regions where the dipole dominates production ($N_d > N_\theta$) and/or decay ($\Gamma_d > \Gamma_\theta$).
  • For small mass splittings ($\delta \to 0$), the channel $N_2 \to N_1 \gamma$ is kinematically closed, and the signal relies entirely on $N \to \nu \gamma$.
• Constraints:
  • BBN: Excludes very light sterile neutrinos ($M_N \lesssim 0.15 \text{ GeV}$) with small dipole couplings if they thermalize and decay too late.
  • Supernovae: Excludes regions with small couplings for $M_N \lesssim 0.6 \text{ GeV}$ due to energy loss constraints.
  • Mixing Limits: The presence of the dipole modifies the effective lifetime and production rates, potentially relaxing or shifting the standard mixing-only bounds, though a dedicated re-analysis of all past data is noted as a future task.

5. Significance

• New Discovery Channel: This work establishes the dipole portal as a viable and potentially dominant discovery channel for GeV-scale sterile neutrinos, independent of the stringent mixing constraints.
• Testing New Physics: The ability to probe $d \sim 10^{-8} \text{ GeV}^{-1}$ allows experiments to test UV completions of the Standard Model at energy scales far beyond the direct reach of colliders.
• Model Discrimination: The distinct signatures (e.g., the vertical sensitivity line due to $d_{EW}$, or the specific flavor-dependent thresholds) allow future experiments to distinguish between different theoretical models (e.g., pure mixing vs. dipole-driven scenarios, or Dirac vs. Majorana sterile neutrinos).
• Dark Matter Connection: The authors note that in the limit of vanishing mixing, the lightest sterile state ($N_1$) becomes stable and could serve as an inelastic dark matter candidate, scattering off matter via the dipole interaction. The paper's results help constrain this scenario.

In conclusion, the paper argues that the next generation of intensity-frontier experiments, particularly SHiP, will revolutionize the search for sterile neutrinos by exploiting the dipole portal, potentially discovering these particles even if their mixing with active neutrinos is extremely small.